CA2283697A1 - Apparatus and method for expanding communication networks - Google Patents

Abstract

A method for increasing the total capacity of a network, the network including a first plurality of communication edges interconnecting a second plurality of communication nodes, the first plurality of communication edges and the second plurality of communication nodes having corresponding first and second pluralities of capacity values respectively, the first and second pluralities of capacity values determining the total capacity of the network. The method comprises expanding the capacity value of at least an individual communication edge from among the first plurality of communication edges, the individual edge connecting first and second communication nodes from among the second plurality of communication nodes, without expanding the capacity value of the first communication node.

Description

APPARATUS AND METHOD FOR EXPANDING COMMUNICATION NETWORKS
FIELD OF THE INVENTION
The present invention relates to apparatus and methods for utilizing communication net-works.
BACKGROUND OF THE INVENTION
C'urrentls' marketed switches and cross-connects are non-blocking. Examples include Alca-tel's 1100 ( HSS and LSS), 16:11 and 16:1 switches. .~T~CT's DAC'.S II and DACS III switches (Lucent technoiogv), TITA~1's 3300 and RN6~t series. 5iemens E~~VSYpress 35190 ATM Core Svvit.ch and Switching Faulty CC15.~ systems, ~e~Vbl'lclge~S :3600, 36=1.~, 36150 and 361 i0 ~Iain~treet switches and the Stinger family of AT~~I switches.
..~ review of <~TyI (a.synchronous transfer mode) ssvitchino products. namely "The ATVI
Report". Broadband Publishing C'.orporation, ISS\ l0 i 20981 ~, 1996 surveys 10 switches of 41'lllCh nine are completely non-blocking and one. C'I5C0. has a positive but very low blocking probability (3% probability of blocking at '? C;hps).
The ITL--T Recommendation G.7S2 ( International Telecommunication Union, Telecom-munication Standardization Sector, Ol/9~) includes Section 4.5 entitled "Blocking'' which states:
''The existence of cross-connections in a cross-connect equipment can prevent the set-up of a new cross-connection. The blocking factor of a cross-connect is the probability that a particular connection request cannot 6e met, normally expressed as a decimal fraction of 1.
Fully non-blocking (i.e. blocking factor = 0) cross-connects can be built.
Some simplification in design, and hence cost, can be realized if a finite blocking factor is acceptable. It is not the invention of this Recommendation to specify target blocking factors for individual cross-connect equipment. The impact of non-zero blocking factor on network performance is dependent on network design and planning rules.
"There is a class of cross-connect matrices known as conditionally non-blocking in which SUBSTITUTE SHEET (RULE 26) there is a finite probability that a. connection request may be blocked. In such cross-connects, it is possible, by re-arranging existing connections, to make a cross-connection which would otherwise be blocked. As an objective, in such cases, rearrangements should be made without interruption to rearranged paths.
"It may be necessary in a nominally non-blocking, or conditionally non-blocking cross-connect, to accept some blocking penalty associated with extensive use of broadcast connec-tions. This is for further study."
A later document "ATM functionality in SOhTET digital cross-connect systems -generic criteria", Generic Requirements CR - 2891-CORE, Issue 1, August 1995, Bellcore (Bell Com-munications Research} states as a requirement that "A SONET DCS with ATM
functionality must meet all existing DCS requirements from TR-NWT-000233". The TR-NWT-000233 publication (Bellcore, Issue 3, November Iq9:3, entitled "Wideband and broadband digital cross-connect systems generic criteria'' ) stipulates the following requirement (R) 4-37:
"For a. two-point unidirectional cross-connection, non-blocking cross-connection shall be provided. Non-blocking means that a cross-connection can be made regardless of other existing connections. Rearranging the existing cross-connections to accommodate a new cross-connection is acceptable only if the rParra.ngement is performed without causing any bit error for the rearranged cross-connections."
The disclosures of all publications mentioned in the specification and of the publications cited therein are hereby incorporated by reference.

SUBSTITUTE SHEET (RULE 26) SUMMARY OF THE INVENTION
The present invention seeks to provide methods and apparatus for expanding the capacity of a network.
There is thus provided in accordance with a preferred embodiment of the present in-vention a method for increasing the total capacity of a network, the network including a first plurality of communication edges (communication links) interconnecting a. second plu-rality of communication nodes (t.ransceivers), the first plurality of communication edges and the second plurality of communication nodes having corresponding first and second plurali-ties of capacity values respectively. The first and second pluralities of capacity values form corresponding topologies which determine the total capacity of the network.
The method includes expanding the ca.pacitv value of at least an individual communication edge from among the first plurality of cornrnunica.tion edges, the individual edge connecting first and second communication nodes from among the second plurality of comrnunicatioo nodes, without expanding the ca.pacitv va.fue of the first communication node.
In conventional methods. to expand total capacity, the capacities of at least a subset of nodes is expanded, plus the capacities of all edges and only those edges which connPCt a pair of nodes within that subset .
There is thus provided. io accorda.nce with a preferred embodiment of thc~
present in-vention, a method for iocrea.sirc' tf~e total capacity of a network, the network includin; a first plurality of communic-at ion edges interconnecting a second plurality of corrwumcatron nodes, the first plurality of corumunication edges and the second plurality of communication nodes having corresponding first. a.nd second pluralities of capacity values respectively, the first and second pluralities of capacity values determining the total capacity of t,t~e network.
the method including expanding the capacity value of at least an individual communication edge from among the first plurafitv of communication edges, the individual edge connecting first and second communication nodes from among the second plurality of communication nodes, without expanding the capacity value of the first communication node.
Further in accordance with a. preferred embodiment of the present invention, the method includes performing the expanding step until the total capacity of the network reaches a desired level, and expanding the capacity values of at least one of the second plurality of communication edges such that all of the second plurality of communication edges have the same capacrty.
Also provided, in accordance with another preferred embodiment of the present invention, is a method for expanding the total capacity of a network, the network including a first SUBSTITUTE SHEET (RULE 26j plurality of communication edges interconnecting a second plurality of communication nodes, the first plurality of communication edges and the second plurality of communication nodes having corresponding first and second pluralities of capacity values respectively, the first and second pluralities of capacity values determining the total capacity of the network. the method including determining, for each individual node from among the second plurality of communication nodes, the amount of traffic entering the network at the individual node, and, for each edge connected to the individual node, if the capacity of the edge is less than the amount of traffic, expanding the capacity of the edge to the amount of tragic.
Also provided, in accordance with another preferred embodiment. of the present invention, is a method for constructing a network, the method including installing a first plurality of communication edges interconnecting a second plurality of communication nodes, and deter-mining first and second pluralities of capacity values for the first plurality of communication edges and the second plurality of communication nodes respect.ivelv such that.
for at least one individual node, the sum of capacity values of the edges connected to that node exceeds the capa.cit.v value of that node.
Further provided, in accordance with another preferred emboclirnent of the present inven-tion, is a network including a first plurality of communication edges lna.ving a first plurality of capacity values respectively, and a second plurality of communic:a.t,ion nodes having a sec-ond plurality of capacity wa.lues respectively, wherein the first plurality of communication edges interconnects the second plurality of communica.tior~ nodes s~~ch that.
for at least one individual node. the sum of capacity values of the edges connect.ecl t,o tha.t node exceeds the capa.cit.v va.l~ae of that node.
Also provided. in accordance with yet another preferred enhodiment of the present in-vention. is a method for allocating traffirc to a network. the me t.hod including providing a network ir~cfuding at least one blocking switches, receiving a t.ratiic requirement. and allo-cating traffic to the network such that the traffic requirement is satisfied a.nd such that each of the a.t least one blocking switches is non-blocking at the service level.
Further in accordance with a preferred embodiment of the present invention, the step of allocating traffic includes selecting a candidate route for an individual traffic demand, and, if the candidate route includes an occupied segment which includes at least one currently inactive link, searching for a switch which would be blocking a.t the service level if the inactive link were activated and which has an unused active link which. if activated, would cause the switch not be blocking at the service level if the currently inactive link were activated, and if the searching step finds such a switch, activating the currently inactive link and inactivating the unused active link.
The network may include a circuit switched network or TDM network or an ATM
net-SUBSTITUTE SHEET (RULE 2fi) work.
also provided, in accordance with another preferred embodiment of the present invention, is apparatus for allocating traffic to a network, the appara.t,us including a traffic requirement input device operative to receive a traffic requirement for a network including at least one blocking switches, and a traffic allocator operative to allocate traffic to the network such that the traffic requirement is satisfied and such that each of the at least one blocking switches is non-blocking at the service level.
SUBSTITUTE SHEET (RULE 26) BRIEF DESCRIPTION OF THE DRAWINGS
The present invention will be understood and appreciated from the following detailed de-scription, taken in conjunction with the drawings in which:
Fig. 1 is a simplified flowchart illustration of a method for allocating traffic to a circuit switch blocking network;
Fig. 2 is an illustration of a. four node non-blocking ring network;
Fig. 3 is an illustration of the adjacency matrix of the network of Fig. 2;
Fig. 4 is an illustration of a. network traffic requirement matrix for the network of Fig.
2, which matrix satisfies non-blocking criteria;
Fig. 5 is an illustration of an initial link state matrix showing initial network link states for the network of Fig. 2 for the traffic requirement matrix of Fig. 4;
Fig. 6 is an illustration of a.n initia.l switch matrix for the traffic requirement matrix of Fig. =1;
Fig. 7 is a simplified flowchart illustration of a method operative in accordance with one embodiment of the present invention for expanding a network by adding links as necessary to satisfy a given traffic requirement:
Fig. 8 is an illustration of anotlter network traffic requirement matrix for the network of Fig. 2;
Fig. J is a.n illustration of a blocking configuration of the ring network of Fig. '~:
Fig. 10 is an illustration of a link state matrix for the blocking ring network of Fig. ~):
Fig. 11 is an illustration of the link state matrix for the ring network of Fig. J once the traffic requirement of Fig. 8 has been allocated thereto according to the method of Fig. 1;
Fig. 12 is an illustration of the switch state matrix for the ring network of Fig. 9 once the traffic requirement of Fig. b has been allocated thereto according to the method of Fig.
l;
Figs. 13 A & B, taken together, form a simplified flowchart illustration of a method for allocating traffic to an ATM (asynchronous transfer mode) or TDM (time division multi-plexing) blocking network.
Fig. 14 is an illustration of a four node non-blocking network;
Fig. 15 is an illustration of a.n a.dja.cency matrix for the network of Fig.
14;

SUBSTITUTE SHEET (RULE 26) WO 98!41040 PCT/IL98/00114 Fig. 16 is a traffic requirement matrix for the network of Fig. 14;
Fig. 17 is an illustration of an initial link state matrix for the network of Fig. 14;
Fig. 18 is an illustration of an initial switch state matrix for the network of Fig. l~l which _ satisfies the requirement matrix of Fig. 16;
Fig. 19 is an illustration of another traffic requirement matrix for the network of Fig. 14 which is impossible to fulfill:
Fig. 20 is an illustration of a. four node blocking network;
Fig. 2i is an illustration of an initial link state matrix for the network of Fig. 20;
Fig. 22 is an illustration of the network link state matrix for the network of Fig. 20, following operation of the method of Fig. I t on the net work of Fig. 20:
Fig. 23 is an illustration of the switch state matrix for the network of Fig.
r0 following operation of the method of Fig. 17 on the network of Fig. '?0:
Fig. 24 is a. modification of the method of Fig. 7 suitable for r'~TM and TDM
networks;
Fig. 25 is an illustration of the network connections of a communication switch c~, a.ttached to a site si;
Fig. 26A is an illustra.t.ion of a network topology based on the =t-vertex clique C.,, the numbers next to the links touching switch yr indicate their capacities:
Fig. 26B is an iilustra.tion of a routing scheme for C4 under a requirement matrix R~, the numbers next, t.o the links indicate the traffic flow they carry;
Fig. '?7 is a.n illustra.tion of a.n expanded network after reconfiguring to fit the traffic requirements;
Fig. '?8A is an illustration of a routing scheme for the 4-vertex ring, each dashed arc denotes a. flow of I25 units:
Fig. 28B is an illustration of a routing scheme for the 5-vertex ring, each dashed arc denotes a flow of 83 units:
Fig. 29 is a.n illustra.tion of a 21 node network example;
Fig. 30 is a.n illustra.tion of expanding a. congested link a along the route:
Fig. 31 is an illustration of the link capacities after redistribution operation;
Fig. 32 is an illustration of an ATM expansion network example;
Fig. 33 is an illustration of the relationship between B and a(~B(C'~, r));
Fig. 34 is an illustration of the relationship between B and a(~'B(Cn, r));

SUBSTITUTE SHEET {RULE 26) Fig. 35 is an illustration of the routing scheme from s; on the chorda.l ring;
Fig. 36 is a.n illustration of the flow on the link (vr, v2) on the ~i-vertex chordal ring with a = z;
Fig. 37 is an illustration of the routing scheme on the 3-chorda.l ring.
Fig. 38 is a simplified functional block diagram of bandwidth allocation apparatus con-structed and operative in accordance with a preferred embodiment of the present invention;
and Fig. 39 is a simplified flowchart illustration of a preferred mode of operation for the apparatus of Fig. 3b.

