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890 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 16, NO. 6, AUGUST 1998

A Route Optimization Algorithm and Its Applicationto Mobile Location Management in ATM Networks

Gopal Dommety,Student Member, IEEE, Malathi Veeraraghavan,Senior Member, IEEE,and Mukesh Singhal,Associate Member, IEEE

Abstract—In this paper, we propose an algorithm for opti-mizing the route of a connectionthat becomes suboptimal dueto operations such as handoffs and location-based reroutes, formobile ATM (asynchronous transfer mode) networks based onthe PNNI (private network-to-network interface) standard. Thisalgorithm uses hierarchical route information of the connectionand summarized topology and loading information of the networkto determine a “crossover node” such that adjusting the con-nection from that crossover node results in an optimally routedconnection. We then apply this algorithm to the mobile locationmanagement problem. Location management schemes have beenproposed in which an incoming call to a mobile is first routedto its home switch (based on summarized reachability data) andthen rerouted to the mobile’s current location. If we considersuch rerouting a “first phase” of mobile connection setup, a“second phase” is required to optimize the paths of such reroutedconnections. Such an approach is considered atwo-phase mobilelocation/connection setup scheme. Alternatively, an incoming callto a mobile can be first routed to its home switch based onsummarized reachability data, and then “cranked back” to anoptimal crossover node before rerouting the connection to themobile’s current location. Such a scheme is aone-phase mobilelocation/connection setup schemesince it directly results in anoptimal path. A comparative performance analysis of the one-and two-phase connection setup schemes is presented. Measuresof comparison are call setup delayand the amount of networkresourcesallocated to a connection. The maximum call setupdelay (worst case call setup delay) is lower in the two-phasescheme, but the average call setup delay is lower in the one-phasescheme. The amount of resources required for a connection in thetwo-phase scheme (prior to route optimization) is significantlygreater than that in the one-phase scheme.

Index Terms—Mobile ATM networks, mobility management,route optimization.

I. INTRODUCTION

I N mobile networks, handoff procedures and location man-agement procedures are needed to support user mobility.

Handoff procedures are needed to reroute connections onwhich the mobile user is communicating while moving.Lo-cation managementconsists of tracking mobiles and locatingthem for incoming call deliveries. In both of these setsof procedures, paths taken by connections could become

Manuscript received July 15, 1997; revised February 15, 1998.G. Dommety and M. Singhal are with the Department of Computer and

Information Science, The Ohio State University, Columbus, OH 43210 USA.M. Veeraraghavan is with Bell Laboratories, Lucent Technologies, Holmdel,

NJ 07733 USA.Publisher Item Identifier S 0733-8716(98)04802-1.

“suboptimal.”1 For example, most handoff schemes proposeperforming a local connection reroute rather than an end-to-end connection reroute to keep handoff latencies low. Suchreroute operations could result in making the connectionpath suboptimal. Similarly, location management schemes thatpropose setting up the connection to the home location ofa mobile and then rerouting the connection to the mobile’scurrent location based on location data provided by the homenode could result in suboptimal connection paths. In otherwords, suboptimality that is introduced during connectionsetup is primarily due to lack of exact information aboutthe location of the mobile at the call originating switch, andsub-optimality occurs after connection setup because of usermovements by a communicating mobile. It is important tooptimize routes of connections since suboptimal paths implyan inefficient usage of network resources.

This paper proposes an algorithm for optimizing the routeof a connection, and applies this algorithm to the locationmanagement problem. Application of this route optimizationalgorithm to handoff management is presented in [1]. Thisroute optimization algorithm is proposed for ATM networksbased on the PNNI (private network-to-network interface)standard [2]. Based on this algorithm,we propose two solutionsfor the mobile location/connection setup problem. In the firstsolution, the route optimization procedure is integrated inthe mobile location/connection setup procedure (one-phasemethod). In this method, a connection to a mobile is setup by first routing the connection to the mobile’s homelocation, and then performing an on-the-fly route optimizationby altering the route of the connection after determining thelocation of the mobile from its home node. In the secondsolution, the route optimization procedure is executed after themobile location/connection setup procedure is completed (two-phase method, in which the first phase consist of connectionsetup to the mobile and the second phase consists of routeoptimization). In this method, the connection setup procedureis continued from the home node to the current location ofthe mobile, and the route optimization procedure is appliedsubsequently. A comparative performance analysis of theone- and two-phase methods for location management isperformed.

Since the route optimization algorithm is proposed formobile ATM networks based on the PNNI standard, we beginby providing background information on the PNNI standard,

1The path of a connection is classified as being “suboptimal” if it is notthe best path between the two endpoints of the connection.

0733–8716/98$10.00 1998 IEEE

DOMMETY et al.: ROUTE OPTIMIZATION ALGORITHM 891

Fig. 1. PNNI-based hierarchical ATM network.

and summarize prior work on location management and routeoptimization in Section II. In Section III, we state the “base”route optimization problem, and provide a solution to thisproblem in Section IV. Section V describes how this solutioncan be integrated with the location management proceduresin one- and two-phase schemes. Finally, Section VI presentsresults of a comparative performance analysis of one- andtwo-phase schemes for location management, and Section VIIconcludes the paper.

II. BACKGROUND

In this section, we first present a brief overview of the PNNIstandards for ATM networks, and then summarize prior workon location management procedures that cause suboptimalroutes and prior work on route optimization.

A. Overview of PNNI Standards

PNNI-based ATM networks [2] are arranged in hierarchicalpeer groups as shown in Fig. 1. The lowest level ( )consists of ATM switches connected in arbitrary topologies.Each peer group has an electedpeer group leader(PGL).Nodes within a peer group exchange topology, loading, andreachability information using thePNNI routing protocol. ThePGL of each peer group represents all nodes within its peergroup at the higher level peer group, and sends summarizedtopology/loading/reachability information about its lower levelpeer group to its peers in the higher level peer group. Eachhigher level peer node broadcasts this summarized informationto all of its nodes in the lower level peer group. Usingthis technique, each node has topology/loading/reachabilitydata about its own peer group and all of its ancestor peergroups. For example, in Fig. 1, node A.1.1 has the topologyinformation of the entire peer group A.1, as well as thetopologies of peer group A and the top level ( ) peergroup.

The PNNI signaling protocol standarddefines ATM con-nection setup and release procedures. In order to set up aconnection, the first switch receiving the connection setuprequest determines the hierarchical source route for that con-nection. The computed hierarchical source routes are carried asDTL (designated transit lists) parameters in the PNNI signalingSETUP messages [2]. A DTL is list of node identifiers, wherea node at the lowest level is an ATM switch, while at higherlevels, a node is a logical group node that represents a peergroup. A stack of DTL’s is used to specify the complete pathof a connection from the current node to the destination with

one DTL for each level. However, the exact list of nodes isnot known due to the hierarchical nature of source routes.The exact path within each peer group is computed at theingress border nodeof the peer group, which then pushes aDTL specifying the path for that peer group on to the stackof DTL’s. While computing the path through a peer group,the ingress border node of a peer group uses the next entry inthe next DTL (the one corresponding to the next higher levelpeer group) as the target for exiting this peer group. In casethere is only one DTL remaining (i.e., the next DTL does notexist), the destination address is used to determine the route.The egress border nodeof a peer group pops DTL’s fromthe stack that are exhausted. A call being set up accordingto a specified stack of DTL’s may be blocked at a nodedue to a lack of sufficient resources or connectivity. In suchsituations, the call is cranked back (released) to the bordernode that created the unusable DTL, and an alternate routeis attempted. The “optimality” of connection paths in PNNI-based networks should be regarded within the context of thishierarchical organization of switches. In other words, becauseof the hierarchical organization, the “shortest path” computedby PNNI may not be the true shortest path. This penalty ispaid in return for network scalability.

As an example, a setup request from an endpoint connectedto switch A.1.4 to an endpoint connected to switch B.2.2(see Fig. 1) results in an initial path computation of the stackof DTL’s [ A.1.4, A.1.3 , A.1, A.2 , A, B ], where eachDTL is specified within . When the SETUP reaches theegress border node A.1.3, it pops the DTLA.1.4, A.1.3from the stack of DTL’s since the connection is completelyestablished through the nodes specified in this DTL. NodeA.2.1, the border node of peer group A.2, computes the paththrough peer group A.2 to reach peer group B (the next entryin the next DTL) as consisting of only node A.2.1. Since itis both the ingress and egress border node of peer group, iteffectively “pushes on and pops off” a DTLA.2.1 from thestack to DTL’s. It also pops off the DTLA.1, A.2 sincethis DTL is also exhausted. The SETUP message generated tonode B.1.5 carries only one DTL in its stack of DTL’s, i.e.,[ A, B ]. At the next node, B.1.5 (the ingress border nodeof peer group B), the path through peer group B is computedto reach the endpoint connected to B.2.2. The new stack ofDTL’s is [ B.1.5, B.1.4 , B.1, B.2 , A, B ], with eachDTL corresponding to a level as viewed by node B.1.5. AtB.1.4, the first DTL is popped out of the stack. At node B.2.3,a new DTL is computed B.2.3, B.2.2 and pushed on tothe stack of DTL’s. Thus, the SETUP from B.2.3 to B.2.2carries the stack of DTL’s [B.2.3, B.2.2 , B.1, B.2 A,B ]. When the SETUP reaches B.2.2, since the egress switchfor the end-to-end connection is reached, all three DTL’s arepopped out.

