Location Management in Wireless ATMCustomer Premises NetworksAlexandros Kaloxylos �agk@di.uoa.gr Evangelos Zervaszervas@di.uoa.gr Lazaros Merakosmerakos@di.uoa.grCommunication Networks LaboratoryDept. of Informatics, University of Athens15784 - AthensTel: +301 7275334Fax: +301 7252116AbstractThe introduction of the ATM technology in wireless CPN environments necessi-tates the design of mobility protocols, since B-ISDN signaling was not developed tosupport terminal movement. The functionality of mobility protocols consists of theprocedures for handover (re-routing of active data connections to a new cell) andfor location management (tracking the exact location of a mobile terminal thatmoves inside a network). Considerable work has been done worldwide for bothprocedure types. This paper focuses on the location management techniques, andintroduces a new mechanism suitable for large private wireless ATM environments,where the switches are inter-connected with the PNNI protocol(Private Networkto Network Interface). An analytical model has been developed to evaluate thee�ciency of this mechanism.Keywords: Wireless ATM, Location management, PNNI, Analytical model.1. IntroductionThe development of Location Management (LM) protocols for Wireless ATM (WATM) Cus-tomer Premises Networks (CPN) environments has been lately an important research topic. Inthis type of environments it is necessary to design a Location Update and a Location Inquiry (orLocation Tracking) mechanism. Location Update is the procedure of updating the appropriatenetwork components about the current location of Mobile Terminals (MTs) when they moveto di�erent cell areas. Location Inquiry is the procedure executed by a network component todetermine the exact location of a MT to deliver an incoming call or any other service.�Supported by a grant from the General Secretary of Research and Technology (G.S.R.T) and INTRACOM

A LM mechanism must meet several requirements [Por97], [Rau97]. Firstly, a LM mech-anism should be scalable in order to handle e�ciently a large number of MTs moving insidepublic and private networks. Furthermore, a user should not be aware of the actions takenby a LM mechanism, while at the same time provision is needed to preserve location and usercon�dentiality. Another important issue is that, optimum paths for data connections should beestablished, after a call delivery, for the e�cient management of network resources. Moreover,a LM mechanism should take into consideration the existence of switches that do not supportmobility procedures. Finally, the LM mechanism needs to create minimum signaling load andto require minimum modi�cations/extensions to existing signaling standards.All location management mechanisms developed until now attempt to satisfy the aforemen-tioned requirements and can be classi�ed in two categories:1. Location Register Schemes: Location registers (databases) are used to store the locationof mobile users and use this information whenever a call has to be delivered to a MT.2. Mobile P-PNNI Schemes: New features are added in the PNNI protocol to achieve therequired mobility support.In this paper we propose a new approach that uses Location Agents on mobility enhancedswitches. These agents are used to track the location of MTs that have moved from theirhome area. The set of switches is logically divided into several control areas. Inside eachcontrol area the routing information provided by PNNI is used to forward calls. We call thisapproach LAMPS (\Location Agent and Mobile PNNI "Scheme). LAMPS can be consideredas a combination of the two aforementioned schemes.The rest of the paper is organized as follows. Section 2 gives an overview of existing locationmanagement mechanisms. In Section 3, the network architecture and the protocol stack usedthroughout this paper, are outlined. A detailed description of the proposed mechanism ispresented in Section 4. Section 5, evaluates the performance of LAMPS using an analyticalmodel. Finally Section 6 contains the conclusions.2. Related WorkAs mentioned in Section 1, there are mainly two types of location management mechanisms,which are based either on the use of Location Registers or on extensions of PNNI to handleterminal mobility.Mechanisms of the �rst category use database servers that store the location of MTs. Lo-cation inquiry always proceeds the execution of a call setup phase. In almost all of thesetechniques, the main issue is to �nd the appropriate percentage between the number of signalsneeded to update the location registers and the number of signals during a location tracking,in order to minimize the overall signaling tra�c and processing load. There is also a cleartrade-o� between call setup delay and the e�ciency of connection routing.Mechanisms of the second category exploit the PNNI routing capabilities to �nd the exactlocation of a MT. In these techniques, location inquiry is performed during the execution of the