SUBSTITUTE SHEET (RULE 26) DETAILED DESCRIPTION OF PREFERRED
EMBODIMENTS
Reference is now made to Fig. 1 which is a simplified flowchart illustration of a method for a.lloca,ting traffic to a circuit switch blocking network. The method of Fig. 1 preferably comprises the following steps for each individual node pair in the blocking network. The method of Fig. 1 is performed repeatedly for a.ll node pairs in the blocking network, using the same fink matrix for all node pairs. The terms "link" and "edge" are used essentially interchangeably in the present specification and claims.
Step I0 defines a loop.
In step '?0, the traffic demands are defined )>v a user. Typically, the traffic demand includes a ctua.ntitv of traffic which is to pass between the two nodes in the node pair.
In step :30, a.ll routes are generated between t he nodes in the node pair, e.g. by using the a.dja.cency matrix of the network. Typically. io pra.ctice, all routes are generated which satisfy certain reasonableness criteria, e.g. which include less than a threshold number of hops.
In step =10, the neht best route is select.ecf. tms~->d on suitable optimizing criteria such as cost. If more than one routes are equal in terms of t:le optimizing criteria, and if more than one demands are defined for the node pair (c-~.g. two demands of l05 iVlb/s each for the same node pair) then typically each of these ront,es are select.ecl simultaneously.
In step :p0. the link size of the next bPSt, rom c>/s is reduced to indicate that that/those routes is/are more occupied or even totally occupied clue to the portion of the traffic that ha.s been allocated to that/those routes.
Step 60 asks whether the demand defined in step ZO has been satisfied. If so, the selected route or routes is/are activated (step 70) and the method returns to step 10 in which the same route-finding process is performed for the next node pair, continuing to use the same link matrix.
If the demand is not satisfied, then, according to a preferred embodiment of the present invention, an attempt is made (step 80) to a.ctivat,e inactive links, if any, in order to allow the demand to be met without resorting to selection of less desirable routes in terms of the optimizing criteria. If no such inactive links exist, the method resorts to selection of less desirable routes in terms of the optimizing criteria by returning to step 40.
If such inactive links e.cist, in occupied segments Qf the selected routes, then it is assumed SU9STiTUTE SHEET (RULE 26) that activation of each of these inactive links would cause a.t least one switch along the selected routes to block on the service level. A switch is considered to "block on the service level" if the traffic allocated to the routes entering the switch exceeds the traf~rc allocated to routes exiting the switch. It is appreciated that a blocking switch may nonetheless be found to be non-blocking on the service level.
Preferably, if a plurality of links exist hetween a pair of switches, the links are assigned priorities by the user such that tyre lowest priority link is activated first and inactivated last and the highest priority link is activated last a.nd ina.ctiva.ted first. If no priorities a.re defined, any inactive link may be selected for a.caivation.
In step 90, the method scans the switches along occupied segments of the selected route and tries to find a switch (or pair of switches) which is (are) preventing an inactive link from being activated and which has (or which each have) an unused active link. Some inactive links are prevented from being activated by only one of the switches they a.re connected to.
In this case, only that switch needs to have an unused active link. Some inactive links a.re prevented from being activated by hoth of the switches they are connected to.
In this case.
each of the two switches needs to have a.n unused active link.
If the test of step 90 is not passed. then the method returns to step 40, i.e.
the method resorts to less desirable routes.
If the test of step 90 if passed. i.e. if an inactive link exists along the occupied segments of the selected route which ca.n 1>e activa.t,ed at the price of inactivating one or two adjacent active unused links, then the active moused links is/are inactivated (steps 9.5 and 100) and the inactive link is activated (stet>s LI0 arrd 120) and the method then.
according to one embodiment of the present, invention, returns to step 30.
Alternatively. in certain applications, the method rr~av return to st ep 40 or step ~0.
A four node non-blocking rirEg network is illustrated in Fig. '?. The adjacency matrix of the network of Fig. 2 is illustrated in Fig. 3. The links connecting adjacent nodes in Fig. 2 each have a capacity of 15a .NIh/s. The application is assumed to be a circuit switch application, i.e. the amount of traffic allocated to each used link may be exactly its capacity either as a single unit or a.s a product of smaller units whose total sums up to the link capacity.
The network of Fig. 2 is to be used to satisfy the network traffic requirement illustrated in Fig. 4. All of the switches in Fig. 2 are non-blocking because their capacities are 155 Mb/s x 8 = 1.24 Gb/s, i.e. 8 times the link capacity (four incoming links and four outgoing links per switch, as shown).
The initial link state matrix is shown in Fig. 5, where the first column indicates the two switches connected by each link, the second column the link's ID, the third column indicates SUBSTITUTE SHEET (RULE 26) ..... ~. . ......... ....."....

the link's capacity, the fourth column indicates the current traffic allocation to each link, the fifth column indicates the extent to which the link is currently ntiiizecl, the sixth column indicates the state of each link (active or inactive), and the seventh column indicates each link's priority for activation.
It is appreciated that the network of Fig. 2 is non-blocking a.nd remains non-blocking.
However, the network of Fig. 2 cannot satisfy all the traffic requirements in Fig. t~. Therefore, the method of Fig. I is preferably employed in conjunction with the blocking network of Fig. J.
EXAiVIPLE 1: The method of Fig. i is now employed in an attempt to expand the network of Fig. 2 such that the network of Fig. 2 can support the traffic requirement of Fig.
8 by using the blocking network of Fig. 9.
The initial link state matrix for Example 1 is shown in Fig. 10.
The operation of the method of Fig. 1 in this example is as follows Step 10 - The node pair A,B is selected.
Step 20 - According to Fig. 8, the traffic demands for the node pair ,-\.B are 155 YIb/s + 155 Mb/s + 155 Mb/s.
Step :30 -- There are two routes between A and B: A, B and A. D. ('. 13.
Step ~0 -- The best route is A, B if a path shortness criterion of opt.irnizatio« is used.
Step 50 -- Demand is not satisfied because only two 155 Mb/s links arc' available between A and B s~~herea.s :; are rectuired, assuming the given requirement inc-luclP~
traffic which is all following a single route. Therefore, the link state matrix is not updated.
Step 60 - The method proceeds to step 80.
Step 80 - The occupied segment of the route is, in this case, the c~r~t.ire route. It is assumed that a 155 Mb/s unsatisfied requirement justifies adding a new link of size 155 Mb/s from A to B. Therefore, the method proceeds to step 90.
Steps 90, 95 - Switches A and B are scanned and the method determines that LN3, LN4, LN5 and LN6 are active unused links and therefore, a link LNX9 of size 1 55 Mb/s can be added between switches A and B if links LN4 and LN6 are inactivated.
Steps I00, 110. I20 - Links LN4 and LN6 are inactivated and deleted from the link state matrix. Link LNX9 is added to the link state matrix. In the switch state matrix, the utilized capacities of switches A and B are each incremented by 155 Mb/s because link LNX9 has been added a.nd are also decremented by the same amount because links LN4 and LN6 respectively have heen inactivated. Therefore, in total, the utilized capacities of switches A
and B in the switch state matrix remain the same:

SUBSTITUTE SHEET (RULE 26) The method now returns t,o step 30.
In step 30, a.ll routes are now generated for the current network configuration. The possible routes are now still A,B and A, D, C, B.
Step ~10 - The next best route is A, B as before.
Step 50 - The demand is now satisfied so the link state matrix is updated by replacing the zero values in the first three rows of Link Utilization column :~ with values of 155 Mb/s.
Step 60 - The method proceeds to step 70.
Step r 0 - The selected routes are activated and the method returns to step 10 and selects the next node pair.
Step 10 - In the present example, the tra$-rc requirements are assumed, for simplicity, to he symmetric, and therefore the node pairs are, apart, from A.B, only A, C: A, D;, B, C;, B, D: a.nd ('. D. It is appreciated that, more generally, the traffic requirements need not be symmetric.
In tle present example, the next four node pairs to 1>e selected are A, C: A, D;, B, C;
a.nd B. D respectively. Since the traffic requirement for each of these pairs is 0, the method of course finds that the demand is satisfied for each node pair trivially and proceeds to the last. mode pair, (.'. D.
~Che rnet.hod now proceeds to analyze the C, D node pair similarly to the manner in which the A, B node pair was analyzed. The method concludes. sirniiarly, that a new link, LNX10, of size t:~::~ ~~Ib/s, should be activated between switches (' and D. In step 250, the demand is aga-in deemed satisfied so the link state matrix is updat.P<1 l>v replacing the zero values in the last three rows of Link Utilization column 5 with values o(~ L:p:~ 1Ib/s.
Tire final link state matrix is illustrated in Fig. 11.
The blocking network of Fig. 9 may be generated by the method of Fig. 7 which is now described.
Reference is now made to Fig. 7 which is a simplified flowchart illustration of a preferred method for expanding a network by adding links a.s necessa.ry to satisfy a given trafCrc requirement.
Steps 210 - 270 in the method of Fig. t are generally similar to steps 10 - r0 in the method of Fig. 1.
In step 280, the method determines whether it is worthwhile to open new links (i.e.
whether links should be added) within the occupied segment of the selected route, in ac-cordance with predetermined criteria of cost and/or utility for the proposed new link. This information is optionally received as an external input.