B. Prior Work on Location Management

In this section, we describe location management schemesproposed to support mobile endpoints in PNNI-based ATMnetworks, and demonstrate how they could result in connec-tions with suboptimal routes.


Location management consists of tracking mobiles andlocating them in order to deliver incoming calls. Mobiletracking procedures update the home node of a mobile withinformation about the location of the mobile. Mobile locationprocedures use the information acquired during the mobiletracking procedures to deliver incoming calls to mobiles. Thereare two approaches to locating a mobile. In thefirst approach,an explicit location query is issued to the mobile’s homeswitch by the calling party’s switch (or some switch en routethat is “mobility enhanced”). The response indicates the exactlocation of the mobile, which allows for a direct connectionto be set up on the optimal path. Several variations of thisapproach have been proposed [3]–[7]. While this approachhas the advantage of resulting in optimal connection paths(which implies that a route optimization procedure is notrequired subsequently), it has certain disadvantages. The maindisadvantage with this approach is that the address space needsto be separated into two spaces, one for mobiles and the otherfor fixed endpoints, to allow the calling party’s switch (orthe en-route mobility-enhanced switch) to readily recognizewhen it must generate a location query before setting up aconnection. In thesecond approach, a call to a mobile isrouted in the same manner as a call to a fixed end-point. Sincesummarized reachability data typically indicate reachability formobiles as being via their home switches, calls to mobilesare first routed to their home switches. Given that the homeswitch of a mobile tracks its current location, the call is thenrerouted to the mobile’s current location. Several variations ofthis approach been proposed [7]–[9].

In [7], we proposedforwarding the call from the homeswitch to the current location.2 Acharya et al. [8] proposeda complete releaseof the connection from the called mobile’shome switch to the calling party’s switch, followed by a setupfrom the calling party’s switch to the current location of themobile. Ayyagari et al. [9] proposed using thecrankbackfeature of PNNI signaling, which allows for the call setupprocedure to be cranked back, and then rerouted. In [9], theauthors note that, typically, crankback will be executed at alocal level, which means that the overall end-to-end path takenby the connection could be “suboptimal.” The crankback pointis dynamically determined in [9], while it is statically assignedto be the home switch in the call forwarding scheme [7] andthe calling party’s switch in the complete release scheme [8].

These three schemes can be classified intoone-phaseor two-phaseschemes as shown in Fig. 2. In one-phase schemes, suchas the complete release scheme of [8], an optimally routedconnection is constructed during the call setup procedure,thereby eliminating the need for route optimization. In two-phase schemes, such as [7] and [9], the call is delivered tothe mobile, possibly on a suboptimal route (first phase), and aroute optimization (second phase) is performed subsequentlyto achieve an optimal route.

2To avoid huge triangular routes, we proposed using the scope feature ofPNNI routing to spread limited reachability updates creating a “neighborhood”around the mobile where all the switches know the mobile’s exact location.For example, if a call originates in San Francisco to a mobile whose home isin New York, but happens to be visiting in Los Angeles, if the “neighborhood”is defined to include all of the switches in the state of California, this call willbe routed directly from San Francisco to Los Angeles.

Fig. 2. Spectrum of mobile connection setup schemes.

The complete release method incurs a high connectionsetup delay,while the call forwarding scheme (in which thecrankback node is statically assigned to be the home node) usesthe greatest amount ofnetwork resources(albeit for a shortperiod of time until the route optimization phase is complete).The crankback case, in which the node to which the connectionis “cranked back” is determined dynamically, is between thesetwo extremes as shown in Fig. 2.

In this paper, we propose a solution to the route optimizationproblem for the second phase of the two phase methods. Wealso demonstrate that the principles of finding the optimal routecan be applied to realize aone-phase crankback connectionsetup scheme. In other words, an optimal route can be achievedusing the crankback approach in one phase by cranking backto the “right” node. This approach is described in Section V-A.

C. Prior Work on Route Optimization

A route optimization procedure has been proposed for IP(Internet protocol) networks to work in conjunction withmobile IP [10], [11]. Mobile IP is an extension to the In-ternet protocol (IP), which enables hosts to change theirpoint of attachment to the Internet without changing their IPaddresses. In this protocol, a packet destined to a mobile hostis routed to the home network of the mobile as identifiedby its permanent IP address. The home network tracks thecurrent location of the mobile, and tunnels the packet tothe current network of the mobile. As an improvement tothis “triangular” routing, route optimization extensions havebeen proposed [12]. These extensions provide a means forcommunicating nodes to maintain a binding between themobile and its current location, and use this binding to tunneldatagrams directly to the mobile. Extensions are also providedto allow datagrams in flight when a mobile node moves, anddatagrams sent based on an outdated binding information, tobe forwarded directly to the mobile. The primary differencebetween the route optimization extensions proposed in [12]and the route optimization procedure being proposed in thispaper is that the former extensions have been proposed forthe connectionless Internet protocol, while the latter is beingproposed for connection-oriented networks (PNNI-based ATMnetworks). In connection-oriented networks, in order to reroutea connection, a new connection segment needs to be setup between a “crossover” node and one of the ends of theconnection, and the user data need to be switched fromthe old path to the new path without loss of ATM cellsequence.


Fig. 3. Rerouting of connectionf–o to form a connectionf–t (base rerout-ing problem).

(a) (b)

Fig. 4. Path after the connection is established in the forwarding scheme:(a) Case A and (b) Case B.

III. PROBLEM STATEMENT

In this section, we state the route optimization problem (alsoreferred to as the base rerouting problem), and demonstratehow the route optimization problems created in the threelocation management schemes can be mapped to the basererouting problem. The solution to this problem is presentedin Section IV. The base rerouting problem is stated below.

Consider a connection between two endpointsand(where is used to denote the “far end” andis used to denotethe “old point”). The problem is to reroute the connection–to create a connection from nodeto node (target node).This problem is referred to as base rerouting problem or thebase route optimization problem, and is illustrated in Fig. 3.Next, we demonstrate how the route optimization problemscreated in three location management schemes described inSection II-B can be mapped to this base problem.

The suboptimality resulting from the call forwarding lo-cation management scheme shown in Fig. 2 is illustrated inFig. 4. The suboptimal path, from(calling party’s switch) to

(home switch) to (visiting location of the mobile), needsto be rerouted to form an optimal path fromto by eitherrerouting the – segment toward the target node(Case Ain Fig. 4), or by rerouting the – segment toward the targetnode (Case B in Fig. 4). In either case, the problem reducesto that illustrated in Fig. 3, where a connection from node(far end) to node (old node) needs to be rerouted to createa connection from node to node (target node).

In the two-phase crankback scheme shown in Fig. 2, theresulting connection is similar to that shown in Fig. 4, exceptthat the connection is routed through some local nodeinsteadof the home node, where the local noderepresents the pointup to which the call was cranked back during call setup (firstphase). This problem again reduces to the problem of Fig. 3after identifying whether the segment– or – needs to bererouted to the corresponding target node (or , respectively).

Finally, as observed in Section II-B, the crankback locationmanagement scheme can be converted from a two-phase

TABLE IMAPPING TO THE BASE REROUTING PROBLEM (FIG. 3)

scheme to a one-phase scheme if the call is cranked back to anoptimal crossover node. Such a scheme can be viewed as onein which route optimization is performed during call setup.In this case, the same problem illustrated in Fig. 3 needs tobe solved, wherein node corresponds to the calling party’sswitch , node corresponds to the home switch, and nodecorresponds to the visiting location of the mobile. The optimalcrossover node is the switch to which the call is cranked backduring call setup to the mobile.

Table I summarizes how the rerouting problem created inthe three location management schemes can be mapped to thebase rerouting problem shown in Fig. 3. The definition of the“closeness” of two nodes needed to select between Case Aand Case B is provided in Section IV.

Next, we address the issue of selecting the node thatinitiates the route optimization procedure. To determine thecrossover node (see Fig. 3), the network needs to computethe shortest path between nodesand , and then determinethe overlap between the new path– and the old path – .In the one-phase crankback scheme, since it is desirable toreroute the connection without having to completely back trackuntil node , it becomes necessary for nodeto initiate theroute optimization procedure. In the rerouting required for thesuboptimal paths caused by the two-phase schemes, nodes,, or could initiate the route optimization procedures. As

shown in Table I, the assignment of nodes (, , or , , )in the two-phase schemes to nodes, , and is such thatand are close while is the distant node (hence, the term“far end”). This implies that selecting either nodesor asthe initiating node will lead to smaller processing delays. Ifwe select node to initiate the crossover node determinationoperation, the solution will be equally applicable to all threelocation management schemes. Hence, we restate the basererouting problem illustrated in Fig. 3 as one in which theold connection – needs to be rerouted to the new targetwith the rerouting procedure being initiated by node. Theprocedure for initiating the route optimization at the targetnode is described in [1].