standard call setup procedure. The main issue in the design of these mechanisms is to achievean optimum route between the calling and the called party, and to modify as less as possiblethe standard signaling procedures.2.1 Location Register SchemesMost of the proposed mechanisms of this category are based on IS-41 [Lin95] and GSMMAP[Mou92], which they try to improve. In GSM a number of network databases are used duringthe execution of mobility management and call control functions.These elements include thelocation registers consisting of the Home Location Register (HLR), and the Visiting LocationRegister (VLR). The HLR stores the location and the pro�le of a user. The VLR maintainsthe same information locally, for a roaming subscriber, and noti�es the appropriate HLR aboutthe location of visiting MTs.[Kri96] suggests the use of forwarding pointers in addition to the HLR to assist in locationmanagement. According to this mechanism, for each MT that crosses the boundaries of aregistration area, its related information (e.g., user pro�le) is transferred to the new locationserver (LS). In addition, a forwarding pointer is created in the old LS to point to the new LS.Updates at the HLR do not take place each time a MT crosses the boundaries of a registrationarea, but movement or search based heuristic algorithms are used instead.In [Noy94], three dynamic location update strategies, time-based, movement-based anddistance-based, are studied. Under these three schemes, location updates are executed based onthe elapsed time, the number of movements performed and the distance traveled, respectively,since the last location update. It is shown that the distance-based algorithm has the bestperformance, but its implementation incurs the highest overhead.[Ho96] introduces a new concept called Local Anchor. The scheme is again based on the IS-41standard and the location tracking signaling load is reduced by not always sending noti�cationto the HLR whenever the MT moves to the control area of a new VLR. The basic concept ofthis mechanism is to associate a VLR with a Local Anchor, and to report this to the HLR.When the MT moves to a new area, only the Local Anchor is noti�ed about this.In [Aky96] the network is divided into zones. Each zone has a Location Manager thatcontains the user information and the new zone in which the MT currently resides. Locationtracking is done again before call setup. A calling user sends the global Id of the called party toits zone manager. The zone manager retrieves the current zone location of the called party andissues a call setup to the zone manager of the called party. This zone manager is responsibleto page the terminal and reply to the setup.The key idea in [Hac97] is that the home area of a MT receives location updates onlywhen the MT enters into a prede�ned set of cells, called \reporting cells". To �nd the exactlocation of a MT, the system searches only in the last reporting cell, and in all of its neighboring\non-reporting"cells.[Vee97] introduces location registers in ATM networks where the switches are inter-connectedusing the PNNI protocol. Location registers are placed within the peer group structure. In

this approach, the LRs track the location of mobiles, and respond to location queries prior toconnection setup. These registers are hierarchically arranged, with the hierarchy limited to acertain scope S. To locate a MT prior to call setup, a chain of location registers has to betraced.In [Por96], the MTs have two addresses, Mobile Home Address (MHA) and Mobile ForeignAddress (MFA), depending if they are in their home area or not. Switches in the network areseparated to Enhanced Mobility Switches (EMS) and standard ATM switches (SW). The MFAfor a MT corresponds to the EMS address it is currently attached to. Whenever a user wantsto call a MT, it issues a call setup using the MHA. The �rst EMS that receives this setup sendsa query to the home location register of the MT to receive its MFA. It then issues a call setupusing the MFA. The setup terminates at the EMS of the MT that is currently attached to. Atthis point the EMS will use a call setup with the MHA of the MT.2.2 Mobile PNNI2.2.1 Overview of PNNIPNNI (Private Network-to-Network Interface) is a signaling protocol used among ATMswitches. PNNI includes a protocol for distributing topology information between switchesand clusters of switches, and a protocol for establishing point-to-point and point-to-multipointconnections. PNNI provides capability for dynamic routing, support for QoS and is based ona subset of the ATM Forum UNI Version 4.0 [ATM96b]. Because of the distribution of routinginformation, PNNI is a good basis for developing mobility protocols.In PNNI the switches are organized into clusters, called peer-groups. E�cient routing isimplemented by de�ning a logical hierarchy on the system, where peer-groups are representedin higher layers by logical nodes. These logical nodes are treated as single nodes by the nexthigher layer. The appropriate pre�x of the address of a PNNI node speci�es its level in thePNNI hierarchy.The switches of the lowest level advertise the addresses with which they have connectivity.Since in a large network a switch cannot advertise to all the nodes its reachability addresses,PNNI uses the concept of address summarization. In other words, reachable addresses aredistributed in the form of pre�xes. These pre�xes indicate reachability for all addresses of thesame pre�x. The same technique is used from the logical nodes of the higher layers. Whenevera node �nds out that it has a new reachable address to advertise, it checks to �nd whether ithas a pre-con�gured summary address that matches the new address. In this case the reachableaddress is called native address of the switch, and only the pre�x will be advertised. Reachableaddresses that do not match any summary address are called foreign addresses of the switch,and are advertised unsummarized. A key point of the PNNI ooding of routing information,is that all nodes inside a peer-group have identical routing tables that contain detailed routinginformation for the nodes and links of this peer-group. For the rest of the network, these nodeshave only a general view.Another interesting point is that the switches can use the same PNNI ooding of routing