SUBSTITUTE SHEET (RULE 26) - _ - _ ... r.._ ~

If step '?80 determines that it is not worthwhile to open any new links along the occupied segment of the selected route, the method returns to step 240 and selects the next best route because the current best route is not feasible.
1f step 280 determines that it is worthwhile to open a new link somewhere along the occupied segment of the selected route. the method proceeds to step 282. In step 282, the method inquires whether any of the proposed new links can be opened without causing any switch to block on the service level. If this is possible, these links are opened or activated (steps 310, 320).
If, however, none of the proposed new links ca.n be opened without causing some switch or other to be blocking on the service level. then the method proceeds to step 290 which is similar to step 90 of Fig. 1. If the test of step 290 is not passed then the method returns to step '?40 and selects the next best route because thc: current best route is not feasible.
If. however, the test of step '?90 is passed then step 300 is performed which is generally similar to step 100 of Fig. 1.
It is appreciated that the applicabilit,v of the method of Fig. i is not limited to circuit switch networks but includes all other t,vpPS of networks such as TDM and ATM
networks.
Fig. 12 is an illustration of the switch st,a.te matrix for the ring network of Fig. 9 once the traffic requirement of Fig. a has been allocated thereto according to the method of Fig.
Reference is now made to Fig. 13 which is a simplified flowchart illustration of a method for allocating traffic to an ATM or TD:~'I l~ior~kiry network .
The method of Fig. 13 is similar to t.lne method of Fi . 1 with the exception that if' a. link is onlv partially utilized, it is possible to allocate t.o that link a proportional amount of the switch capacity, i.e. proportionally less than would he allocated if the link were completely utilized. In circuit switch applications, iu contrast. the amount of switch capacity allocated to a link depends only on the links capa.citv and IIOt on the extent to which the link's capacity is actually utilized.
A new step 400 is added before step 80 in which an attempt is made to identify partially utilized active links so that a larger proportion of these ca.n be utilized.
If all of the active links are totally utilized, i.e. if none of the active links are only partially utilized, then the method proceeds to step 80.
If there is at least one active link which is only partially utilized then the method proceeds to new step 410.
In step 410, the method searches among switches along the occupied segment of the selected route which are preventing the partially "utilized link or links from being further SU9ST1TUTE SHEET (F~ULE 2fi) utilized. These switches are identifiable as those which are shown by the switch state matrix to be completely utilized. Among these switches, the method searches for those which have an active link which has unutilized~bandwidth because the link is partially or wholly unutilized. If no such switch is found. the method returns to step 40 and selects the next best route since the current best route is not feasible.
If, however, such a switch is found, the method proceeds to new step 420 in which the following operations are performed:
The un-utilized bandwidth is "transferred" to where it is needed; and in the link state matrix, the link allocation column (e.g. Fig. 17, column =1), is incre-mented in the row which describes the link which is ''accepting" the bandwidth. The link allocation column is decrementecf ire the row which describes the link which is "contributing'' the bandwidth.
The method now returns t.o st.c~p 30.
EXAMPLE 2: Given is a four node non-blocking network as illustrated in Fig.
14.
Solid lines indicate physical links whereas virtual paths are indicated by dashed lines. The adjacency matrix of the rlet.wOl'lv of Fig. 14 is illustrated in Fig. 15. The links connecting adjacent nodes in Fig. 1=1. L~ l t.o L~9. each have a capacity of 155 Mb/s.
The application is assumed to be an ATNI application.
The network of Fig. 1I satisfies the network trafFrc requirement illustrated in Fig. 16.
Assuming there are three input ports per switch, all of the switches in Fig. I-f are non-blocking. Specifically. the cat>a.uit ies of switches A, C and D are 155 NIb/s x fi = (J.f).'3 C~b~s and the capacity of switc:lW3 is l:i:> vlb/s x I2 = 1.86 Gb/s.
The initial link state matrix is shown in Fig. 1 r. 4vhere the first column indicates tloe t.wo switches connected by each link. tine second column the link's ID, the third column indicates the link's capacity, the fourth column indicates the current traffic allocation to each virtual Path Identifier (VPI) in a given link. The fifth column typically indicates the extent to which the link is currently utilized. The six column indicates the state of the link (active or in-active) and the seventh column indicates each link's priority for activation.
The initial switch matrix for ti a above example is shown in Fig. I8 which satisfies the requirement matrix of Fig. 16.
The network in Fig. 1-1 is non-blocking and remains non-blocking for the requirement shown in Fig. I6. However. the network of Fig. 14 cannot satisfy the additional traffic requirement of Fig. 19. Therefore, the blocking network of Fig. 20 is employed, initially carrying the traffic requirement of Fig. 16; and the link and switch states illustrated in the matrices of Figs. 1 t and 18 respectively. In Fig. 20, existing links are indicated by thin lines SUBSTITUTE SHEET (RULE 26) and new expansion links a.re indicated by heavy lines.
The method of Fig. 13 is employed in.an attempt to expand the non-blocking network of Fig. 14 to function like the blocking network of Fig. 20 such that it can support the added traffic requirement of Fig. 19. The initial link state matrix, for Example ?
is shown in Fig.
21. The initial switch state matrix for Example 2 is shown in Fig. 18.
The operation of the method of Fig. 13 for this example is as follows:
Step 10 - The node pair A, B is selected.
Step 20 - According to the traffic demand matrix of Fig. I9. the traffic demand for A, B is 100 Mb/s.
Step 30 - all routes are generated for the current network configuration. The possible routes include only A. B. Therefore, Step =1() --- The next best route is A, B.
Step 50 -- ~o active links are available to satisfy the demand illustrated in the matrix of Fig. 21.
Step 60 - Demand is not satisfied and the method proceeds to step =100.
Step 100 - ~ es. there are active links that can be utilized. However, they can support only up to l:~j l~Ib/s. Therefore, no active link with spare ca.pa.citv is available a.nd the method proceeds f O step ~O.
Step b0 - 1'es. there are links such as LNX10 as shown in Fig. '?I. The method proceeds to step 90.
Step 1~0 - ~EVitclies A and B scan their links for inactive ba.odwidth tlra.t would enable activation of the L\X10. Switch A has allocated three tunes 1.:~.~ :Vlb/s, i.e. =165 Mb/s.
whereas only 300 Vlb/s is utilized as shown in Fig. 21, column 6. Therefore, the inactive link can be activated with 100 Mb/s and the links LN2 and LN3 a.re allocated only 100 Mb/s each. The method now proceeds to step 95.
Step 95 - No active link has been deleted so no update is needed.
Steps 100, 11U. I20 update the link LN2 such that its VPI ID is '? and its capacity is 100, update the link LN3 such that its VPI ID is 3 and its capacity is 100, and update the link LNX10 such that its VPI ID is 4 and its capacity is 100. The switch matrix is updated accordingly and the method proceeds to step 30 to generate the routes. If, however, the step 95 is not passe then the method goes to step 40 to try the next best route.
Step 30 - All route a.re now generated for current network configuration.
There is only one possible route: A, B.
SUBSTITUTE SHEET (RULE 2B) Step ~10 - The next best route is A, B.
Step 50 - LNX10 is available with 100 Mb/s.
Step 60 - Demand is satisfied and the method proceeds to step 70.
Step i0 - The path is realized and activated a.n the method proceeds to step IO and selects A, C.
The method proceeds to select the next traffic demand or requirements (step I0). The next node pair is A, C. The method preferably selects acrd tries to fulfill all remaining node pair requirements as shown in Fig. 19.
The method satisfied the remaining requirements between B.C and B, D. The remaining requirement cannot be fulfilled, due to the network blocking. The network link states, following operation of the method of Fig. 17 are shown in Fig. 22. Similarly, the node state matrix appears in Fig. ?3.
The method of Fig. r may be employed to add links in ATM and TDNI networks, if step 2S)0 in Fig. 7 is modified, as shown in F'ig. '?-1. to additionally take into consideration partially utilized links when evaluating whether to adcl new links. Lising Fig. '~=I, a blocking version of Fig. 14 is generated, as shown in Fig. 20.
General capacity extended channels in communication networla provided in accordance with a preferred embodiment of the present: invention are now described. This a.na.lvsis was derived by Dr. Raphael Ben-Ami from BAR~'E;~I' Communication Intelligence Ltd, ISRAEL. and Professor David Peleg from the Departrnerrt. of Applied l~Ia.thematics and ('omput.er Science, The VVeczmann Institute of Scienew. I~ehovot:, 76100 ISRAEL. Professor I)avicl Fele~ is not an inventor of the invention clainmcl herein.
A Introduction One of the basic rules used for governing the design of most traditional communication networks is the capacity conservation rule for the network switches. Simply stated, this rule requires that the total capacity of incoming communication links connected to a switch must not exceed the switch capacity. (As the outgoing communication links connected to the switch have the same total capacity as the incoming links, the same applies to them as well.) This rule is desirable since it serves to prevent blocking situations, in which the total amount of traffic entering the switch exceeds its capacity, a.nd consequently blocks the switch. In fact, the requirement of non-blocking cross-connection is adopted in a. number of standards (cf. ~Be193, Be195~).
The disadvantage of the capacity conservation rule is that it may in some cases cause poor SUBSTITUTE SHEET (RULE 26) .~ , ..

utilization of the switch capacity. As long a.s traffic over the links entering and exiting the switch is well-balanced, the switch can be utilized up to its full capacity.
However, if some of the incoming links are more heavily loaded than others (and the same for the outgoing links), then part of the switch capacity must remain unused.
This paper proposes a more flexible approach to capacity conservation and blocking prevention. The idea is to allow a switch of a. given capacity c to be physically connected to links with total capacity exceeding c. Capacity conservation, and subsequently blocking prevention, should be enforced by lorkin.g some of the capacity of each link, at any given moment, and allowing it to use only part of its capacity. As the traffic pattern dynamically changes in the network, usable link capacities can he changed. This is done by locking some of the currently free capacity in lightly loaded links, and a.t the same time releasing some of the locked capacity in highly loaded links. ,\t all times. the usable portions of the link capacities must preserve the capacity conservation rule.
This approach results in considerable improvements in the utilization of switches. Con-sider the common situation in which increases in the traffic requiremer:ts have brought the network to the stage where the trafF~c c-~trrentlv saturates the capacities of the network switches, with some traffic requirements cmsat.isfied. In this case it is necessary to expand the network in order to accommodate this additional traffic. Designing the network upgrade while insisting on following the traditional capacity conservation rule would force the network designer to increase the capacity in E>ot:h t he switches and links in question. In contrast, by switching to our more flexible conservation rule. considerable gains in the amount of trafF~c ma.y be possible in some cases, by adclin<_; capacity only to the links, and utilizing the current.
switch capacities more efficiently.
(Let us remark that our approach is clFarlv heneficia.l also for the design of new networks.
However, network expansions are increasingly becoming a more and more significant fraction of the market. This trend was identified in a recent study made by the Pelorus Group (Pe196~.
According to this report, installations of expansion units in existing communication networks accounted for 40% of the installations of network units in 1996, and are expected to constitute the majority of the installations from 1998 on. ) In what follows, we begin (in the next section) by formally defining the network model we rely on, and then present formally the link expansion paradigm (in Section C).
In Section D
we provide some examples for the potential benefits in our approach. Section E
presents the protocol used for dynamically controlling the available capacities of channels in the network as a function of continuous changes in the traffic patterns. Finally, Section F discusses the advantages of the proposed approach in ATM networks.

SUBSTITUTE SHEET (RULE 26) B The model B.1 The network architecture The model can be formalized as follows. The communication network connects n sites, sr, . . . , sn. Each site s~ is connected to the rest of the world via a communication switch, denoted wi. The switches are connected by a network of some arbitrary topology. For the sake of generality, we assume that the links are unidirectional. Thus, each switch has a number of incoming links a,nd a number of outgoing links. Formally, the topology of the network is represented by an underlying directed graph G = (t ; E), where the vertex set V = ~vl, . . . , v.~ ~ is the set of switches the network, and E C V x V is the collection of uni-directional links connecting these switches (For rotational convenience we may occasionally refer to the switch v~ simply as c:, and to the link (v;, u~) as (i, j).). In addition. each switch v.i always has both a.n incoming and an outgoing link to its local site s;:
tl~e site transmits (and receives) all its traffic to (and front) other sites through these two links. Let ~'' denote the set of these links.
Formally, we will adopt t.lne following notation concerning the link structure of a switch Ui. Denote the links connecting it to it.s site s~ by e~ (for the Link from st to v; y a.nd e~"t (for the link from vt to .s.; ). We refer to these links a.s the site-s~tvitch links. Denote the remaining adjacent ingoing links of r~ by e~'' _ (r~t,uJt) for 1 < l < k, and the adjacent or~tsoing links by el"c = (u;,u.~~~) for I < I < kw'. These links are referred to a.s the inter-.s~nitctr Li~ak~, or simply the network linker. ~Cle link structure of the switch vt is illustrated in E ig. '?.:~.
Let us now turn to <loscribP another major factor of the network design.
narrmly. the capacity of switches and links. Each link a = (i., j) has a certain cupacit~
c(r ) associated with it (In reality. it is often the case that the links are bidirectiona.l and have. w-mmetric capacity, namely, c(i, j) = c( j, i). Likewise, it may often be assumed that the roc~uirements are symmetric, namely, r;,.; = ry,,~.), bounding the maximum amount of traffic that, can be transmitted on it from i to j. In addition to link capacities, each switch z>
of the network also has a capacity c(v) associated with it.
The standard model assumes that the capacities assigned to the edges connected to any particular switch sum up to no more than the capacity of that switch.
Formally, each switch must obey the following rule.
Capacity conservation rule:
t) _ ~ o(et)~
o<t<k o<t<k~
We shall refer to a network obeying this conservation rule as a conservative network.

SUBSTITUTE SHEET (RULE 26) B.2 'I~affic requirements and routing The traffic requirements among pairs of sites are specified by an n x ra requirement matrix R = (r2,~), where r;.,~ is the amount of traffic required to he transmitted from site si to site s~. (~Ve will assume that traffic internal to the site si, i.e., between different clients in that site. is handled locally a.nd does not go through the network, hence in the traffic requirement matrix R to be handled by the network, r;.t = 0 for every i.) Note that the traffic requirenoents matrix R can change dynamically with time, as the result of new user requests, session formations and disconnections, and so on.
Let us define the following notation concerning traffic requirements. For every site s;, denote the total traffic originated (respectively, destined) at s; 1>y R~ui(a) _ ~~ y';,~ (resp., Rtn(i) _ ~.J r.~_; ). Let Rsu."1(i) = Rout(i) -1- j~n(i). For each of the subscripts sub, let Rsub = ma:C~ { h,.,ub~ t ~ } .
~ given requirements matrix R is resolved by assigning to each pair of srteS
2, j a collection of routes from i to j, {pi.~, .. , pL,~}, over which the traffic rt,~ twill bP
split. That is, each path pi.~ will carry f'~.~ units of traffic from i to j, such that k l ft,~ = ri,.i-r»
The collection of routes for all vertex pairs is denoted p.
Once thf~ rorrt.es are determined, we know exactly how much traffic will k>e tra.nsrnitted over each f~~lg~ arrcl through each switch of the network. Specifically, given a route collection p and a. network elernent a~ E l~ U E U E' (which may be either a.n edge a or a switch n), let C~(a~) denot.c~ t1<~ collection of routes going through ~, Q(:r) _ ~(i, j, l) ~ ~: occurs on pi_~}.
(Note that the switch v ma.v never occur on a path as a.n end-point: all routes start and end at sites, and thus - formally speaking - outside the network.) Define the load induced by p on the network element x E V U E U E' (an edge or a switch) as 9(x~ _ (2,.9,1)E~(x) Observe that the traffic flows in v; and its adjacent links must satisfy the following rule.
Flow conservation rule:
9(vt) _ ~ q(e~n) _ ~ q(Fi ~t) o<t<k ~ o<t<k~

SUBSTITUTE SHEET (RULE 2B) Moreover, g(eon) = R~u~(i) and g(eo"t) = Rtn(i), and subsequently.
g(el") > R«(i) . and ~ cl(elue) > Ro,~~(i) r<r<x ~<r<k (these inequa.Iities might be strict, since the switch ui nra.y participate in transmitting traffic belonging to other endpoints as well). Consequently, 9('~t) ~ R~~(2) + Ro~.t(z) = RS-~~~, (i).
C,'lea.rly, in order for our link assignment to be feasible. the links and switches must satisfy the following rule.
Flow feasibility rule: q(x) < e(x) for each Link or switch x.
In view of bound (2), this means that a. requirement matrix R with Rsum > c cannot be satisfied a.t all, hence it suffrces to consider matrices with RS~~ < c (henceforth termed legal requirement matrices). Call a requirement matrix R rraaxzr-nrxl if R9,~~,, =
c, namely, at least one of the switches saturates its capacity. Note that every matrix satisfying R9~~, _< c can be norrna.lized so that it becomes maximal. Hence in what follows we shall concentrate on the behavior of networks on maximal requirement, matrices.
C The channel expansion model The idea proposed in this paper is to expand tlEe ca.pacitv of channels beyond that of the switch. :fit first sight, this may seem wasteful, as the potential traffic through a switch cannot exceed its capacity. Nonetheless, it is argued that, such expansion may lead to increased total throughput under many natural scenarios, since allowing the total capacity of the links adjacent to a switch v to be at most the capacity of the switch means that it is only possible to fully utilize the switch if the route distribution is uniform over all the links. In practice, a. given trafprc requirement matrix may impose a non-uniform distribution of traffic over different links. and thus force the switch to utilize less than its full capacity. Increasing the capacity of the links would enable us to utilize the switch to its fullest capacity even when the traffic pattern is non-uniform.
It is important to note that the added channels need not be dedicated to potential expansion, but rather can be used for serving multiple functionalities in the network. For instance, the extra channel capacity can be used a.s protection lines, serving to protect against line failures. iVloreover, some network designers are considering network with reserved bandwidth to reroute traf)ic in causes of failure. We claim that the expansion could be performed as well a.s considering bandwidth for reroute traffic in causes of failure.
SUBSTITUTE SHEET (RULE 28) r... .... ,. ..