IV. ROUTE OPTIMIZATION ALGORITHM

In this section, we propose a solution to the base reroutingproblem. In Section V, we apply this algorithm, and presenttwo solutions to the location management problem.


There are three steps involved in solving the base reroutingproblem: 1) determining a crossover node, 2) establishing anew segment to , and 3) releasing the old segment fromto. Given that standard ATM signaling procedures can be used

for the latter two steps, only the crossover node determinationstep needs a solution. Thus, we only present a solution tothe problem of determining a crossover nodefor the basererouting problem illustrated in Fig. 3. Ideally, the crossovernode should be such that the path– – is the shortest pathbetween and , while at the same time, there should be amaximal overlap in the paths of the old connection– andthe new connection– . We refer to such a crossover node asthe minimal crossover nodefor the two paths – and – .

While finding the minimal crossover node has both theadvantages of minimizing the resources required by the newconnection and minimizing the new segment setup/old seg-ment release overhead, there are certain constraints in thePNNI standard (in its current form) that do not allow forthe determination of this node. In the PNNI standard, thereis currently:

1) no requirement mandating that all nodes retain thehierarchical path of a connection after it is established,and

2) a restriction that only nodes that created a DTL (desig-nated transit list) can change that DTL.

The minimal crossover node determined under these con-straints is defined as theoptimal crossover nodesince it is anode such that – – is an optimal path, and as much overlapas is possible between the old and new paths is achieved withinthe constraints of the PNNI standard.

Thus, we have defined two types of crossover nodes, theoptimal crossover node and the minimal crossover node. Thereare obvious advantages in selecting the minimal crossovernode, as will be evident in the analysis of Section VI, butthe modifications required to the PNNI standard to supportthis procedure need to be defined. We present our solutionfor determining the optimal crossover node in Section IV-A.In Section IV-B, we present a solution for determining theminimal crossover node under the assumption that it is possibleto make minor modifications to the PNNI standard to allow forthe relaxation of these constraints. The relationship betweenthe optimal and minimal crossover node determination proce-dures is illustrated in Fig. 5. It shows that if either hierarchicalpath information is not available or only the nodes thatcreated the DTL can change the DTL, the procedure terminatesafter determining the optimal crossover node. Otherwise, theprocedure to determine the minimal crossover node is alsoexecuted. Fig. 5 also shows the details of the two procedures.

A. Optimal Crossover Node Determination

In this section, the procedure to determine the optimalcrossover node is described. Two aspects of the PNNI-basednetworks that are fundamental to this procedure are: 1) everynode only has summarized information regarding the topologyof the network (nodes outside a peer groupdo not haveinformation regarding the internal structure of peer group

) and 2) connections are routed using hierarchical source

routing. The basis of this procedure is that, if a connection isrouted using source routing and the nodes outside a peer groupdo not know the internal details of the peer group, then theconnection to any node within the peer group will follow thesame route until the first node (ingress border node) of thatpeer group. The procedure to determine an optimal crossovernode is described next. The notation used in this descriptionis defined below.

Definition: The ancestors-are-siblings peer group,denotedby , of two nodes and is the lowest peer group in thehierarchy at which ancestors of both nodes belong to the samepeer group. For example, in Fig. 1, ancestors-are-siblings peergroup of nodes A.1.1 and A.2.1 is A.

Definition: The ancestors-are-siblings levelof two nodesand , denoted by , is the level3 at which the ancestors ofthe two nodes and belong to the same peer group, i.e., thelevel of their ancestors-are-siblings peer group. For example,in Fig. 1, the ancestors-are-siblings level of A.1.1 and A.2.1is 2 since the level of peer group A is 2.

The location of the optimal crossover node depends on theexact relation between the ancestors-are-siblings levels of thenodes , , and . In the two-phase location managementschemes listed in Table I, only the Case I scenario of Fig. 6will occur since is always chosen to be the “far-end” node.However, in the one-phase crankback scheme, any of the threescenarios shown in Fig. 6 may occur based on the positionsof , , and .

If (Case I of Fig. 6), the scenario is one in whichthe target node () is closer4 to the old node () than the farend ( ). In this case, the optimal crossover node is the ingressborder node of theancestors-are-siblings peer groupof theold and the target nodes ( ) through which the connectionsetup procedure for the– connection entered peer group

. Since nodes contain only the summarized topology andreachability information, nodes outside a peer group cannotdistinguish between exact locations of the different nodesreachable through that peer group. Therefore, a connectionfrom the far end to either the target or the old node willfollow the same route until it reaches the ingress node () ofthe ancestors-are-siblings peer groupof the old and the targetnodes ( ). Once the connection setup arrives at the ingressnode , it computes the source route to the exact location.Therefore, at , the connection to the target node () wouldhave a different source route than a connection to the oldnode ( ). Hence, an optimal path can be obtain by adjustingthe existing connection from the crossover switch.

Example: Consider the scenario in which there is an exist-ing connection between A.1.1 (far end) and B.3.1 (old node),and a new connection between A.1.1 and B.2.1 (target node)is desired (see Fig. 7). In this case, , , and are1, 2, and B, respectively. Since , the crossovernode is the ingress border node of peer group B, which is

3The numbering of levels in the hierarchy is such that lower level peergroups have higher level values assigned to them, i.e., the level numbersincrease from top to bottom in the hierarchy.

4Closeness is defined with respect to the node relationships defined by thepeer groups. Note that closeness according to this criterion is not necessarilyclose with respect to the number of hops or geographical distance.


Fig. 5. Determination of optimal and minimal crossover nodes.

(a) (b) (c)

Fig. 6. Relative positions of nodesf , o, andn: (a) Case I, (b) Case IIa,and (c) Case IIb.

B.1.1. Therefore, the optimal path between A.1.1 and B.2.1 isachieved by setting up a new segment from B.1.1 to B.2.1,as shown in Fig. 7.

Fig. 7. Rerouting connections.

If (Case IIa of Fig. 6), the scenario is one inwhich the old node () is closer to the far end () than to thetarget node (). In this situation, there may not be any segment


common between the existing connection and the new desiredconnection. Therefore, the optimal crossover node is the farend ( ). The new path is optimal since the entire path betweenthe far end and the target node is being set up.

If (Case IIb of Fig. 6), the scenario is one inwhich the target node is closer ( ) to the far end thanto the old node or equidistant ( ) to the far end and theold node. In this situation too, there may not be any segmentcommon between the existing connection and the new desiredconnection. The optimal crossover node is the far end ().

Fig. 5 shows the optimal crossover node determinationprocedure described above. The significance of the optimalcrossover node is threefold. First, if a new connection isestablished from this node to the target node, then the resultingconnection path between the far end and the target node willbe optimal. Second, the optimal crossover node is determinedwithout the use of the hierarchical path information of theexisting connection. Third, the current PNNI standards stip-ulate that only the node that created a hierarchical DTL canchange that DTL. This optimal crossover node is the node thatcreated the DTL that needs to be changed. Therefore, reroutingof the connection at this optimal crossover node conforms tothe stipulation. Next, we describe the procedure to determinethe minimal crossover node.

B. Minimal Crossover Node Determination

As explained earlier, it is possible for a part of the existingsegment from the optimal crossover node to the old node tobe in common with the new segment from the crossover nodeto the target node. For example, in Fig. 7, while B.1.1 is theoptimal crossover node, B.2.3 is the minimal crossover node.In this section, we describe the procedure to determine theminimal crossover node. Before presenting the details of thisprocedure, the main principle of this procedure is illustratedby an example.

Consider the scenario in which the far-end switch, oldswitch, and the target switch are in the same level-peergroup, as shown in Fig. 8. In this case, the optimal crossovernode is the far-end switch since (Case IIb ofFig. 6). The minimal crossover node determination procedureis initiated at node as specified in the problem definition(see Section III). Node first computes the shortest path fromnode to node and then compares it with the old path– .The minimal crossover node is the point of intersectionof the two paths. Since the PNNI routing protocol is a link-state routing scheme (and not a “distance-vector” scheme),this operation can be performed easily. Nodes, , andmaintain the same topological information about the peergroup allowing a node (in this case, node) to determinethe shortest path between two other nodes (in this case, nodes

and ).For the scenario shown in Fig. 8, nodecomputes the short-

est path between and to be .It knows the path of the old connection as being

. For the scenario shownin Fig. 8, the minimal crossover node, the point of intersectionof the two paths, is . Henceforth, we refer to the above-

Fig. 8. Minimal crossover node determination.

described procedure as thesingle PG minimal crossover nodedetermination routine, and it is applied on paths through asingle peer group.