information to advertise reachability information for all their UNI-attached end systems. Ifthis feature is used for mobile end-points, the PNNI can be used for location management.2.2.2 Mobile PNNI SchemesIn [Vee97], the PNNI ooding of reachability information about end-points is used betweenswitches. In order to cut down the amount of the aforementioned tra�c, the PNNI scope pa-rameter is used. This parameter de�nes the area of nodes that receive reachability informationwhenever a speci�c MT moves to the control area of another switch. Location tracking is doneusing the call setup and the routing information stored in the switches. Whenever a terminalattempts to call a MT that resides in an area di�erent from its home and di�erent from thehome area of the calling terminal, the setup will be headed to the home area of the MT andfrom there it will be forwarded to the current location of the MT. In this proposal there is aneed to store forwarding pointers in the home switch. Furthermore, a procedure to optimizethe �nal route may also be used.Another approach is proposed in [Ach97] where uni�cation of call setup with location track-ing is considered. In this scenario the MT's address has topological meaning. In other words,the MT address corresponds to a home switch. Whenever the MT attaches itself to a switchdi�erent from its home, it is assigned a new address relative to the attached switch, and thehome switch is noti�ed about the new address. When a user wants to call a MT, it issues acall setup to the home-switch of the MT, and if the MT is not attached there, then a releasesignal is sent back. This signal contains the new address (location) of the MT. The calling usercan then call directly the MT at its new location. Optionally, location caching can be used inintermediate switches [Ach96].2.3 Comparison of the SchemesAs described in [Vee96] the �rst category of LM mechanisms can be described as the \thecellular telephony approach", while the second one can be viewed as \mobile computing ap-proach".Both categories of location management techniques present advantages and disadvantages.For the location register scheme one may say that it is already used as a type of acceptablesolution in the telecommunications industry. The existing standards (e.g., GSM/MAP) canbe used to serve the needs of a CPN mobile population. Even if this solution is inadequate,some of the new proposals can be used instead, since they claim that they can work withvery large numbers of mobile users more e�ciently. Moreover, the main achievement of thesemechanisms is that a connection has always an optimum routing, since the exact location of aMT is retrieved prior to a call setup.Solutions of this type present however some drawbacks. Firstly, in a wireless CPN environ-ment both �xed terminals and MTs exist. Whenever a call setup is issued, a distinction on thetype of the called terminal is needed, since location tracking is needed only for the MTs. Thisimposes a separation on the addressing space [Ach97], [Raj97]. Furthermore, these mechanismswill need extra-routing procedures for the communication between LRs, which leads to the

deployment of new routing protocols and to an increase of network administration procedures.Finally, when the PNNI protocol is used for the interconnection of switches, the overall systemmay end up with duplication of routing information and functionality, since the PNNI oodingof routing information can be used instead.For the Mobile PNNI schemes, with minor modi�cations in the PNNI (i.e., new informationelements or call forwarding procedures), administration and duplication of information is tack-led e�ciently. Another important issue is that no distinction between MTs and �xed terminalsis required. Finally, these mechanisms behave extremely well when the called MT is attachedto its home switch or near it.The major drawback of these mechanisms is that, the P-NNI setup messages used forlocation tracking are heavier in comparison to the signals used in the \location registers"schemesboth in terms of computation and bandwidth. Another drawback is that in some cases (e.g.,[Vee97]) route optimization may be required after the establishment of a connection.The location management mechanism we present in this paper can be considered as acombination of [POR97] and the mobile PNNI mechanism of [VEE97]. Our mechanism usesthe PNNI routing tables to route calls for the MTs that are inside a pre-de�ned area. If thecalledMT is outside this area, then the �rst EMS that intercepts a call setup for the speci�cMT,it executes location tracking. This is accomplished by communicating with an agent located atthe home switch of the called MT. This mechanism is described in detail in subsequent sections.3. Network Topology and Protocol StacksA CPN installation may consist of many buildings and a large number of users [Raj97]. Itcan also be assumed that a network of this size could be logically partitioned in \Radio Islands(RI)", each one of them covering an area with several buildings, e.g., campus area, companybuildings. A RI is the area of continuous radio coverage (i.e., the RI is the largest area a MTcan move inside without losing connection to the network). Figure 1 gives an overview of thenetwork topology.Each RI contains a large number of switches some of which are Enhanced Mobility Switchessuch as described in [Kal98]. Every EMS has attached to it several Base Stations (BS), theprimary role of which is the adaptation of ATM cells to radio packets and vice versa. BSsare controlled by the EMS by means of a specialized protocol called Base Station ControlProtocol (BSMP). BS management related messages are exchanged through a pre-reservedVirtual Channel (VC) in the EMS-BS link.All other switches, called SW in Figure 1, are typical ATM switches without any mobilitycapabilities. All switches inside a RI are interconnected through the PNNI protocol. TheRadio Islands may be inter-connected through a public or private ATM network. The networkprotocol to be used for these connections can be PNNI, B-ISUP [ITU94c], or B-ICI [ATM95].Assuming the topology of Figure 1, a MT can roam in the coverage area of only one switch,or it can move through the coverage areas of di�erent switches inside the same RI, or movethrough di�erent RIs. The ability of a MT to move in the coverage area of multiple EMSs,