A potential difficulty with a naive implementation of this idea is that it might violate the highly desirable raon-blocking property required of communication switches. In order for a switch to be non-blocking, it is required to ensure that whenever an incoming link has free capacity, both the switch Itself and (at least) one of its outgoing links can match it with free capacity of their own. This guarantees that it is irrlpossible for incoming traffic to ever "get stuck'' in the switch.
Hence in order to be able to utilize capacity expanded links, it is necessary to design the link-switch connection in a. way that al]ows us to temporarily "lock" part of the link capacity, allowing the link to transmit only a fraction of its real capacity.
Then, whenever a switch of capacity c is connected to links whose total capacity is c.' > c, it is necessary to lock the extra link capacity, to a total of c' - e.~ capacity units, and allow only a. total capacity of c units to reach the switch.
Obviously, in order to enable us to take advantage of the extra capacity, the link locking mechanism must be reconJigurable, na.me~lv, allow changes in the fraction of locked capacity.
This will allow the capacities of the links connected to a. particular switch to be dynamically reconfigured at any given moment, according to the changes in traffic requirements. We will describe a protocol for dynamically controlling link capacities in the network in Section C.
Let us next present a formal definlt,lorl for a. communication network model supporting expanded capacity channels. The main wange is that the capacity of each link e, c(e), is partitioned at any given time t into two parts, rla.mely, the usable capacity ci~(e) and the locked capacity cL(e). These two quantities may change over time, but at any given tune I
they must satisfy ~'r (~ ) + c:~ (e1 = c(e).
At time t, the only part of the capacity t hat ca.n he used for transferring traffic is the usa.blP
capacity; the locked part is effPCtivc~iy disconnected from the switch (by software means.
although it is still physically attached to the switches), and cannot be utilized for traffic.
That is, denoting the load on the link a at time t by qt(e), the flow feasibility rule for links becomes:
Modified flow feasibility rule: .at a.rly given time t, qt{e) < cU{e) for each link e.
The capacity conservation rule observed by the switches must also be modified now, so that it refers only to usable capacity.
Modified capacity conservation rule: At any given time t, ~Lr(e!) _ ~ ~il(e()~
0<1<k 0<f<k' SUBSTITUTE SHEET (RULE 2fi) D Examples for potential benefits Let us illustrate this idea. via a. nurrrber of simple examples. In these examples. the traffic pattern is semi-rigid, in the sense that the system remains under one traffic requirements matrix R for a.n extended period of time, and while this matrix is in effect, the traffic values behave precisely as prescribed by it (i.e., there a.re no significant traffic fluctuations).
That is, traffic volume chanhes occur sparsely. Later on, we will discuss the way we handle dynamically changing systems. at this stage, let us only point out that it is clear that in a. dynamic setting, tlae potential profits from the utilization of dynamic capacity expansions are even greater than in the semi-rigid setting.
D.1 Paired traffic on the 4-node clique Consider the complete network over four switches, cy to r~4, connecting the sites .~, to s4.
Suppose that the capacity ol' ea.ch switch is 600. and that the network obeys the conservative model, allocating the link capacities a.s in Fig 26 (a).
Suppose that at a given moment. it is required to establish communication of tot al volume 600 from ur to r~., and f'ron~ y t,o y. In the given network, a.t most 100 units of the traffic from yr may proceed on the direct link (ul,v2), and the rest (in t.wo equal parts of ~0 units each) must follovc> patiw of length '?, via the other two vertices. The sa.rrre a~>plies to the traffic from ua to u:j. Once t his is done, a.ll the edges leading from i.~l a.ndm:, to n., and t~-r are saturated ( see Fi ~. '?6 ( l 1.
In this case, if the network consists of capacity-expanded links. say, with capacvitv c(e) 600 for each link. t hen it iv possible to route all requested traffic by recortfigurirrg t he network so that the adrnissihlc~ capacities are as in Fig. 27.
D.2 Uniform traffic on small ring networks Next, we consider the effects of expansion on ring networks of four and five nodes. assume that the node capacities dr'e 1000 units, trafi=rc is uniform and network link capacities a.re 250 units each (i.e., the site-switch links have 500 unit capacities). Also assume that each node is required to send each other node a total of 167 units. Calculations presented elsewhere (BP96b~ show that io the conservative setting (i.e., with no link expa.nsion), only 3/4 of this trafFrc, i.e., f't.~ = 125 for every 1 < i, j < 4, can be transmitted.
:fit this point, the trafFrc saturates the inter-switch links, whose capacity is 250 units. (See Fig. 2f3(a)). Hence this trafl~rc pattern causes a blocking of 25%. In contrast, expanding the ring network by a factor of 8/7, namely. increasing the link sizes to 286 units, will reduce the blocking to 14%, SUBSTITUTE SHEET (RULE 26) allowing a traffic of f;,~; = 113 for every 1 < a, j < 4.
Vow consider the 5-vertex ring, under the same assumptions on capacities and traffic requirements. In the conservative model we have 33~, blocking. with f;,,; = 83 for every l < i, j < :-r. (See Fig. 28(b).) However, assuming the links are expanded by a factor of fi~5, i.e., their capacity becomes 300, it becomes possible to transmit =1/5 of the traffic, i.e., f~.~ = 100 for every 1 < i, j < 5, hence the blocking is reduced t,o 20%~.
D.3 Uniform traffic on a 21-node general network In the following example (see Fig. 29) we consider a larger network of 2l nodes, with each node connected to four other nodes. We assume a uniforrrr traflrc requirement matrix between the nodes. with each node sending l2fi units of traffic t,o every other node. Further, we assume t.ioat the node capacity is 5040, and the capacity of each network link is 630 units (leaving v5'?0 units for the capacity of site-switch links). In tine conservative setting, it is shown io ~BP~)6h~ that only .'.35 units can be sent between every pair of nodes ( f;,~ _ 35 units for ewers l ' i, j < 20), as at that point the traffic saturates a.t, the inter-switch link, whose capacity is f>:30 units. This means that 72% of the tragic is blocked.
This rmtwork can be expanded by increasing the networl: link capacities to 1296 units.
This woolcl enable each node to send up to 72 units of traffic t.o every other node, thus reducirr~ tire blocking to 43%.
E Dynamic capacity expansion control In t.hi~ ac~cn.ion wP describe our approach to the problem of clvnamicallv controlling the a.vaila.hlt~ capacities of channels in the network as a function of continuous changes in the traffic patterns. Specifically, we give a schematic description of a protocol whose task is to control the capacity expansions and reductions of channels in the network in response to dynamic requests for session formations or disconnections.
The capacity control protocol is in fact integrated with the route selection method used by the svst.em. The method responds to connection requests issued by end users. Each such request includes the identities of the two endpoints, and a volume parameter representing the traffic volume expected to be transmitted between these endpoints (and hence, the size of the requested bandwidth slice).
Let rrs start with a high-level overview of the method. A new connection request ~ _ (s;, s~, r). representing two end users from sites s~ a.nd s~ requesting to form a session with r units of bandwidth, is handled as follows. First, a, procedure PathGen is invoked, whose SUBSTITUTE SHEET (RULE 25) task is to generate candidate paths. Of those candidates, we then select a ,vreferred rote according to pre-specified optimization criteria.. T'he choice of criteria is the subject of much discussion in the literature, and there is ~a wide range of design choices that can be made here, and are largely independent of our scheme, so we will make no attempt to specify them here. One parameter that is not taken into consideration a.t this stage, though, is feasibility.
Nameiv, the protocol does not try to verify that tire selected route has sufficient capacity a.t the moment in order to meet the entire demand specified by the request.
The selected route is now allocated to this session. At this point, the method checks to see what part of the request has been fulfilled. In case there is still an unsatisfied fraction of r' units, the method now tests to see whether it is possible to expand the congested segments of the selected route by the required amount. The congested segments of the route are defined as those links along the route whose flow is currently identical to their usable capacity.
Expanding the capacity of such a congested link f is done as follows. Suppose that a connects the vertices v~ and v., along the seler-ted route from s; to s~.
Suppose further that there exist some unsaturated edges emanating from r~r , i.e., edges whose current load is less than their usable capacity, and some unsaturated edges entering v2.
Let ~1 denote the total "free" (namely, usa.hle hut currently unused) capacity in the un-saturated outgoing links of ul, and let D2 denote the total ''free" capacity in the unsaturated ingoing links of v2. Let ~1 = min~.~r,:,2, r~. ~'L(r-)~~
~Ve will only expand the capacity of a by ~ units. This is done as follows.
First, unlock units of capacity on link e, setting cL(e) E-- cL(e) - ~ and ci.(e) E- c~(e) +:~. At the same time. balance the capacities at the switches r:, arid r~.> by locking ~ units of capacity in the unsaturated outgoing edges of ry and in the ansa.turat.ecl ingoing edges of v2. Clearly, the conservation rules a.re maintained, and link a is now able to transmit L1 additional traffic units.
Of course, the traffic increase along the route depends on the least e~gandable link, namely, the link a for which D is smallest. If that e1 is strictly smaller than r', then the selected route cannot be expanded any more, and part of the traffic must be routed along some alternate routes.
Example: We illustrate the expansion process via an example, depicted in Fig.
30. In this example, the total capacity of network finks is 12 units. The link a is congested as q'(e) = cU(e) = 9, but it still ha,s some locked capacity (c~(e) = 3). Suppose that r' = 2, i.e., two additional units of flow are needed along the route from s; to s~. The only unsaturated' edge emanating from yr is the edge e~, for which cU(er) = 10 and qt(er) = 8.
The only unsaturated edge entering v2 is the edge ~.,, for which c~(e2) = 10 and qt(e2) = 5.