Next, consider how this minimal crossover node determi-nation procedure can be extended to the more general case inwhich nodes , , and belong to different levelpeer groups.The extensions are based on the following observations.

1) The end-to-end hierarchical route stored at a node onthe path consists of a stack of DTL’s, with each DTLrepresenting a path through a peer group at a level ofthe hierarchy as viewed by that node (see Section II-A).

2) There is always a peer group at which the ancestorsof the three nodes, , and belong to the same peergroup.

3) Determining the minimal crossover node is an improve-ment over finding the optimal crossover node.

Given these observations, we begin the minimal crossovernode determination by having node exercise thesingle PGminimal crossover node determination routinefor the pathsthrough the peer group at which ancestors of nodes, , and

are siblings, where is the optimal crossover node. Thisleads to the determination of aminimal crossover peer grouprather than the identification of the actual minimal crossovernode. The minimal crossover peer group contains the minimalcrossover node, but given the hierarchical structure of thenetwork, node has no detailed information about the insidestructure of this minimal crossover peer group. This makes itnecessary to execute the next step of the procedure at a nodethat lies inside this minimal crossover peer group.

For this purpose, the old connection is traced from nodeuntil the egress border node of the identified minimal

crossover peer group on the old connection is reached. Thisnode can then perform the single PG minimal crossovernode determination routine for the paths through the minimalcrossover peer group to determine the next lower level minimalcrossover peer group. This procedure is applied recursivelyuntil a physical ATM switch is identified as the minimalcrossover node.

Details of the Algorithm:Fig. 5 shows the details of theminimal crossover node determination procedure. The notationused in the description of this algorithm is listed in Table II.

First, the optimal crossover node is determined using theprocedures described in Section IV-A. Next, in order to deter-mine the minimal crossover node, the procedure of identifyingthe minimal crossover peergroup at levelis repeated itera-tively at levels – . The minimal crossover peer group atlevel is identified by executing the single PG minimalcrossover node determination routine at the egress border node


TABLE IINOTATION

Fig. 9. Minimal crossover node determination.

of the minimal crossover peer group at level– on the existingpath ( ).

Initially, i.e., for level , is node . Node , with itsinformation on the hierarchical path of the existing connection( ) and the location of the optimal crossover node, deter-mines . Node using its summarized informationof the topology/loading conditions, computes the shortest path( ) between and . After computing ,node determines (minimal crossover peer group at level) by comparing and (see Fig. 9). In other words,

the new and old connections have a common path up to thepeer group . Therefore, the minimal crossover node is anode

in the peer group . The node also computes which isused to determine at the node .

After computing , the connection is traced from nodeuntil it reaches the egress border node of . If

the value of is equal to , is the minimal crossovernode (see Fig. 9). Otherwise, the single PG minimal crossovernode determination routine is executed by the nodeto determine the minimal crossover peer group . Thisiterative procedure is illustrated in Fig. 9. On identification ofthe minimal crossover node, a new segment setup is initiatedfrom this physical crossover node to the target node. Note that,by this procedure, the minimal crossover node is determined


Fig. 10. Rerouting connections.

in less than iterations. By thisselection of the minimal crossover node, the length of thenew segment to be set up is minimized, thereby reducingthe associated setup delays and the signaling load. However,there is processing overhead associated with this procedure.Heuristics can be used to terminate the search process at somelevel ( ) instead of repeating the procedure to compute theminimal crossover node at the egress border node of ,the ingress border node of can be selected as thecrossover node.

Example: Consider the scenario in which an existing con-nection between A.1.1 (far end) and B.3.1 (old node) is to bererouted to form a connection between A.1.1 and A.1.3 (targetnode) (see Fig. 10). In this case, , , and are 1, 1,and A, respectively. Since , the optimal crossovernode is the calling switch (A.1.1). We determine the minimalcrossover node following the steps shown in Fig. 5.

At B.3.1, the values of , , , and are B , A ,A , and 1, respectively. It determines the values of ,

, , and to be A , A, B , A , and , respectively.The connection is traced from the old node to the egress bordernode of peer group A, A.2.2.

At A.2.2, the values of , and , , and are A.2 ,A.1 , A.1 , and 2, respectively. It determines the values of

, , , and to be A.1 , A.1, A.2 , A.1 , and, respectively. The connection is then traced until the egress

border node of peer group A.1, A.1.2.At A.1.2, the values of , , , and are A.1.2 ,

A.1.3 , A.1.1 , and 3, respectively. It determines the valuesof , , , and to be A.1.1, A.1.2, A.1.3, A.1.1,A.1.2 , A.1.2 , and , respectively. Since (A.1.2)is the minimal crossover node. Therefore, A.1.2 is the minimalcrossover node (see Fig. 10).

V. APPLICATION TO LOCATION MANAGEMENT

In this section, we integrate the crossover node deter-mination algorithm into the location management schemesdescribed in Section II-B. For location management, the al-gorithm can be applied while setting up a connection (routeoptimization during call setup) or after a connection is com-pletely setup (route optimization after call setup).

A. One-Phase Crankback Scheme (Route OptimizationDuring Mobile Connection Setup)

In this section, we present aone-phase mobile connectionsetup schemein which an optimal connection path is achievedwhile setting up the connection to a mobile. As mentionedin Section II-B, the crankback location management scheme

classified as a two-phase scheme (see Fig. 2) can be modifiedto a one-phase scheme if the call is cranked back to the optimalor minimal crossover node, and then rerouted to the currentlocation of the mobile.

In order to reroute the connection, first, the call is crankedback until the optimal or minimal crossover node, and thenrouted to the visiting location of the mobile. The optimalcrossover node is determined using the procedure describedin Section IV-A by considering as the calling party’s switch

as the home switch of the called mobile andas the currentswitch of the called mobile. A parameter indicating the leveland identity of peer group at the ancestors-are-siblings level

is carried in the crankback message. Each switch receivingthe crankback message checks to see if it is the ingress bordernode for the peer group identified in the parameter. The switchthat happens to be the ingress border node of this peer grouprecognizes itself to be the optimal crossover node, and startssetting up the new segment.

If the minimal crossover node is to be used, two conditionsneed to be met. The first condition, described in Section IV(and illustrated in Fig. 5), is that the hierarchical path shouldbe available. This condition is met in this one-phase crankbackprocedure since hierarchical routes are available during callsetup [2]. If the second condition described in Section IV forminimal crossover node determination, i.e., all nodes beingpermitted to change DTL’s, is met, then the connection iscranked back to the minimal crossover node. In this case, theprocedure specified by the flowchart in Fig. 5 is used to crankback to the minimal crossover node. At the minimal crossovernode, the connection is rerouted to the current location ofthe mobile. This rerouting procedure results in an optimalconnection, thereby achieving a one-phase mobile connectionsetup procedure.

B. Second Phase of Two-Phase Location ManagementSchemes (Route Optimization After Mobile Connection Setup)

In this section, we present a route optimization procedurethat can be used to reroute a connection after a connection isset up to a mobile, thus proposing thesecond phaseof two-phase mobile location/connection setupschemes. In the firstphase, when a call setup arrives at the home switch of themobile, a fast local rerouting of the connection to the mobileis performed [7], [9]. This results in a connection suboptimallyrouted through the home switch (or some other local node).In order to optimize the connection route that resulted fromthe fast rerouting, a route optimization procedure is executed.The need for route optimization is dictated by several factors,such as optimality of the current path, duration of the call,QoS (quality of service) requirements of the connection, etc.A simple criterion is theoptimality of the current path,whichcan be determined at the home switch by comparing the“local view” of existing and the optimal paths between thecalling switch and the current switch of the mobile. Once theneed for optimizing the existing route is detected, this routeoptimization procedure is executed.

The route optimization procedure after call setup consists offour steps. First, the connection segment and the corresponding


Fig. 11. Buffering of upstream cells at the COS and downstream cells at the target node.

target node are selected. Second, a crossover node between theold and the new paths is determined, and a new segment isset up between that crossover node and the target node. Third,using “tail” signals and buffering, user data are switched overfrom the old path to the new path. Fourth, the old segment isreleased using standard ATM signaling procedures.