SUBSTITUTE SHEET (RULE 26) WO 98!41040 PCT/IL98/00114 Under these assumptions, :,r = 2 a.nd 02 = ,~, a.nd hence Q = 2. Therefore, on ~, it is possible to unlock 2 capacity units, thus setting cL(c) ~- 1 and cU(e) E-11. For e1 and e2 this entails setting cL{er) <- c~{e) -E- 2, cu(er ) ~ cU(e) - 2, c~(e2) E-- cl,(e) ~- 2 a.nd cU(e2) f-- c~,(e) - 2. The resulting capacity distribution is depicted in Fig.
31.
F ATM Network Expansion In an ATM network, a virtual pcctla coranaection (VPC) is a. labeled path which can be used to transport a bundle of virtual chan~n.el connections (VCC's), and to manage the resources used by these connections. Llsing the virtual path concept, the network is organized as a.
collection of VPC's which form a VPC, or a logical overlay network. Generally.
the VP(.' can be either permanent or semi-permanent, and have a reserved capacity of the physical links.
VPC provisioning activities include VPC topology and VPC capacity allocation decisions.
V'PC is defined in the standard ~(TL.'~, a.nd plays a significant role in both tra.f~fio control a.nd network resource ma.na.gement. Some of the main uses of the virtual path concept a.re for achieving simplified routing. adaptability to varying trafFrc and network failures through dynamic resource management, simple connection admission, and the ability to irnplernent priority control by segregating traffic 4vith different quality of service.
The e:ctent to which ~'P(" provisiorring is able to improve efficiency is highly dependent on its ability to provide V('C'~s with low setup and switching costs, while ma.intainin~ low blocking probability for the required network connectivities. This, in turn, depends orr the VPC topology and ca.pa.citv alloc:at ion from resource rnana.gement decisions.
In particular, the choice of V'P(~ topology, or layout, greatly impacts the corrnect.ion setup and switching costs, the network's resilience to unexpected trafbrc conditions and c.ompc>rrents failures, as well as the abilit.v to change the topology when required.
Genera.llv. thc~ VPC
topology is affected by the phvsica.l network.
A main characteristic property of ATM networks that differentiates it from our previous model is the following. In an ATM network, two nodes A and B may be connected by a.
number of communication links (t.ypica.llv of the same type and capacity).
However, each VPC must be allocated in it,s entirety via. a single link along each segment of the path. i.e., splitting a VPC between two or more links is forbidden. (On the other hand, note that a given link ca.n have several VPC'.'s.) This property affects the issue of capacity allocation discussed earlier, and complicates the derived solutions, particularly with regard to blocking. For instance, suppose that each of the links connecting the nodes A a.nd B has fewer than .~' units of free capacity. Then a new VPC request requiring .~~ ca.pa.city units cannot be accommodated, despite the fact SUBSTITUTE SHEET (RULE 26) that the total free capacity between A a.nd B is much greater than needed.
This problem can be alleviated by expanding communication channels beyond the switch capacities. Such expansion can be achieved by adding some extra communication links. It is then possible to utilize extra. space by fixing the usable capacity of each link to be precisely the used capacity, a.nd locking the remaining capacity, thus freeing the ayaiia.ble capacity of the switch for use via other links.
Let us illustrate this point by an example. Fig. 32 describes a four node :~TM1 network, where each node has three links connecting to the neighboring nodes as shown.
In the setting depicted in the example, each link emanating from node A belongs to sole V'P.
VVe assume that each fink capa.cit,y is 155 Mb/s and the node capacity can support rrp to twelve 155 Mb/s links. Therefore each node is assigned three site-switch linlcs and three links for each inter-switch connection it is involved in. (Hence the capacity of the links touching node B
equals the node capacity, and the other nodes have superfluous capacity at thc: switches.) Assume a traffic rc~clrtirements matrix by which Node A has to send lU() ~(h/s to each of the other three nodes B. (.' a.nd D. Therefore, bandwidth allocation for tinese demands will result in the allocation of 100 NIb/s to VPI, VP2 a.nd VP3. Note that a new request for a forth VPC' of 100 ~Ih/s between any node pair cannot be satisfied, due to the Iron-splitting constraint on ~'P(''a. despite the fact that sufficient capacity is ava.ilal,lP within the links to support a.ll the denranc.ls. This will cause blocking in the network, which in the worse case can reach up t.o :B)'~ of t:he network connectivity.
We resolve tl'e /hocking problem by expanding tire network via addirr~ n link (or several links) between ay- mvo connected nodes. These new links could utilize the renrairring unused bandwidth for ac-<~ornrnodat.ing a, new connection request. This is done by I«~~kinh the usable capacity in the links serving the initial three VPC's on their currently used rapa.citv of 100 ll~Ib/s, and allocwt.in~ free usable capacity in the amount requested to the new VPC' over the currently unused links.
References ~Be193J Wideband a.nd broadband digital cross-connect systems -- generic criteria, Bell-core, publication TR-NWT-000233, Issue 3, November 1993.
~Be195~ ATM functionality in SONET digital cross-connect systems - generic criteria, Beilcore, C;eneric Requirements CR - 2891-CORE, Issue 1, ,-~rtgust 1995.
(BP96aj R. Ben-Ami and D. Peleg. Analysis of Capacity-Expanded C.'hannels in a Com-plete Communication Network. Manuscript, 1996.

SUBSTtTUTE SHEET (RULE 26) _ ....-.~ ,-..__ - ~., - , .

(BP9f>ly I~. Ben-Ami and D. Peleg. Capacity-Expa.nde_d Channels in C'.ommunication Networks tinder Uniform Traffic Requirements. Manuscript, 1996.
~Pe196~ Ttre Pelorus Group. Digital Cross-C'.onnect Sv st,erns Strategies, Markets & Op-portunities - Through 2000. Report, November. 1996.
[IT(T] ITU-T Rec. I-375. Traffic Control and Congestion C'.ontrol in B-ISDN.
July 1995.
(.'omputational relationships in capacity-extended channels in communication networks generally provided in accordance with a preferred embodiment of the present invention are now described. Tlris analysis was derived by Dr. Raphael Ben-Ami from BARNET
Com-munica.t,ion Intelligence Ltd, ISRAEL, and Professor David Peleg from the Depa.rtrnent of Applied Mathematics and Computer Science, The Weizrriann Institute of Science, Rehovot, 76100 ISRAEL. Professor David Peleg is not an inventor of the invention claimed herein.
G The network model The model can be formalized as follows. The communica.t.ion network connects n sites, .~~.. . . ..s". The traffic requirements among pairs of sites are specified by an n x ra requirement matrix I3 = (r~..;), where r;.~ is the amount of tra.flic ro<tnirocl t.o lie tra.nsrnitted from site s;
to site _~~. (~Ve swill assume that tra.fT-tc internal to the site .s;, i.e., between different clients in that site. is handled locally a.nd does not go t,hrorrhh tloe network, hence in the traffic reqaire~rnent ma.triX R to be handled by the network. r,,; _ !) for every i.) Lot, us define the following notation concerning traffic requirements. For every site s;, denote the total traffic originated (respectively, destirredl at .s; by R~,~r(i) _ ~~ rt,,; (resp., R~~(i) _ ~~ r'~,;). Let R,SU",(i) = Rout(i) -1- R«(i.). For each of the subscripts sub, let R.sub = nl aX.~ { Rsub ( L ) Each site s~ is connected to the rest of the world via a communication switch, denoted r~~. Tlre switches are connected by a network of some arbitrary topology. For the sake of genera.iity, we assume that the links are unidirectional. Thus, each switch has a number of incoming links and a number of outgoing links. Formally, the topology of the network is rep-resented by an underlying directed graph G = (V, E), where the vertex set V =
{vr, . . . , u.~}
is the set of switches the network, and E C V x V is the collection of unidirectional links connecting these switches (for rotational convenience we may occasionally refer to the switch ry simply a.s i, and to the link (vt, v~) as (i, j ).). In addition. each switch vt always ha.s both an incoming and an outgoing link to its focal site s;: the site transmits (and receives) all its traffic to (and from) other sites through these t4vo links. Lot E' denote the set of these links.

SUBSTITUTE SHEET (RULE 2B) ~ given requirements matrix R is resolved by assigning to each pair of sites i, j a collection of routes from i to j, {p=.~, . . . , pi.~ ~, over which the traf~rc r~,.i will be split. That is, each path p~.~ will carry ft~.~ units of traffic from i t.o j, such that k ~r t>r The collection of routes for a.ll vertex pairs is denoted p.
Once the routes a.re determined, we know exactly how much trafFrc will be transmitted over each edge and through each switch of the network. Specifically, given a route collection y and a network element x E V U E U E' (which may be either an edge a or a switch v), let Q(x) denote the collection of routes ~;oin~ through x, Q{x) _ ~(c.J.l) ~ .r occurs on pi,j}.
(Note that the switch v may never occur on a path a.s an end-point; all routes start a.nd end at sites, and thus - formally speaking --- outside the network.) Define the l«ad induced by p on the network element x E V U E U E' (a.n edge or a. switch) as 9(~') _ ~ f~::i (i.,i.1)E42(i'l C'.onsider a switch v.t. denote the links connecting it to its site si by e~;~
(for the link from .s; t.o ut ) a.nd e~"~ (for the link from v; t.o .s~ ). Denote the remaining (network) adjacent ingoing links of ~~ by ein = (vt, u~t) for 1 < l < ~'. anti t,hcadjacent outgoing links by el"t = (v.l, wJ~) for ! < l < 1,~' {see Fig. 25), Observe that the traffic flows in r~~ anti its acl.ja.cent links must satisfy q(v2) _ ~ rl(F,i«) _ ~ 9{clot).
a<I<k 0<f<k' ll~Ioreover, q(e~ ) = Rout{i) and q(eout) = f~tn(i), and subsequently, q(ein) ~ ~n(l ) a.nd ~ 9(eiut) ~ R~ut(t) 1<1<k 1<t<k (these inequalities might be strict, since the switch v; may participate in transmitting traf~rc belonging to other endpoints as well ). C'onsequently, q{vi) ~ Rin(t ) '~ l~out(t) - Rautn(t)' Let us now turn to describe another major factor of the network design, namely, the capacity of switches and links. Each link a = (i, j) has a certain capacity c(e) associated with it (in reality, it is often the case t,ha.t the links are bidirectional and have symmetric '?8 SUBSTITUTE SHEET (RULE 26) capacity, namely, c(i,,j) = c(j,i). Likewise, it may often be assumed that the requirements are symmetric, namely, rt.,; = r~.;.), bounding the maximum amount of traffic that ca.n be transmitted on it from i t,o j. In addition to link capacities. each switch v of the network also ha.s a capacity c(v) associa.ted with it.
Clearly, in order for our link assignment to be feasible, each link or switch x must have at least q(a:) capacity. In view of bound (2), this means that a requirement matrix R. with Rsu,n > c cannot be satisfied at all, hence it suffices to consider matrices with f~.S-u,n < c.
(henceforth termed legal requirement matrices). Call a requirement matrix R
rraaxirnal if Rsum = ~> namely, at least one of the switches saturates it,s capacity. Note that every matrix satisfying Rsum < c can be normalized so that it becomes maximal. Hence in what follows we shall concentrate on the 1->Fha.vior of networks on ma.Yimal requirement matrices.
The standard model assumes that the capacities assigned to the edges connected to any particular switch sum up precisely to the capacity of that switch, namely, ) _ ~ ~~P11 = ~ ~(~l)~
O<l« 0<1<k~
~Ve Shall refer t0 a network obe vlng this conservatloll rule as a conservatLUf' rretrnork.
G.1 The channel expansion model The idea proposed in this paper is to expand the capacity of channels hf r/oarl t lat, of the switch. At first sight, this n~av seem wasteful, as the potential traffic through a wvit.ch cannot, exceed its capacity. \onet fmic~ss. it is argued that such expansion may lead to increased total throughput under many natural scenarios, since allowing the total capa.cit.v of the links adjacent to a. switch n t,o l>t~ ~t most the capacity of the switch means that it is only possible.
to fully utilize the switch iI t.lle route distribution is uniform over all the links. U t>ractice, a given traffic requirement rlia.trix may impose a non-uniform distribution of traffic over different links, and thus force the switch to utilize less than its full capacity. Increasing the capacity of the links would enable us to utilize the switch to its fullest capacity even when the traffic pattern is non-uniform.
Let us illustrate this idea via a. simple example. Consider the complete network over four vertices, vl to v4. Suppose that the capacity of each switch is c, and that it, is required to establish communication with total volume c from vl to vq. In the basic conservative network, the capacity of each of the links is only c/3, and therefore at most c/:3 of the traffic from vl may proceed on the direct link (vl, v4), and the rest (in two equal parts of volume c/3 as well) must follow pa.t,hs of length 2, via the other two vertices. Once this is done, the vertices vl and v2 have a.lrea.dv utilized a.ll of their capacity, while the vertices ~~.~ and ~~3 have already utilized c/3 of their capacity, so less is left'for other traffic. In contrast., if the links SUBSTITUTE SHEET (RULE 26) were allowed to have greater capacity, sa.v, c. then it would have been possible to send all traffic from r~, to z.>~ on the direct link between them. This would still exhaust the capacity at yr a.nd r~.,. but leave i~2 and r.~ unused, with all of their ca.pacitv intact.
To illustrate the profit potential of the channel expansion approach, we analyze the increase in throughput in a. tire following model. Given a network H. with its switch and link capacities, define the B-expanded network over H, denoted ~~(H), by uniformly expanding (naturally. nonuniform expansions should be considered as well, but, we iea.ve that for future study.) the ca.pa.city of each link a to B ~ c(e). We will try to evaluate the transmission capability of the 0-expanded network ~'B(H) w.r.t. the basic conservative network H, for B > 1 (for H = 1 the two networks coincide).
To evaluate the transmission level of a given network we will usP the following parameter.
For a network fl and a. requirement matrix R, define the R-tran.snai.s,sio~r quality of H on R
as m(H, h') = rnax{a > 0 ~ requirement matrix a ~ R can f» satisfied on H}, where n ~ R is the requirement matrix (a ~ ri,~), namely, multiplE~in~ the requirement rt.; for every pair i. j by a.
Obser~r~ t hat for a rnaxima.l requirement matrix R, 0 < cr( H. R) < i .
Intuitively, the better tlm network fl, the greater a(H, R) is. Hence we will bc~ irlt.erPatPd in the value of cr(H, R) for t ile worst possible R.. This leads to the following do finition.
For a network H, define tl-le tr-nrt.srrra.s.si.on. qucalit;~ of H as a-(H) = min {rx(H, R)}.
maximal x For a oonservatiwe network H, it is natural to compare Cllr ti'af15Tr115s1oi1 quality of the B-expanrlFOl artwork ~'~(H) with that of H, and examine the iml>rownlent in this duality due to the exparlsion. For the network H and the expansion factor H. we ~lE~fine the improvement ratio to hE~
a(~B(H)' R) ~ .
'Ys(H) = max maximal R cx(H, R) I.e., -~~~(FI) measures the ma.Yimum gain in transmission qualit.v (lrre to expanding the link capacit,v of the conservative network H by a factor of B. Clearly. this factor is always at least 1, and the higher it is, the more profitable it is to expand the capacity.
H Restricted comparative model Let us start. by a.na.lyzing the potential gains from the expansion of link capacities in a restricted alld simplified model. We will consider a conservative network based on a 0-regular n.-vertex undirected graph G (with each edge composed of two unidirectional links, SUBSTITUTE SHEET (RULE 26) ,.

one ire ea.ch direction). V'e will further assume that the switch capacities are uniform, namely, ea.cia of the vertices has capacity c. Similarly, eve will assume that all network links are of the same ca.pacitv. More precisely, given a fixed parameter 0 < r < 1. it is assumed that for overv switch v;, the links e~"r and e~ connecting it to its site s; are of capacity (1 -. r)c, and every network link (connecting switch v~ to switch ry;) is of capacity rc/0. Denote the resulting conservative network over the underlying graph G (with the switch capacities c-let,errnined by the parameter r) by ,L3(G, r ). Denote the B-expanded network over L3(G,T) by Fn(G, r ).
Z'he na.tr.rral extremal point for the expansion parameter B is at fJ = :,/ r . as the initial capacity of interswitch links in B(G, r) is rc/J, and it is pointless to expand the capacity of a link hevond c..
In this section we will focus on studying the properties of ~A{Ca, r) for the complete n-vertex network G' = G'n. Observe that for fl = ,,/r = ( a - 1 )/r, the network ~n_r (Cn, T) is capable of satisfying every legal requirement matrix. arid hence in particular every max-imal rna.trix, since for every i and j, the traffic r',., from i t.o ,j can be transmitted (exclu-sively) on the direct, link connecting them. C'onsequentlv c~-(~'(n_,~~T(C'n, r )) = l, and hence -,t,,_ y~r(C~, r) = 1/a(,G(Cn, r)). Hence to evaluate ;tr_,~~_(C~", r) we shall need to derive hounds on a(,(3(GTn, r )). iVlore generally, we will now derive some (upper and lower) bounds c~r~ u(~:~(C'", r)) for values of 1 < B < (n - 1)/r.
H.1 Upper bound Lemma H.1 Th.e transrraission quality of th.e B-E.rpcra.rlerl netreorv f'r~(C.'n. r ) i.s bor~nded above «.: ./~nlln«~.~.
1. For every r > 2/3.
d(1-r), 1 <B< 2 3(1-z) ' a(~B(~'n.,T)) ~.. 3(n~l) .
'. For every r < 2/3, BT/2 . 1 ~ ~ C 3z ' a(~9{Cn,T)) <
2 + rB ~ > 4 3 3(n-7 ) ' 3z ' Proof: To prove the Lemma, we have to show that there exists a maximal requirement matrix R. such that if the B-expanded network ~e(C"n, r) can satisfy the traffrc matrix a ~ R, then a is bounded above as in the lemma.

SUBSTITUTE SHEET (RULE 26) assume n is even, and consider the following requirement matrix RM based on a.
matching among the sites (2i - 1, 2i) for I < i < n/'>, with requirement c from 2i - 1 to Zi. I.e..
rr.2 = rs,a = .. . _ ?"n-r,n = ~ and r;_~ = 0 for all other pairs. This is a maximal matrix (in particular, for every odd vertex. R~,~r(2i - 1) = c, and for every even vertex, Ri.~(2i) = c).
We consider the traffic requirement matrix a ~ R for some constant 0 < a < 1.
Let us examine the way in which this tra.fFc requirement can be satisfied on the 0-expanded network Ee(C~, r) for some fixed 0 < r < 1. In particular, consider the tragic:
from 2i - 1 to 2i, for some 1 < i. < n/2. ~ first immediate constraint on this tragic is that it must be transmitted from the site s.2;_r to its switch o2~_r (and likewise, from the switch a>z;
to its site s2z), and therefore the capacity of e2r'~ r and ezi must exceed ac, i.e., B( 1- r )c > ac.
or ~r < 9(1 - r ). (;;) The volume of traffic that can he transmitted on the direct link from 2i - 1 to '~i is at, most its capacity, BTC/(n - 1 ). .-III t1e remaining tratlic must follow alternate routes, which must consist of at least two links a.nd hence a.t least one additional intermediate switch.
Let q~(i) denote the load (i.e.. the t.ota.l amount of traffic volume used) a.t all switches as a result of the traffic from 2i - 1 t,o '?i. Then qY,(t) > (:3CY - ~T/(n - I))C, as a volume of cY-r22-r.at = crc is asecl at each of the endpoints 2i - I and 2i. and in aclclitiou.
a traffic volume of at least ac - Urr/(~r - I ) goes through alternate routes of length two or more, a.nd hence must occupy at Ic:ast one more switch.
Denoting the total volume med ire switches for transmitting the matrix Rnl by q,- arrd noting that this value is bounded by the total switch capacities, we get that nc > qy~ - ~ qv(i) > ~ (3cr - BT/(n - I))c.
This gives us the following bound on cr:

a < - -1- ( ~ ) 3 3{n - 1) Next, let us derive a bound on cx based on link capacities. Consider the directed cut in the network separating the odd vertices from the even ones. The total capacity of the cut {in the direction from the odd to the even vertices) is ~z~2 nTi. On the other hand, the total SUBSTITUTE SHEET (RULE 26) t ,.

t.ra$'ic requirements on this cut (frorrr odd to even vertices) are l - ac.
Therefore, we must h ave acn . Brcn2 :a _ ~(n _ y , hence a < fJrn/2(n - 1 ). Fixing B and r and taking n to infinity we get the following bound on a:
HT
cr < -. (5) The bourrds expressed by inequalities (:3) and (~) coincide when r = 2/3. In case r < 2/3, the bound expressed by inequality (:3) is dominated by that of inequality (.~), Finally, in case r > 2/3, the bound expressed by inequality (3) dominates that of inequality (:i). Hence the bounds specified in the lemma follow.
The relationship between the expansion factor D and the transmission cyralitv measure cx(~B(Cn)) are expressed in t1e nraphs of Fig. 33. Here 1-r, r>2/3, .start =
r/2 , r < '?/3 , and H.2 Lower bound r>2/3, f~break r<2/3, Lemma H.2 The tran..,nu.s.ion qr~alit.z! of the fJ-expanded nettvork E'9(C',;.
r ~ i.~ borr.rrrled belo2v as f ollouvs.
1. For every r > '~/:3.
8(1 - r) , 1 < B < 3(lz ?~
~(~A(Cn, T~) 2 + (2T-1 )B B >
3 3n-5 ~ - 3(1-r) ' For every r < 2/3, Br/2 , 1 < a < 3T , ~(~e(Cn, r)) 2 + r9 ~ > 4 3 2(3n-5) ~ 3r ' SUBSTITUTE SHEET (RULE 26) Proof: Consider the d-expanded network ~B(Cn, r) over the complete graph C."n for some fixed r and 0. To prove the lemma, we need to show that for every maximal reduirement matrix R, ~'9(Cn, r) ca.n satisfy a trafFtc matrix a ~ R, where cr is hounded below a.s in the lemma. Let R be given. Observe that in order for a site i to be able to send out the traffic it is required to send, we must have aRo~t(i) < p(I - r)c and aR~~,(i) < 9(1 -r)c. As Rsu,n < c. it is clear that in order to satisfy these two requirements it suffices to ensure that CY<t9(1-r).
We select the routing as follows. F'or every pair (i, j ), the requirement a-r;,~ from i to j will k>e transmit,ted as follows. Let x and y be parameters to be fixed later.
First. a slice of volume xrt..; will be transmitted over the direct edge between them. In addition, for every switch k: c~ { i., j }, a traffic slice of volume yr~2 ~ will be transmitted over the length-2 path t~rom i to k~ to j .
Let us noGV identify the requirements that x, y and cr must satist;y in order for the specified routing t.o hP valid. First, for every i and j, the total traffic volume transmitted from i to j, which 1S ,l'7'i,~ -~ (n - 2) yr~.;, must exceed the requirement ar;_,;, he nce we get -1' (rt - '~):~I > c~. (7) text.. w-e need to ensure that the prescribed paths do not exceed the switch and Iink capacities available t.o tlue network. Let us first consider a w~itrln ~~, and calculate the traffic volume going through it. This traffic first includes traffic for whi<~h k is are endpoint, of volume aR,w-",(~~) < nc'. Iu addition, the total traf~rc volume going tfnrough ~- as an intermediate switch is ~~,,~~k r~r;,~. Letting Z = ~i.~~k r2,~, we note that 7 ~ ~ ri-.t ~(Rout(t) - r~i.k) _ ~ Rout(l) - ~ f~e.l; _ ~ Rnut(L) - f~in(.~).
~,~k .j~k ifk ilk ilk ilk By a similar argument we also have Z = ~.;~k Rtn(a) - R,~,~t(~~). Put together, we get that ~.sum(Z) - RsuTn(~) C c~ ~,Rsum(t) C ~(~t - I)Rsum C (n - I)C/2.
.. =~k ~ i#k "
Therefore the total traffic in the switch is bounded by yZ -f- ar = (y(rt -1)/2 -f- cr)c, and it is necessary to ensure that this volume is smaller than the s4vltCh capacity, which is c, namely, that y(n - 1)~2 -I- a < 1. (8) Finally, we need to ensure that the prescribed paths clo not. exceed the link capacities available t,o the network. Consider a link a = (i, j), a.nd calcuiat.e the traffic volume going through it. This traffic first includes a volume of ~r';,J of direct traffic from s= to s~. In SUBSTITUTE SHEET (RULE 2fi~
r ,.

addition, for every other switch k, the link a transmits traffic of volume ,yr~,~ along a route from >i: to ,j, a.nd traffic of volume yr~.k along a route from i to ~:. Thus the total volume of traffic over a is 4(c) - xri,~ + ~ ~ (Ti,k + Tk.J ) - :CT%,J '+ y(Rout(l) "_ ri.j) + y(Rin,(3 ) -Ti,J) - (~ - ~y)r=,~ '+ y(~o'~t(2) + Rin(J)) C (~~ - 2y)T~,,i + 2yc.
Hence to verify tltat this volume is smaller than the link capacity, we have to ensure that ('~ - 2y)Ti,.) + ~~'yC < HTC/(Tb - 1}.
Restricting ourselves to a choice of ~ and y satisf:ving '~y < .l (lp) allows us. noting that r.~,~ < c, to replace requirement (9) by the stronger one (z -'~,t~)c-~'~:Tlc < ~JTC~(TT - 1)' or z~ < BT/(rT - I ). (11) Thus any choice of ~, y, cx satisfying constraints (fi), ( r); (8), (10) and (11) will yield a.
valid routing satisfying the requirement a- ~ h'.
Let us fix x = 8T/(n - 1 ) and thus sat ist;v constraint ( 11 ), and get rid of the occurrence of .r in c:onstra.ints (7) and (10}. Rewritinn constraints ( r), (8) a.nd (t0) as lk - OT/~TI - 1 ) y ~ .
IT - ~~
'~(1 -cr) If - I I
VT
y C
?(7l - t ) we see that in order for a solution y to exist., we must have the following two inequalities:
cx - 9T/(n - 1 ) C 2( 1 - ck) (rT, - ?) - (n - 1) ' c~ - 9T/(ra - 1 ) ' 9T
(n - 2) - 2(n - 1) Rearranging, we get '?n - -1 -I- 8T ( 12) cx < 3n-5 BTn a < ~(,n - l.) (13) SUBSTITUTE SHEET (RULE 26) Noting that DT/2 < .,~gT"~~, we strengthen constraint (13) by requiring a to satisfy a < DT/2 . (14) We are left with a. set of three constraints, (6), {12) and (14), such that any choice of a satisfying all three is achievable (i.e.. the requirement matrix a ~ R
can be satisfied).
The breakpoint between constraints (6) and (14) is for T = 2/3. Let us first consider the case r > 2/3. In this case. constraint {6) dominates (14). Further, in the range of I < D < 312 T~ constraint (6) dominates also constraint (1?), hence the best that can be achieved is a = D(1 - r). In the range of D > 3t12 T~ constraint (12) is dominant, and it is possible to achieve a = 2 3n ~°T . Noting that in this range (of T >
2/3) we have 2 + D(2r - 1 ) ~ 2n - 4 + Br :3 :;rz - :~ - 3-n - 5 ' the first claim of the lemma follows.
Let us next consider the case r < '~~3. In this case, constraint (14) dominates (6).
Further, in the range of 1 < 0 < ~T constraint (14) dominates also constraint (1'?), hence the best that can be achieved is ct- = DT/2. In the range of D > 3T constraint (12) is domina.rnt, and again it is possible to achieve w = ~-''~n'' ~°T . Note that in this range (of T < 2~3) we have '? Dr 2n-4-~-8T
:3 2(:3n - ~~) 3n-5 ' and hence the second claim follows as well.
H.3 Extending the transmission capability by h;
Suppose we wish to expand the tra.nsrnission capability of the complete network by a large factor k. It seems from our discussion that the most efficient way to do so would be as follows.
Start by expanding only the edge capacities by a factor Of B6,-eak~ From that point and on, continue by expanding both edge and switch capacities uniformly (by a factor of k~DbTe,,k)~
Overall, the edges are expanded by a. factor of k, whereas the switches are expanded only by a factor of k/DbTeak-Computational relationships in capacity-extended channels in communication, specifi-ca.ily under uniform traffic requirements provided in accordance with a.
preferred embodi-ment of the present invention a.re now described. This analysis was derived by Dr. Raphael Ben-Ami from BARNET Communication Intelligence Ltd, ISRAEL, and Professor David Peleg from the Department of Applied Mlathematics and Computer Science, The Weizmann Institute of Science, Rehovot, 7fi100 ISRAEL. Professor David Peleg is not a.n inventor of the invention claimed herein.