Step 1—Connection Segment and Target Node Determina-tion: As illustrated in the two cases of Fig. 4, the first task inoptimizing the route of a connection set up through the homenode (local node instead of the home nodein the case of atwo-phase crankback scheme) is to identify which of the twosegments – or – ( – or – ) needs to be rerouted. Thecorresponding target nodes for the rerouting operation become

and , respectively.Table I presents a method of choosing the connection seg-

ment and the target node based on the relative “closeness” ofthe nodes to each other. Ideally, the choice of the connectionsegment and the target node should be such that the length ofthe new connection segment is minimized, thereby reducingthe signaling load, route optimization delay, and the numberof cells that need to be buffered (see Step 3). A definition ofcloseness(based on the assumption that the distance betweentwo nodes is inversely proportional to their ancestors-are-siblings level) with the objective of minimizing the lengthof the new segment is as follows: For three nodes, ,and , node is closer to node than to node if theancestors-are-sibling level of nodesand is less than theancestors-are-sibling level of nodesand , i.e., .Using this definition of closeness and the information givenin Table I, the connection segment– and the target nodecan be determined. It should be noted that the optimality ofthe resulting connection path isindependent of the choice ofthe target node.

Step 2—Determination of the Crossover Node (COS) andSetting Up of the New Segment:The crossover node is deter-mined using the procedures described in Section IV. If eitherhierarchical path information is not available or only the nodesthat created the DTL can change the DTL, the procedure(see Fig. 5) determines the peer group whose ingress bordernode is the optimal crossover node. In order to set up a newsegment between the target node and the crossover node, theidentity of the crossover switch is required. Therefore, theexisting connection is traced until the optimal crossover node,and the new segment is then set up. If the hierarchical pathinformation is available and any node can change the DTL’s,the connection is traced until the minimal crossover node, andthe new segment is set up.

Step 3—Switching of User Data From the Old to the NewPath: Procedures to switch user cells from the old to the newpath depend on the acceptable amount of cell loss and out-of-sequence cells, and the support for switching and bufferingavailable in various network elements. For applications thatdo not require lossless handoffs, once the new segment isformed, user data are switched to the new path as soon as thenew segment is set up. In other words, the switching fabricin the target node (or COS) is configured to transmit/receiveon the new path without coordinating with the COS (or targetnode).

For applications requiring lossless and in-sequence cells,“tail” signals and buffering are used to switch user data fromthe old path to the new path. Tail signals are special cellssent on the same virtual circuit as the user cells (in-bandsignals). Tail signals should be easily distinguishable fromuser cells. For instance, they could be special RM (resourcemanagement) cells [14]. These tail signals are sent to signal theswitching of user data to the new segment. For bidirectionalconnections, user data need to be switched in both directions,downstream (from COS to the target node) and upstream(from the target node to the COS). For each direction, wecan buffer either at the COS or at the target node. Therefore,there are four possible alternatives for switching bidirectionalconnections. We will illustrate the procedures for the followingtwo alternatives: 1) upstream cells are buffered in the COSand the downstream cells are buffered in the target node and2) both upstream and downstream cells are buffered in thetarget node. Procedures for the other two alternatives can beobtained similarly.

Buffering of Upstream Cells at the COS and DownstreamCells at the Target Node:Fig. 11 illustrates the procedure forbuffering cells and switching data flow while maintaining cellsequence. After the new segment is set up, tail signals aresent in the downstream direction (toward the target node)by the crossover switch, and upstream direction (toward thecrossover switch) by the target node. After sending thetailsignals, the crossover switch configures the switching fabricin the downstream direction, and the target node configuresthe switching fabric in the upstream direction. Since cellssent on the new path may arrive before cells are depletedon the old path (given that the old path could be longer),the target node and the COS need to buffer cells receivedon the new segment until they each receive thetail signalsent by the other end. After receiving the tail signals fromthe other end, the buffered cells are first sent, and thenthe switching fabric is configured for the opposite direction


Fig. 12. Switching of user cells from the old to the new path by buffering at the target node.

in both the target node and the COS. All of the transitnodes on the old path can release the connection in theappropriate direction as and when they see the correspondingTail signal.

Buffering of Both Upstream and Downstream Cells at theTarget Node:Fig. 12 illustrates the procedure for switchingof user cells by buffering only at the target node. After thenew segment is set up, the upstream cells and the downstreamcells received on the new path are buffered, and a tail signal(shown as Tail-1 in Fig. 12) is sent in the upstream direction(toward the COS) by the target node. After receiving this tailsignal, the switch fabric (to receive/transmit cells on the newpath) is configured at the COS, and a tail signal (shown asTail-2 in Fig. 12) is sent in the downstream direction. Onreceipt of the tail signal from the COS, cells in the upstreamand downstream buffers are sent first, and then the switchfabric at the target node is configured. All of the transit nodeson the old path can release the connection in the appropriatedirection as and when they see the correspondingtail signals.Analysis of these buffering alternatives is beyond the scopeof this paper.

VI. PERFORMANCE ANALYSIS

In this section, a comparative performance analysis of one-phase (route optimization during call setup) and two-phase(route optimization after call setup) methods for locationmanagement is performed. Two variations are consideredwhile analyzing the performance of the one-phase scheme.In the first variation, referred to as theone-phase scheme(optimal), the call is rerouted from the optimal crossover node(see Section IV-A) to the current location of the mobile. Inthe second variation, referred to as theone-phase scheme(minimal), the call is rerouted from the minimal crossovernode (see Section IV-B).

As discussed earlier, there is a tradeoff between call setupdelay and resource utilization in the one- and two-phasemethods. Using a simple analytic model, we analyze this trade-off between resource utilization and connection setup delaysfor these methods. Later, we present details of simulationmodeling, and the results obtained from simulation of threedifferent topologies. These results help in validating the trendsobserved from the analytical results, and also give accurateestimates of performance of the one- and two-phase methodsfor the three topologies. In this performance analysis, thesecond phase (route optimization) of the two-phase schemesis not considered since it does not affect the parameters used

to compare these methods (amount of resources allocatedto a connection during call setup and the call setup delay)significantly. This issue is discussed further in Section VI-A3.

Other considerations to compare the performance of theseschemes are signaling load and processing requirements tohandle the signaling procedures associated with these schemes.These considerations are not discussed in this paper. Discus-sion on qualitative considerations, such as the simplicity ofsignaling procedures, impact on standards, networking withnonmobile-enhanced ATM switches (backward compatibility),etc., is omitted due to space considerations [15].

A. Analytical Model

In this section, we present the details of the analytic modelused to analyze the performance of the one- and two-phaseschemes. We first define the notation used in this analysis,and then describe a basic property of PNNI standards-basedhierarchical networks that is repeatedly used in the analysis.In Section VI-A3, the modeling details are presented. Finally,the numerical results obtained are presented in Section VI-A4.

1) Notation: Table III lists the symbols used in this analy-sis section, along with their definitions.

2) Property: For three nodes , , and , the followingrelations hold between theirancestors-are-sibling levels:

Case I: (1)

Case II: (2)

The proof of this property can be inferred from Fig. 13. Ifthe arrangement of nodes is shown in Case I

of Fig. 13, from which it is clear that . A similarargument extends for Case II. Also, note that since ,we use these terms interchangeably.

3) Location Management Schemes:In this section, we an-alyze the performance of one- and two-phase location man-agement schemes. In particular, we analyze the proposedone-phase method (optimal and minimal), and the two-phaselocation management scheme in which the first phase consistsof a quick forwarding of the connection to the mobile bythe home switch [7], and the second phase is the proposedroute optimization scheme. Measures of analysis include theconnection setup delaysincurred in these schemes and theamount ofnetwork resourcesrequired. Since the bandwidthrequirement of a connection is independent of the scheme used,we use thenumber of hopsin the connection to estimate thenetwork resource allocation required in each scheme.


TABLE IIINOTATION

(a)

(b)

Fig. 13. Relative positions ofx, y, andz. (a) Case I. (b) Case II.

In this two-phase connection setup scheme, the connectionis set up with each switch believing in its reachability infor-mation. The connection setup delay Delayin this methodis given in (3). The first case, , implies that thecalling party is within the neighborhood (see Table III) of thecalled mobile, where , defined in Table III, corresponds to thelevel up to which the reachability information is propagated.Therefore, the connection setup delay can be approximated by

, where denotes the delay at each switch on the pathand is the number of nodes on route from node(callingparty) to node (visiting location of the mobile).

The second case of (3) corresponds to the scenario when amobile is in its home neighborhood. In this situation, the entirenetwork has the correct reachability information about the mo-bile, and hence the call is routed directly to the mobile. All ofthe nodes within the neighborhood of the mobile have correctreachability information as a result of localized reachability

updates. The summarized reachability information in the nodesoutside the neighborhood of the mobile (default information)indicates that the mobile is in its home neighborhood. Thisinformation is sufficient to route a call directly to the mobilesince, in PNNI networks, hierarchical source routing is usedto route the connection.