SUBSTITUTE SHEET (RULE 26) I Analysis of Uniform Traffic Requirements We now analyze the potential gains from the expansion of link capacities in the same model studied before. but under the assumption that the requirements matrix is R~', characterized by rt,~ = 2ln'-ry This is a rrzaxirrzal matrix, as for every switch v; we have R~ut(i) = R;,~(i) _ (ra - 1) x .stn' r~, hence Rsum(i) = c. We will now derive some tight bounds on cx(~a(G,r)) for various values of B and various simple regular topologies G.
Let us remark Lhat as it turns out, in all of the cases examined. the general dependency of a(~'B(C~. r)) on 9 looks a.s in the graph of Fig. 34, or more formally, astart ' B , 1 C 9 C 96reak , Q'(~B(~T, r)) _ ~rraax ~ B ~ Bbreak , where a",a~ = Q'start ' break a,rld the values Of (kstarf, Amax and 9nreak df'pE'nd Or1 the SpeClf~1C
topology at hand (as wall a.s on r). In what follows we refer to this type of function as a plateau fartctiorr., and denote it by Plateau(astart, a",,ax).
(In most of our bounds, the description of the function is slightly complicated by the fact that a,scart is dependent on the value of r; in particular, it. assumes a different value according to whet. her r is smaller or greater than some thresiuold value rr,r.,ak.) L1 The Complete Network Lemma L1 Thr lrun~rri.i..ssio'n qt~alaty of the B-expanded network ~'A(C',;. r ~ rtnder tlr.e u'n.iforrn requi.rem.e'nt.~ rncttri:r fire is a(FA(C'n, r)) = Plateau(a,Start, amax) rvlreuf c~,,"rt = 2 min(r, 1 -r } and a-m",. = 1.
Proof: Since Rr' is uniform and and the underlying network is complete. it is easy to verify by symmetry arguments that the most efficient solution would be to transmit the traffic from i to j along a single path, namely, the direct edge connecting them. The requirement that the edge ca.pacitv suffices for the intended traffic translates for an inter-switch edge into the inequality Brc cxc n-I - 2(n-1)' or a < 297-. ( 15 ) For a site-stvitch edge we get the inequality B(1 - r)c > txc/2, or a < 2B(1 - r). (16) SUBSTITUTE SHEET (RULE 2fi) The choice of routes ensures that the switch capacity suffices for transmitting the entire requirement for a rnaxima.l matrix, and nothing more, nameiv.
a < 1. (I7) The bounds expressed by inequalities (15) and (1G) coincide when T = 1/2. In case T < 1/'?, the bound expressed by inequality (16) is dominated by that of inequality (15), and the opposite holds in case T > 1/2. Hence the bounds specified in the lemma follow.
I.2 Rings Let us next consider the simple ring topology R. For simplicity of presentation we assume that ra is odd. a.nd the switches are numbered consecutively by 0 through n -1.
Lemma L2 Th.e transmission qr~ality of the B-expanded rt-.site r'.etwoork ~'9(R, r) (for odd n) under ti'f ~crzifornz requirements matrix Rt' is a(~A(R.,r)) =
Plateau(CY,start,«~,Qy~); where amax -rZ + :J
and f 'Il r' $T
,n,+r , T ~ T brF.ak astart -2(1 - T ) , T break C T ~ 1 n ~- 1 Tbreak =
rt -~ n Proof: :~~ain. by symmetry considerations we can show that tlve best solution is obtained if one transmits the traffic from st to s~ along the shorter of t im t.wo paths connecting them on the rin~, for every i and j. ~Ve now have to estimate thc, loads on switches and links under this routing pattern.
Let us sum the total traf~rc load on the ring edges. <.'onsider first the traffic originated at Sate si. For every 1 < j < (n - 1)/2, there are two routes o~~ length j out of si (one clockwise and one counterclockwise). Each such route loads j edges with ac/2(n - 1 ) traf~rc. Hence the total traffic load generated by s2 is l~, rll2 ac (n -~ 1 )crc 2j .
~_1 2(n - 1) w a.nd the tota.i traffic load overall is n(n -I- 1)ac/$. As this load distributes evenly among the 2rz directed links, the load on each link of the ring is (ru. -1- 1)ac/16.
This must be bounded by the link capacity, hence we get Brc > (n -f- 1 )ac SUBSTITUTE SHEET (RULE 26) r i . . ~..

or a < . (lg}
( n ~- 1 ) A similar calculation should be performed for the switches. Again, we first consider the traffic originated at site s2. For every 1 < j < (ra - 1 )/2, there are two routes of length j out of s;. Each such route loads j -~- 1 sites (including the endpoints) with ac/2(n - 1) trafFrc.
Hence the total traffic load generated by .st is (n-3 )/2 ac (n -1- a)ac Z(~ + I) ' Z(n, - 1 ) 8 , j=1 and the total trafFrc load overall is n(n + 5)ac ~1s this load distributes evenly among the rc sites, the load on each site on the ring is (rr -~ 5)ac/b. This must be bounded by the site capacity. c, hence we get a < . (lg) (re + i) Finally, for a site-switch edge we get, a.s hefore. the inequality o < 2H( 1 - T ). {20) Of the three inequalities (18), (19) and ('?0), bound (19) does not depend on 0, and therefore limits the value of a-",a~. The value ol' cx,5c".~ depends on T. The bounds expressed by inequalities (18) and (20) coincide when T = (ra -~ 1 )/(r~, -f- ~). In case T < (n-~- 1 )/(rc -I-.~), bound (20) is dominated by bound (.l8), and the opposite holds in case T >
(rc+1)/(ra-I-p).
For each of these cases, the bounds speciF~ecl in the lemma now follow by a straightforward case a.nalvsis.
For the case of even n, the bounds we get a.re similar. The main difference in estimating the toad caused by site s; is that in addition to the routes considered for the odd case, there~s also a single route of length n/2 out of s~, to the farthest (diagonally opposing) site.
Lemma L3 The transmission. quality of the H-e:rpanded n-site network EB(R, T) (for even n) under the uniform requirements rrcatrix Rt' is cx(~'B(R,T)) =
Plateau(asraTi,a",,a~), where 8(n - 1}
may =
and for rl" ~- 41Z - 4 s ~-r T
nl , T < Tbreak , ascaTa =
2( I - T } , Tbreak C T ~ l, , n2 Tbreak =
rc 1 -I- 4 n '- ~l SUBSTITUTE SHEET (RULE 26) Example: Consider the 4-vertex ring in a. configuration of T = 1/2 a.nd switch capacity c = 1000. In this setting we have aseart = 3/4 and cx",,dx = 6/ 7 , hence 9bTeax = 8/ 7 . The traffic requirements are ri,~ = 1000/6 ~ 167 for every 1 < i, j < 4. For H = 1 (no link expansion) we get that 3/-I of this traffic, i.e., fi,~ = 125 for every i _<
i, j _< 4, ca.n be transmitted. At this point. the traffic saturates the inter-switch links, whose capacity is 250 units. (See Fig. 28(a).) Now suppose the links are expanded to the maximum possible ratio of 8 = 8/7, i.e., their capacity becomes 2000/7 ~ 086. It then becomes possible to transmit 6/7 of the traffic, i.e., ft,~ = 1000/7 :., 143 for every 1 < a, j < 4. This saturates both the inter-switch links and the switches. (At this point, each switch handle a flow of 3000/ i ~ 429 units from its site to the other sites, a similar How in the opposite direction, and an additional amount of 1000/ 7 .:; 143 units of flow bPt.ween other sites, as an intermediate switch alone the route).
Hence further expansions of the links without a.ny corresponding expansion of the switches will not increase the network t hroughput.
As an example for a.n odd-size network, consider the 5-vertex ring, again iru a configuration of T = 1/2 and switch capacity r = 1000. In this setting we have a,s~4,.t =
2/3 and a,na~. _ 4/5, hence Bb,.eak = 6/5. The traffic requirements a.re rt,~ = 1000/8 = 125 for every 1 <_ i, j < 5, For B = 1 we get that '2/:3 of this traffic, i.e., f~,~ = 250/3 ..: 83 for every 1 <_ i, j <_ .->. can be transmitted. r1t this point, the traffic saturates the inter-switch links, whose capacity is still 250 units.
Now suppose the links nre wpa.nded to the maximum possible ratio of H = 6/5.
i.e.. t,heir capacity becomes :300. It then 1>ecomes possible to transmit 4/5 of the traffic, i.e., ,f~,,.; = 100 for every 1 < i, j < :~. This s~tura.tes both the inter-switch links a.nd the switches. !,-fit, this point, each switch handle a flow of 400 units from its site to the other sites. a sirnila.r How in the opposite direction. a~icl on additional amount of 200 units of flow as an intermediate switch between its two neighboring sites). Again, further increases in throughput. would require increasing both the link a.rrd the switch capacities.
L3 Chordal Rings Next we consider the simple chordal ring topology CR. For simplicity of presentation, assume that n is divisible by 4, and the switches are numbered consecutively by 0 through n. - 1, where each pair of diametrically opposite switches is connected by a chord.
Lemma L4 Tlre tran.srni.s.sian quality of tFte B-expanded network ~B(CR,T) of sire n >_ 12 under the uniform. requirN-rnFnts m.atri~ Rc' is cx(EB(CR,T)) =
Plateau(aSraT~~cr~,ay). inhere _ 16(n - 1) n2~-12n-16 SUBSTITUTE SHEET (RULE 26) r ~ , and for 32T n-I
3n2 , T < Tbreak , astart = ' 2( 1 - T ) , Tbreak ~ T < 1 , 3n2 Tbreak = 3n2 + lfirt - 16 Proof: By symmetry considerations, the best solution is based on breaking traffic originated at s2 into two classes: traffic destined at a site within distance < C from st on the ring (either clockwise or counterclockwise), will be sent entirely over the ring. Traffic destined a.t farther sites will be sent first over the chord to vf;+~~2}n,oan, and continue on the ring from there (either clockwise or counterclockwise). see Fig. 35 for a schematic description of this routing with a = n/~I.
As done for the ring, let us sum the load on the ring edges created by tra.flic originated at site s;. For every 1 < j < P, there are two routes of length j out of s.~
(one clockwise and one counterclockwise), and each such route loads j edges with crc/2(n - 1 ) traffic. In addition, for every 1 < j < n/2 - a - l, there are two routes of length j -~ 1 out of s; via the chord. Hence the total tra.~c load generated by s; over ring edges is crc n~~ r j ac - ~(~-~ 1) + (rc -'?f - 2)(n - 2f) ac -I 2.l ' .~(n, - 1 ) + J-I Z ' 2(n - 1) ~ 2 8 ~ rr - 1 - (n2/2 - 2raf~ -E- Oft - n -f- ~C')4 n C 1 ( ).
The total traffic load Overall is n times larger, and as this load distributes evenly among the 2n directed riry links, the load on each link of the ring' is (nz/. -. ref'-E-=1Pl - r~ -~4f)s~n"'r} .
This must be hounded by the link capacity, BTC/3, hence we ~;et, 166T(n - 1) (21) cY <
3(n2 -1- 8P2 - 4n2 - 2n + t3f ) ~Ve next carry a similar calculation for the switches. Summing separately over direct routes on the ring and routes going through the chord, the total traffic load generated by s~
over ring sw itches is ac n~2 a ~ ac 2(J + 1) ' 2~n - 1) + 2 + ~ ~(J + ~?) ' ~(n - 1) j=I j~l ac _ (n2 - 4n~ -1- 8~2 -i- 6n - 8) . 8(n - 1 ) .
The total tra.fl7c load overall is n times larger, but it is distributed evenly among the n switches. The load on each switch must be bounded by its capa.citv, c, yielding the inequality (n2 - 4n~ -~ 8~2 + 6n - g) ., ~~ C
8(n - t) ' SUBSTtI'UTE SHEET (RULE 26) or 8(n _ 1) (22) a <
nz -.4n~' -f- 8e2 -1- 6n - 8 For a. site-switch edge we get, as before, the inequality a < 2B(1 - r). (23) Finally, we need to estimate the load on chord edges. This is done similar to the analysis for ringe edges, and yields the bound 287-(n - 1 ) a < 3(n - 2f _ 1) , (24) For small values of n (up to n = 11), the best choice of (' and hence the resulting values of a ca.n be determined from the bounds specified by inequalities (21), (22), (23) and (24) by direct, examination. For n > 12. simple analysis reveals t.ha.t bound (24) is always dominated by bound (21 ), and hence can be discarded. W'e a.re thus left with the bounds (21 ), ( 22) and (23). To maximize a, we need to minimize fr (e) = n2 -b 8e~ - 4n(' - '?rz + t3f and f2(e) = rte - 4n~ -I- 8P2 -~- 6rr - 12P - 8.
,~s ca.n be expected, both functions are minimized vPrv close to ~ = n/4, which therefore becomes a. natural choice for ~. Under this choice. our mounds ca.n be summarized as 32BT(n - () a <
3~2 ' 16(n - i) a <
ra Z -I- I 2 n - 1 f i a < 2B( 1 - r ).
The analysis continues from here on along the lines of that of the ring, yielding the bounds specified in the lemma.
Example: Consider the 8-vertex chordal ring in a configuration of T = 1/2 and switch capacity c = 1200. The traffic requirements are r;.~; = 600/7 ~ 86 for every 1 < i, j < 8.
As n < 11, we examine the possible values for ( (which are 0 < ~ < 4), and calculate the resulting bounds on a from inequalities (21), (22), (23) a.nd (24). It turns out that the best choice is ~ = 2. For this choice, the smallest bound on cr for B = 1 is aStaTt < 7/I2. This means that it is possible to transmit a.n amount of f~,.; = 50 units for every I < i, j < 8.
At this point, the traffic saturates the inter-switch links. whose capacity is 200 units. For example, supposing the vertices of the ring are y through v8, the link from v~
to v2 carries the 50 traffic units from sj, ss and s8 to s2, as well as from sr to s3 (see Fig 36).

SUBSTITUTE SHEET (RULE 26) In case the link capacities are expanded by a factor of B, the bounds we get on a from inequalities (21), (22), (23) and (24) for ( = Z are a < 7H/12, a < 7/9, a < B
and a < 7H/9.
Hence am,az = 7/9, and Bbreak = 4/3. Expanding the links to the maximum possible ratio of B = 4/'.3 brings their capacity to 800/3 ~ 2fi 7. It then becomes possible to transmit 7/9 of the traffic, i.e., f;,~ = 200/3 .~: 67 for every I < a, j < 8. This saturates both the inter-switch links and the switches. (At this point, each switch handle a flow of 1400/3 units from its site to the other sites, a similar flow in the opposite direction, and an additional amount of 800/3 units of flow between other sites, as art intermediate switch alone the route, summing up to 1200 flow units).
L4 ~:-Chordal Rings The next network we consider is the chordal ring with li > 2 chords, CR(li ).
For simplicity we assume that n is of the form ra = {2f ~- 1 )( li -I- 1 ) for integer Q > l, and the switches are numbered consecutively by 0 through ra - t. Each switch i is connected by a chord to the switches (i -I- jn/(li -f- 1)) mod n for j = 1. . . . , Ii .
Lemma L5 The transmission. qualitt~ o~ th.e H-expanded network E'B(CR(K),T) vender the uniform. requirements matrix R« is a(fA(CR(li ), r)) = Plateau(aStart,CYmax)~
2DlLere ~~(n - 1) amar = (h~ + 1 I(z -~- E:ols + 3)e + 21i and foT
:y r( n-t (IV+1 )( Ivi-?1!(~i-I ~ , T C Tbreak , a.stnrt - i ) . Tbreak C T C 1 , (!i + 1)(li + 2)L'(~-~ 1) Tbreak =
(li +1)(Ii +2)~(e+1)-I-2(n-1) Proof: By symmetry considerations similar to the case of the simple chordal ring it is clear that a near optimal solution is obtained by breaking traffic originated at s;
into li -E-1 classes.
The first class consists of traffic destined at a site within distance < a from sT on the ring (either clockwise or counterclockwise). Tltis traficte will be sent entirely over the ring. Traffic destined a.t farther sites cvill be sent first over one of the chords, and continue on the ring from there (either clockwise or counterclockwise). See Fig. 37 for a schematic description of this routing on the 3-chordal ring with f = n/8.
Let us sum the load on the ring edges created by traffic originated at site s;. For every 1 < j < 2, there are two routes of Length j out of s~ (one clockwise and one counterclockwise), and each such route loads j edges with cxc/2(n - 1) traffic. In addition, for every 1 < j < (~, SUBSTITUTE SHEET (RULE 26) there are 2Ii routes consisting of one chord plus j ring edges out of sz via the li chords.
Hence the total traffic load generated by s; over ring edges is ac ac(Ii -~ 1)~($ ~- 1) (li + 1)~'?j ~ -2(n - 1) 2(n - 1) ,7-1 Summing the total traffic load over all sources si and averaging over the 2n directed ring links, the load on each link of the ring is a't 4~n>;t~~~. This must be bounded by the link capacity, BTC~(Ii -f- 2), hence we get a < 48T(n - 1) (25) (li + 1)(Ii + 2}~(~ + 1) .
A similar calculation for the switches reveals that the load generated by the traffic originating at a site s; is V
P
li ~ 2(,j +'2) ~ ~( ac l) -~ '? . Z(~ ~ 1) --~- ~ 2(~ -1- 1) . ~(~YC 1 ) .1=~ j=1 ac((Ii + 1)fz + (5Ii -1- 3)Q + 2h) '?(rt - 1 ) (The first main summa.nd represents loads on routes through chords, counting separately the unique route to the diagonally opposite site; the second main summand represents loads on direct routes, not using a chord). Summing over all n sources and averaging on n. switches yields the inequa.lit,v 2(n 1) (26) ( li -~ 1 ) ~2 -~ ( 51i + 3 } a -+- 2Ii For a site-switch edge wY et. as before, the inequality a < 28(1 - r). (27) Finally, for a chord e<lgP the get 28T(n - 1) (28) (Is -f 2)(2~ -(- 1) .
This bound is dominated by (25) whenever Ii > 3 (or Ii = 2 and ~ > 2), and therefore can be ignored (say, for rc > ~)). The analysis continues from here on along the lines of that of the ring, yielding the hounds specified in the lemma. i Example: Consider the 21-vertex 2-chordal ring in a configuration of r = 1/2 a.nd switch capacity c = 5040. As h' = 2 and ~ = 3, we get Tbreak = 18/23 > T, and hence for B = 1 we get asta,.t = 5/18. The traffic requirements are rt,j = 5040/40 = 126 for every 1 < i, j < 20, of which it is possible to transmit an amount of fZ,~ = 35 units for every 1 <
i, j < 20. At this point, the traffic saturates the inter-switch Links, whose capacity is 630 units. For example, SUBSTITUTE SHEET (RULE 26) r.. , .

supposing the vertices of the ring a.re zy through v2~, the link from ~~i to r.a., participates in 18 routes, carrying the 35 traffic units for each (specifrcallv, it is involved in six direct routes, namely, p~_J for (i, j) E ~(1, 2), (1, 3), (l, ~), (21, 2), ('?l, 3), (20, 2) ~. six routes via the chords leading to r~r. na.mely, p~,~ for (i, j) E ~(8, 2), (8, 3), (8, 4), (15, 2), ( 15. 3), (15, 4)}, four routes via the chords leading to v~r, namely, pi,~ for (i, j ) E {(7, 2), (7, 3), ( 14, 2), (1=I, 3)}, and two routes via the chords leading to v2o, namely, pt,~ for (i, j) E ~(6,2), (1.'3.2).) The link capacities can be expanded by a maximal factor of f~hr~.~k = i2/35 >
2, leading to a",,al = I/7. Expanding the links by this ratio brings their capacity to fi30 ~ i2/35 = 1296.
It then becomes possible to transmit 4/7 of the traffic, i.e., ~flt,~ = 12(> ~
~/ l = 72 for every 1 < i, j < '~0. This saturates both the inter-switch links a.nd the switches, requiring any further expansion to include the switches as well.
Reference is now made to Fig. 38 which is a simplified functional block diagram of bandwidth allocation a.ppa.ratus constructed and operative in accordance with a preferred embodiment of the present invention. Reference is also made to F'ig. 30 which is a simplified flowchart illustration of a preferred mode of operation for the apparatus of Fig. 38. As shown, the ahpa.ra.tus of Fig. 38 includes a conventional routing svstern 500 such as PNNI
(Private ~i~twork-Vetwork Interface) Recommended ATM Forum Technical C,'ommittee. The routing svstern :i00 may either be a centralized system, as shown, or a distributed system distribrrt,ecl ow~r the nodes of the network. The routing system allocates traffic to a network 510. The rontinsystem 500 is monitored by a routing system monitor 7'20 which typically accesses t h<~ rout,ing table maintained by routing system 500. If' the routing system 500 is centralizf~cl. t he routing system monitor is also typically centralized and conversely, if the routing y~t~rn is distributed, the routing system monitor is also tv~picallv distributed.
Tlre routing svst.em monitor 520 continually or periodically sPa.rches the routing table for con~est,PCl licks or. more generally, for links which have been utilized beyond a. predetermined threshold of ut.iliza.tion. Information regarding congested links or. more generally, regarding links which have been utilized beyond the threshold, is provided to a link expander 530. Link expander .x:30 may either be centralized, as shown, or may be distributed over the nodes of the network. The link expander may be centralized both if the routing system monitor is centralized a.nd if the routing system monitor is distributed. Similarly, the link expander may be distributed both if the routing system monitor is centralized and if the routing system monitor is distributed. Link expander 530 is operative to expand, if possible, the congested or beyond-threshold utilized links and to provide updates regarding the expanded links to the routing system 500.
It is appreciated that various features of the invention which are, for clarity, described in the contexts of separate embodiments may also be provided in combination in a single embodiment. (:onversely, various features of the invention which are, for brevity, described SUBSTITUTE SHEET (RULE 26) in the context of a. single embodiment ma.v also be provided separately or in any suitable subcombination.
It will be appreciated by persons skilled in the a.rt that the present invention is not limited to what has been particularly shown and described hereir~above. Rather, the scope of the present invention is defined only by the claims that. follow:

SUBSTITUTE SHEET (RULE 26) ....... ........ .

Claims (13)

1. A method for increasing the total capacity of a network, the network including a first plurality of communication edges interconnecting a second plurality of communication nodes, the first plurality of communication edges and the second plurality of communication nodes having corresponding first and second pluralities of capacity values respectively, said first and second pluralities of capacity values determining the total capacity of the network, the method comprising:
expanding the capacity value of at least an individual communication edge from among said first plurality of communication edges, the individual edge connecting first and second communication nodes from among said second plurality of communication nodes, without expanding the capacity value of said first communication node.

2. A method according to claim 1 and also comprising:
performing said expanding step until the total capacity of the network reaches a desired level; and expanding the capacity values of at least one of the second plurality of communication edges such that all of the second plurality of communication edges have the same capa.cit,v.

3. A method for expanding the total capacity of a network, the network including a first plurality of communication edges interconnecting a second plurality of communication nodes, the first plurality of communication edges and the second plurality of communication nodes having corresponding first and second pluralities of capacity values respectively said first and second pluralities of capacity values determining the total capacity of the network the method comprising:
for each individual node from among the second plurality of communication nodes:
determining the amount of traffic entering the network at the individual node:
and for each edge connected to the individual node, if the capacity of the edge is less than said amount of traffic, expanding the capacity of the edge to said amount of traffic.

4. A method for constructing a network, the method comprising:
installing a first plurality of communication edges interconnecting a second plurality of communication nodes; and determining first and second pluralities of capacity values for the first plurality of communication edges and the second plurality of communication nodes respectively such that, for at least one individual node the sum of capacity values of the edges connected to that node exceeds the capacity value of that node.

5. A network comprising:
a first plurality of communication edges having a first plurality of capacity values respectively; and a second plurality of communication nodes having a second plurality of capacity values respectively, and wherein said first plurality of communication edges interconnects said second plurality of communication nodes such that, for at least one individual node, the sum of capacity values of the edges connected to that node exceeds the capacity value of that node.

6. A method for allocating traffic to a network, the method comprising:
providing a network including at least one blocking switches;
receiving a traffic requirement: and allocating traffic to the network such that the traffic requirement is satisfied and such that each of the at least one blocking switches is non-blocking at the service level.

7. A method according to claim 6 wherein said step of allocating traffic comprises:
selecting a candidate route for an individual traffic demand;
if the candidate route includes an occupied segment which include at least one currently inactive link, searching for a switch which would be blocking at the service level if the inactive link were activated and which has an unused active link which, if activated would cause the switch not he blocking at the service level if the currently inactive link were activated: and if the searching step finds such a switch, activating the currently inactive link and inactivating the unused active link.

8. A method according to claim 6 wherein said network comprises an ATM
network.

9. A method according to claim 6 wherein said network comprises a TDM network.

10. Apparatus for allocating traffic to a network, the apparatus comprising:
a traffic requirement input device operative to receive a traffic requirement for a network including at least one blocking switches; and a traffic allocator operative to allocate traffic to the network such that the traffic requirement is satisfied and such that each of the at least one blocking switches is non-blocking at the service level.

11. A method according to claim 6 wherein said network comprises a circuit switched network.

12. Network expansion apparatus for use in conjunction with a routing system operative to allocate traffic to routes within a communication network including a multiplicity of nodes, each route including at least one link, the apparatus comprising:
a routing system monitor operative to monitor operation of a routing system in order to detect instances of high-level utilization of individual links; and a link expanding system operative to perform expansions of individual links, if expandable, at which high-level utilization has been detected by the routing system monitor and to providL, a corresponding update regarding each link expansion to the routing system.

13. Apparatus for allocating bandwidth within a communication network, the apparatus comprising:
a routing system operative to allocate traffic to routes within the communication network, each route including at least one link;
a local link expander operative to expand at least one link within the communication network in response to high-level utilization of the link by the routing system.