The third case corresponds to the scenario in which the callis first routed to the home of the called mobile (), and is thenforwarded by the home to the current location of the mobile( ). Therefore, the connection setup delay comprises the delayin setting up the connection from the calling party switch ()to the home of the called mobile and the setup delay for theconnection between the home and the visiting location of themobile

Delay

independent ofindependent ofand

(3)

Next, we provide a method for estimating , and derivethe expression for estimating the average connection setupdelay. The distance between nodesand is approximatedas

(4)

where is the average (among all node pairs) length ofthe “shortest path” between nodes of a peer group at level

. For the worst case performance, the maximum length(among all node pairs) of the “shortest path” can be taken.By this definition, the distance between nodes and

depends on the value of theirancestors-are-siblings level. From the property described in (1)–(2), the relationship

between theancestors-are-siblings levelsof different nodes isknown. Using (1)–(4), an expression to estimate the average


connection setup delay Avg is obtained in (5):

Avg

(5)

In the two-phase scheme being analyzed, i.e., the callforwarding scheme, since the connection is not “backtracked”at any point, thenumber of hopsin the connection can beestimated from (3) and (5) by setting the value of to 1.The expression to estimate the average number of hops in aconnection Avg is given in (6). We expect that the secondphase, i.e., the route optimization phase, is performed soonafter the connection setup is completed. Hence, the additionalnetwork resources needed for extra hops in a connection areonly needed for a short period of time. Note that, in thisanalysis, the second phase (route optimization) of the two-phase method is not considered because of the following tworeasons. 1) It does not affect the amount of resources allocatedto a connection during connection setup. However, it shouldbe noted that the number of hops in a connection after thesecond phase is executed is equal to the number of hops inthe connection set up by the one-phase scheme. 2) It does notaffect the connection setup delay significantly5

Avg

(6)

In the one-phase connection setup scheme (optimal), likethe two-phase scheme, the connection is set up with eachswitch “believing” in its reachability information. But onconnection arrival to the home switch of the mobile, insteadof forwarding the connection, the connection is cranked backto an optimal crossover point and rerouted to the mobile. Theconnection setup delay Delay in this method is given in(7). The first two cases of this equation are the same as thoseof (3). The third case corresponds to the scenario in which

5Increase in signaling load due to the second phase results in a higher callsetup delay due to an increase is queueing delays.

the connection proceeds to the home of the called mobile( ), then cranked back from the home to the crossovernode ( , where denotes the delay at each node toperform crankback), and then rerouted from the crossover node( ) to the current location of the mobile ( )

Delayindependent ofindependent of

and

(7)

Using the approximation given in (4) (the distance be-tween nodes and depends on the value of theirancestors-are-siblings level ), the expression to estimate the averagecall setup delay [given in (8)] can be obtained from (7)

Avg

(8)

Applying the properties described in (1)–(2) (which givethe relationship between theancestors-are-siblings levelofdifferent nodes), (8) can be rewritten as below:

Avg

(9)

The third term of the equation corresponds to Case IIb ofFig. 14, where and are equidistant from the home of themobile ( ). The fourth and fifth terms correspond toCases I and IIa of Fig. 14, respectively.

Next, we consider the variation of the one-phase scheme(minimal) in which the call is cranked back to the minimal


(a) (b) (c)

Fig. 14. Relative positions of nodesc, h, andv. (a) Case I. (b) Case IIa.(c) Case IIb.

Fig. 15. Estimation of number of crankback nodes.

crossover point. The average delay while cranking back tothe minimal crossover point is expected to be lower thanwhile cranking back to the optimal crossover point. In orderto compute the average delay while cranking back to theminimal crossover node and then rerouting the call, we makethe assumption that the minimal crossover peer group (referto Section IV-B) at each level is equidistant from the corre-sponding level LGN of the ingress border node of that peergroup and the egress peer node performing the computation.In other words, the minimal crossover peer group at levelis assumed to be equidistant from LGN’s and (seeFig. 15). Assuming that there is an odd number of peer groupson the path between theses two nodes (i.e.,is odd), thenumber of nodes involved in the crankback at level, ,can be approximated by (10), where is the average (amongall node pairs) length of the “shortest path” between nodes of apeer group at level , and is the average number of nodeson the route between nodesand whose is equal to ,i.e., is equal to [see (4)]. Note that thenumber ofnodes on the common path(including the minimal crossovernode) in this peer group of level is also equal to

(10)

The average delay while cranking back to the minimalcrossover node can be approximated by

Avg

(a)

(b)

(c)

Fig. 16. Relative positions of nodesc, h, andv. (a) Case I. (b) Case IIa.(c) Case IIb.

(11)

The third term of the equation corresponds to Case IIb ofFig. 16, where and are equidistant from the home of themobile ( ). The fourth and fifth terms correspond toCases I and IIa of Fig. 16, respectively. Note that in the worstcase, the optimal crossover node is the minimal crossovernode. Hence, in the worst case, the maximum call setup delayin the one-phase (minimal) scheme is equal to the maximumcall setup delay in the one-phase (optimal) scheme.

In the one-phase crankback scheme (in both variations), theconnection is rerouted during call setup such that the resultingconnection traverses an optimal path. Hence, the number ofhops in the connection depends only on the optimal pathbetween the calling party and the current location of the mobile( ). The expression to estimate the average number of hopsin a connection Avg is given in (12)

Avg (12)

4) Numerical Results:In this section, wequantitativelycomparethe one-phase (route optimization during call setup)and the two-phase (route optimization after call setup)schemes. The measures of comparison include the averageand maximum call setup delays and the amount of networkresources required (number of hops in the connection).


TABLE IVINPUT PARAMETERS

Input Data: Values of input parameters assumed for thisnumerical computation are shown in Table IV (see Table IIIfor definitions of these parameters). Input parametersand

are estimated from measured data [13]. The probabilitydistributions used for calling patterns and user location arepresented in the Appendix. We observe that the exact numeri-cal results are dependent on the exact values chosen for theseparameters. However, the trends observed are more or lessindependent of these values. Sensitivity of the comparativeresults to these input parameters has been studied, but notincluded in this paper due to space considerations.

The variation of connection setup delays (average andmaximum delays) and the resource requirement (average andmaximum number of hops) with the variation of (whichdefines the extent of the “neighborhood”) for the one- and two-phase methods is shown in Fig. 17. From the plot showingthe variation inconnection setup delay, the following fourobservations are made. 1) The average call setup delay inthe one-phase scheme (minimal) is lower than that of thetwo-phase scheme. 2) The average call setup delay in the one-phase scheme (optimal) is higher than that of the two-phasescheme. 3) The maximum call setup delay in the one-phasescheme is higher than that of the two-phase scheme. Since, inthis section, we are not considering any specific topology, themaximum delay in the one-phase (minimal) scheme is assumedto be equal to the maximum delay in the one-phase (optimal)scheme. Maximum delays in the one-phase scheme for the twovariations (optimal and minimal) can be different for a specifictopology. This is illustrated in Section VI-B1. 4) The estimatesof the average delays for both methods are comparable, butthere is a significant difference in the maximum delay incurredin both of these methods. For example, the average delay inthe one-phase scheme (optimal) is approximately 10% higherthan that of the forwarding scheme ( ), but the maximumdelay in the one-phase scheme is approximately 30% higherthan that of the forwarding scheme.

It should be noted that the call setup delay depends on thelocations of the calling party, called mobile, and the home ofthe called mobile, and the topology and loading conditions ofthe network. Therefore, changing the calling scenario (fixingthe locations of the calling party, called mobile, and the homeof the called mobile) and the topology and loading conditionsof the network, the relative performance of these schemesmay vary. In the one-phase scheme (optimal), the worst casescenario occurs when the calling party, the home of the calledmobile, and the current location of the mobile are far away

Fig. 17. Delay and resource comparisons.

from each other. In this scenario, the call is routed to thehome of the called mobile, cranked back all the way to thecalling party switch, and then rerouted to the current locationof the mobile leading to large delays. Such a scenario canoccur in the one-phase scheme (minimal) also when there isno common segment between the old and the new paths.

The variation of has a similar effect on the call setupdelays in all of the schemes. At lower values of(neighbor-hood to which reachability data are propagated is larger), thecall setup delays are lower since most of the calls are routeddirectly to the mobile, instead of routing to the home and thenrerouting to the mobile. When , since all of the calls arerouted directly to the mobile in both schemes, the call setup de-lays are minimum. The disadvantage of having a large neigh-borhood (i.e., low value of ) is that the cost of updating reach-ability information regarding the location of a mobile, when amobile moves from one location to another, is very high [7].

From the plot showing the variation in thenumber of hopsin a connection,we observe that both the average and the max-imum number of hops in connections resulting from the two-phase scheme are higher than that in the one-phase scheme.This is an expected trend since the one-phase scheme resultsin optimal connection paths. It should be noted that both of thevariations of the one-phase scheme (optimal and minimal) re-sult in a connection with the same number of hops. The plot ofthe average number of hops in a connection show that signif-icant improvements in resource utilization can be achieved bythe one-phase scheme. In the worst case (the plot for maximumnumber of hops), the two-phase forwarding scheme (prior toroute optimization) requires twice the amount of communi-cation resources as the one-phase scheme (route optimizationduring call setup). In the two-phase scheme, the number of


Fig. 18. Switch model.

hops in connection after the route optimization phase is equalto the number of hops in a connection set up by the one-phase scheme. At low values of(i.e., neighborhood to whichreachability data are propagated is large), the number of hopsin a connection is lower in the two-phase method since most ofthe calls are routed directly to the mobile, instead of routing tothe home and then rerouting to the mobile. Since the one-phasemethod results in an optimally routed connection, the numberof hops in a connection does not vary with the variation in.

B. Simulation Model

In this section, we describe the details of the simulationmodel developed to study the performance of the one- andtwo-phase schemes, and we discuss the results obtained fromthe simulations. The simulation modeling was performed usingthe OPNET6 modeling tool [16].

In this simulation study, the network model consists ofswitches and links interconnecting them. Each switch is mod-eled as a combination of a queue, message-processing module,call generator, and message transmitters and receivers asshown in Fig. 18. The queue is an infinite queue with aspecifiable service rate, and accounts for the queueing delaysexperienced in the switch. The message-processing modulecontains the logic to perform topology discovery and summa-rization, shortest path computation, call setup, call forwarding,crankback to the optimal crossover node, and crankback to theminimal crossover node. During the topology discovery phase,the switch sends “hello” packets on all of its outgoing links(transmitters), and learns about its neighbors (switch address)from the hello packets received from them. This information isused to set up the routing tables that are used to route call setupand crankback messages. After exchanging hello packets,nodes broadcast their link information to other nodes in theirlowest level peer groups (level). Summarized informationregarding these links is broadcast to nodes of other peergroups. From the information received through these broadcastmessages, nodes compute their local view of the network.

The call generator module is used to generate calls withan exponential distribution and a specified call interarrivalrate. The mobile to which this call is intended (called party)is chosen randomly. The mobility pattern is also assumedto follow a random distribution, i.e., the switch at whichthe called mobile is currently located is chosen randomly.On call arrival at a switch the hierarchical source route iscomputed based on the link weights and the summarized

6OPNET is a registered trademark of MIL 3, Inc.

topology information, and the call setup packet is routed tothe next switch (see Section II-A). The message-processingmodule also implements other functions of call setup, callforwarding [7], crankback to the optimal crossover node (seeSection IV-A), and crankback to the minimal crossover node(see Section IV-B).

A desired network configuration is obtained by creating asmany switch modules as there are nodes in that configuration,and then interconnecting the switches according to the topol-ogy of that configuration. An interconnecting link between twoswitches is specified in each direction by a transmitter and areceiver. A transmitter transmits the messages it receives fromthe message processing module to the corresponding receiver.The receiver in turn sends the received message to the queuemodule of the switch.

1) Simulation Results:In this section, we present the sim-ulation results comparing the one-phase (route optimizationduring call setup) and the two-phase (route optimization aftercall setup) schemes. The measures of comparison include theaverage and maximum call setup delays, the amount of net-work resources required (number of hops in the connection),and the number of nodes involved in the crankback proce-dure (in the one-phase scheme). The results obtained in thesimulation study help in validating the trends observed fromthe analytical results. They also provide accurate estimates ofthe call setup delay and the number of hops in a connectionin the one- and two-phase methods for the topologies beingconsidered.

Input Data: In this study, we simulated three differentnetwork configurations (see Table V). The network configu-rations that are simulated include the following. 1) A networkconsisting of 20 nodes organized in a single peer group. Thetopology of this network configuration was generated usinga random connected graph generator [17]. The connectivity(fraction of the number of edges possible in a complete graph)of the random graph generated 0.15. 2) A network consistingof 200 nodes organized as a hierarchical network of two levels.The 200 nodes are arranged into ten level-1 peer groups,each consisting of 20 switches. The topology of this networkconfiguration is also generated using a random connectedgraph generator with a connectivity of 0.15. 3) A networkconsisting of 480 nodes organized as a three-level hierarchicalnetwork. These 480 nodes are arranged into five level-1 peergroups, each consisting of eight level-2 peer groups. Each ofthe level-2 peer groups comprise 12 switches. The topologyfor the level-2 peer group was generated using a randomconnected graph generator with a connectivity of 0.15. Thenetwork configuration was obtained by making five replicas ofthe level-2 peer group, and then interconnecting these level-2peer groups in a star topology. Values of the input parametersthat were used in this simulation study are shown in Table VI.

The average call setup delay in the one- and two-phaseschemes for the three configurations is shown in Fig. 19. FromFig. 19, we observe that, for all of the configurations, theaverage call setup delay in the one-phase scheme (optimal) isthe highest and the average call setup delay in the one-phase(minimal) is the lowest. These observations are in agreementwith the results obtained in Section VI-A4.


TABLE VSIMULATED NETWORK CONFIGURATIONS

TABLE VIINPUT PARAMETERS

Fig. 19. Comparison of average call setup delays.

The maximum call setup delay in the one- and two-phaseschemes for the three configurations is shown in Fig. 20.The maximum call setup delay in the one-phase scheme(optimal) is higher than in the two-phase and the one-phase(minimal) schemes. The maximum call setup delay in theone-phase (minimal) scheme is marginally greater than thatin the two-phase scheme for first two network configurations,and lower than that in the two-phase scheme for the thirdnetwork configuration (see Table V). In Section VI-A4, plotsof maximum call setup delay (see Fig. 17) show that themaximum call setup delay in both variations of the one-phasescheme is the same, and it is significantly greater than themaximum call setup delay in the two-phase scheme. Thisdiscrepancy can be explained as follows: in Section VI-A4,while computing the maximum call setup delay, we consideredthe worst case scenario in which the minimal crossover node

Fig. 20. Maximum call setup delay.

Fig. 21. Number of hops in a connection.

is always the optimal crossover node. But if we consider aspecific network configuration, the worst case scenario in theseschemes could be different, and will depend on the topologyof the network. In other words, the worst case scenario ofthese schemes is a function of the topology of the network.Since we are considering specific network configurations inthis section, the plots of the maximum call setup delay showa different trend than the ones shown in Fig. 17. It shouldbe noted that for certain topologies, the maximum call setupdelay in the one-phase (minimal) scheme is smaller than thatin the two-phase scheme. An example of such a topology is thestar topology (see maximum call setup delays correspondingto configuration 3 in Fig. 20).

Fig. 21 shows the average and maximum number of hopsin a connection in the one- and two-phase schemes. Both inthe average case (the plot for the average number of hops) andthe worst case (the plot for the maximum number of hops),the two-phase forwarding scheme (prior to route optimization)requires twice the amount of communication resources as theone-phase scheme. Since the number of hops in a connectionafter the route optimization phase in the two-phase schemeis equal to the number of hops in the one-phase scheme,the above observation indicates that the route optimizationresults in a significant reduction of resources required fora connection. These results are in agreement with the trendobserved in Section VI-A4.

The number of nodes that participate in the crankbackprocedure (crankback nodes) during the one-phase (optimal)and the one-phase (minimal) schemes for the different con-figurations is shown in Fig. 22. We observe that the number


Fig. 22. Crankback nodes involved in a connection setup.

of crankback nodes (both average and maximum number ofnodes) in the one-phase scheme (minimal) is lower than thenumber of crankback nodes in the one-phase scheme (optimal).Since the number of crankback nodes is smaller in the one-phase (minimal) scheme, a larger part of the existing segmentis identified as the common segment (see Fig. 8), therebyresulting in smaller call setup delays as shown in Fig. 19.

We can also infer that the signaling load in the one-phaseminimal scheme is lower than the signaling load in theone-phase optimal scheme since the average number ofnodes involved in the crankback process is lower in theone-phase minimal scheme. On average, the signaling loadin the two-phase scheme will be approximately equal tothe signaling load in the one-phase minimal scheme priorto route optimization. If we add in the signaling load ofthe route optimization phase for the two-phase schemes,clearly, the signaling load for such schemes will be greaterthan the one-phase minimal scheme. A formal treatment ofsignaling load comparisons is needed. Also, implicationsof the proposed procedures on the PNNI standard and theeffects of having “mobility-enhanced” switches mixed inwith “nonmobility-enhanced switches” need to be studied.

In summary, the following observations are made about theaverage case performance of the one- and two-phase schemes.1) The average call setup delay in the one-phase (minimal)scheme is lower than that in the two-phase scheme, and theaverage call setup delay in the one-phase (optimal) schemeis higher than that in the two-phase scheme. 2) The numberof hops in a connection in the two-phase scheme (prior toroute optimization) is significantly greater than the number ofhops in the one-phase scheme. Besides the extra amount ofresources required prior to route optimization phase, the two-phase call setup method has an overhead of route optimizationsignaling and buffering of cells. In order to minimize theamount of resources required for a connection and to avoid theadditional signaling overhead of the second phase in the two-phase scheme, it is preferable to execute route optimizationduring call setup (one-phase scheme).

However, from the worst case analysis, we observe thatthe one-phase scheme can lead to high worst case call setupdelays. These high worst case call setup delays associated withthe one-phase scheme may not be acceptable for certain ap-plications. Therefore, in such situations, a fast local reroutingof the connection is required, and in order to minimize thenumber of hops in a connection, route optimization should be

executed subsequently. Since the connection setup delay inthese schemes depends on the topology of the network andthe exact locations of the calling party, called mobile, andhome of the called mobile, we propose that, on call arrivalat the home of the called mobile, the home switch decideswhich scheme to execute, the one-phase scheme or the two-phase scheme. Some of the factors on which this decision canbe based include: QoS (quality of service) requirements ofthe connection, duration of the call, the associated call setupdelays, location of the calling party and the called mobile,topology and loading conditions of the network, and numberof hops in the connection. From the analysis, we can alsoinfer that the one-phase (minimal) scheme shows significantperformance gains over the one-phase (optimal) scheme, bothin terms of call setup delay and signaling load.

VII. CONCLUSION

In this paper, we proposed analgorithm for optimizingthe route of a connectionthat becomes suboptimal due tooperations such as handoffs and location-based reroutes, formobile ATM networks based on the PNNI standard. Thisalgorithm uses hierarchical route information of the con-nection and summarized topology and loading informationof the network to determine a “crossover node” such thatadjusting the connection from that crossover node results inan optimally routed connection. Variations of the algorithmconsist of methods to determine two types of crossover nodes,optimal and minimal crossover nodes. The second part ofthis paper described the application of this algorithm tothe location management problem. We demonstrated howthis route optimization procedure can be executed duringmobile connection setup, resulting in aone-phase mobilelocation/connection setupscheme. We also demonstrated howthis route optimization procedure can be executed after aconnection is set up to a mobile as a thesecond phaseof a two-phase mobile location/connection setupscheme. Acomparative performance analysis of the one-phase (minimaland optimal) and two-phase connection setup schemes waspresented. Measures of comparison arecall setup delayandthe amount ofnetwork resourcesallocated to a connection.

The average connection setup delay in the one-phase op-timal scheme is higher than in the two-phase scheme, andthe average connection setup delay in the one-phase minimalscheme is lower than in the two-phase scheme. For the specificnetwork topologies considered, the maximum call setup delay(worst case call setup delay) in the two-phase scheme is lowerthan in the one-phase optimal scheme, and is similar to thatin the one-phase minimal scheme. The amount of resourcesrequired for a connection in the two-phase scheme (prior toroute optimization) is significantly greater than that in the one-phase scheme. Results also show that the route optimizationphase in the two-phase methods leads to a significant reductionin the amount of network resources required for a connection.

APPENDIX

In this section, we describe the probability distributions, and the conditional probabilities used


to compute the average call setup delay and the number ofhops in a connection, in (5), (6), (9), and (12).

We assume that the distribution of calls to a mobile followsa uniform distribution, i.e., it is equally probable for a mobileto receive a call originating at any switch. So the probability ofa call originating from a switch for which depends onthe number of nodes for which and the total number ofnodes in the network. At level, we exclude the peer group oflevel to which the called mobile belongs, and determinethe number of nodes at levelthat belong to other peer groupsof level . Thus, the probability is given by

(13)

Since a call can originate from anywhere, the distributionof is the same as the distribution of . The conditionalprobability is given by (14):

(14)

Next, we consider the distribution of . The choice ofthis distribution is based on the premise that a majority of themobiles roam in and around their respective homes. We choosea distribution such that the probability of being located closeto home is high. The distribution is such that the probabilityof being located at the home switch is, in the th level peergroup of the home switch is , in the th peer groupis , etc. When , then and the probability ofbeing located further and further away from the home switchdecreases. Given that a mobile is located somewhere in thenetwork,

or (15)

Under this assumption, the distribution of is given by(16):

(16)

REFERENCES

[1] G. Dommety, M. Veeraraghavan, and M. Singhal, “Route optimizationin mobile ATM networks,” inACM/Baltzer Mobile Networks Appl. J.,to be published.

[2] ATM Forum Technical Committee, “Private network–network specifi-cation interface v1.0 (PNNI 1.0),” af-pnni-0055.000, Mar. 1996.

[3] EIA/TIA IS-41 Rev. C, “Cellular radio telecommunications intersystemoperations,” TIA/EIA PN-2991, Nov. 1995.

[4] M. Mouly and M. B. Pautet,The GSM System for Mobile Communica-tions, 49 rue Louise Bruneau, Palaiseau, France, 1992.

[5] J. S. M. Ho and I. F. Akylidiz, “Local anchor scheme for reducinglocation tracking costs in PCN’s,”IEEE/ACM Trans. Networking, vol.4, pp. 709–725, Oct. 1996.

[6] S. Mohan and R. Jain, “Two user location strategies for personalcommunications services,”IEEE Personal Commun., pp. 42–50, FirstQuarter 1994.

[7] M. Veeraraghavan and G. Dommety, “Mobile location managementin ATM networks,” IEEE J. Select. Areas Commun., vol. 15, pp.1437–1454, Oct. 1997.

[8] A. Acharya, S. Biswas, L. French, J. Li, and D. Raychaudhuri, “Handoffand location management in mobile ATM networks,” inProc. 3rd Int.Workshop Mobile Multimedia Commun., Princeton, NJ, Sept. 1996.

[9] A. Ayyagari, J. Harrang, and S. Ray, “Call establishment/termination inwireless PNNI,” ATM Forum 96-1410, Oct. 1996.

[10] C. Perkins, “IP mobility support,” RFC 2002, Oct. 1996.[11] D. B. Johnson and C. Perkins, “Mobility support in IPv6,” Internet Draft,

draft-ietf-mobileip-ipv6-02.txt, Nov. 1996, work in progress.[12] , “Route optimization in Mobile IP,” Internet Draft, draft-ietf-

mobileip-optim-04.txt, Feb. 1996, work in progress.[13] M. Veeraraghavan, G. L. Choudhury, and M. Kshirsagar, “Imple-

mentation and analysis of PCC (parallel connection control),”IEEEINFOCOM, Kobe, Japan, Apr. 1997.

[14] ATM Forum Technical Committee, “ATM user-network interface (UNI)signaling specification version 4.0,” ATM Forum/95-1434R9, Jan. 1996.

[15] G. Dommety, M. Veeraraghavan, and M. Singhal, “Route optimization inmobile ATM networks,” inACM/IEEE Int. Conf. Mobile Computing andNetworking (MobiCom’97), Budapest, Hungary, Sept. 1997, pp. 43–54.

[16] A. Cohenet al., OPNET Modeling Manual, MIL 3, Inc., 3400 Interna-tional Dr. NW, Washington, DC.

[17] S. Srinivasan, “Low overhead fault tolerance schemes for distributedsystems,” Ph.D. dissertation, Princeton Univ., Princeton, NJ, 1995.

Gopal Dommety (S’97) received the B.Tech. de-gree (with Honors) in computer science and en-gineering from the Indian Institute of Technology,Kharagpur, in 1993, and the M.S. degree in com-puter and information science from the Ohio StateUniversity, Columbus, in 1995.

He is currently a Ph.D. candidate in the Depart-ment of Computer and Information Science, TheOhio State University. During 1997, he was a vis-iting member of the Broadband Systems ResearchDepartment, Bell Laboratories, Lucent Technolo-

gies. His current research interests include high-speed networks, wirelessnetworks, mobile computing, performance modeling, and parallel and dis-tributed systems.

Mr. Dommety is a student member of the ACM.

Malathi Veeraraghavan (M’88–SM’97) receivedthe B.Tech. degree in electrical engineering fromthe Indian Institute of Technology, Madras, in 1984,and the M.S. and Ph.D. degrees in electrical engi-neering from Duke University in 1985 and 1988,respectively.

She is currently a Distinguished Member of Tech-nical Staff at Bell Laboratories, Lucent Technolo-gies, in the Networking Research Laboratory. Herresearch interests include signaling and control ofnetworks and network and mobility management.

Dr. Veeraraghavan served as an Associate Editor of the IEEE TRANSACTIONS

ON RELIABILITY from 1992 to 1994.

Mukesh Singhal (A’92) received the Bachelor ofEngineering degree in electronics and communi-cation engineering with high distinction from theUniversity of Roorkee, Roorkee, India, in 1980,and the Ph.D. degree in computer science fromUniversity of Maryland, College Park, in 1986.

He is an Associate Professor of Computer andInformation Science at The Ohio State University,Columbus. His current research interests includeoperating systems, distributed systems, mobile com-puting, high-speed networks, computer security, and

performance modeling. He has published more than 100 refereed articlesin these areas. He has coauthored two books, entitledAdvanced Conceptsin Operating Systems(McGraw-Hill, New York, 1994) andReadings inDistributed Computing Systems(IEEE Computer Society Press, 1993).

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