raises the need to design an appropriate \inter-switch handover functionality"[Noe97], as wellas an e�cient location management scheme.The RIs are considered to be located in long distances the one from the other, thus no\inter-RI handover"procedure can take place. The only need in such a case is to design therequired location update and tracking mechanisms.The functional entities needed to support the considered WATM architecture are as fol-lows. In the MT, a specialized entity performing mobility control is introduced. This entity isreferred to as Mobility Management and Control (MMC). MMC is responsible for registering(de-registering) the MT in the network, and requesting handover or location update. MMC,upon noti�cation by the lower layers on the changes experienced over the radio channel, is ableto determine the type of handover (backward or forward), or location update that should berequested from the �xed network entities. Conventional signaling is left to an ATMF UNI 3.1[ATM94] compatible entity. On top of this, a new entity, called Call Control and Signaling(CCS), is introduced to communicate with MMC (e.g., respond to queries for connection char-acteristics, receive the MT addresses). Both the MMC and ATM Forum UNI 3.1 protocolsrely on Signaling ATM Adaptation Layer (SAAL) [ITU94a],[ITU94b] for assured transfer ofsignaling information.Further to the above-mentioned entities, in the MT, there is a need for the introduction ofa wireless Medium Access Control (WMAC) entity [Bau96]. WMAC helps obtaining control ofthe shared medium, performs association or de-association with BSs, routes ATM cells to thephysical layer (and vice versa) and noti�es MMC on the status of the radio link. Its counterpartis located in the BS. In the BS, apart from the MAC layer, a Radio Resource Manager (RRM)is also needed. Such entity retrieves long and short term tra�c characteristics from the MACentity and performs Connection Admission Control (CAC) for the wireless part of the network(Wireless CAC - WCAC).The EMS incorporates conventional signaling entities (Q.2931 [ITU95], PNNI protocol) aswell as a signaling entity intended for mobility management and control (MMC). The latterentity communicates with RRM by means of the BSMP. On top of the Q.2931 and NNI signalingmodules there is a module called Resource Manager (RM) that is responsible for performing thenecessary Call Admission Control (Fixed CAC -FCAC), Routing and Addressing proceduresfor the �xed part of the network. New or diverted (due to handover) connections are admittedin a speci�c BS, only if both the WCAC and the FCAC prove successful. MMC is responsiblefor coordinating both tasks and reaching a combined decision.In terms of module-entity instances, there is a one-to-one mapping between RRM and BSs(each BS has an RRM instance). There is also a one-to-one relationship between active MTsand MMC instances residing within the EMS. The same applies to RM. In each MT, only oneMMC and one CCS instance are needed.The entity responsible for the execution of the location management and registration mech-anisms is called Location Agent and is located in every EMS. Each location agent has three

roles:1. \Home location agent"maintains the user pro�le of the MTs using the EMS as its homeswitch; it maintains the current location of the aforementioned MTs (in terms of MFAs);it replies to inquiries received by other location agents, and assigns to the MTs theirMobile Home Address upon registration.2. \Visited location agent"located in the serving EMS, maintains part of the user pro�le ofthe visited MTs, and provides to those belonging in a di�erent home area, their ForeignMobile Address.3. \Inquiring location agent"performs queries about the current location of a MT (i.e., thecurrent MFA), and triggers the routing of a connection setup to the address received asresponse.Figure 2 presents the control plane deployed in the various components of the networkarchitecture. Gray lines denote logical interfaces between the various higher layers of thearchitecture. As can been seen from this �gure, standard signaling is left una�ected. The onlymodi�cations done to the existing infrastructure, involves the addition of new interfaces withthe controlling entities of standard signaling (i.e., CCS, RM). These entities receive signals fromthe mobility related modules (i.e.,MMC, location agent), and translate them internally, to theappropriate primitives used on their interface with the standard signaling, and vice versa.It is apparent that for the NNI interface two new protocols are needed:1. Inter-MMC (IM): For the communication of two EMS-MMCs2. Location Management Protocol (LAMPS): For the communication of two location agents.The �rst protocol is used for the execution of inter-switch handovers and is out of the scopeof this paper. The second protocol is used for location update, user pro�le distribution andlocation inquiries. This protocol will be presented in detail below.The ow of the signals by these two new protocols can be carried either on pre-reserved VCsor using a connectionless protocol. These VCs are called Mobility Control Channel (MCC) andLocation Control Channel (LCC) accordingly. Note that MMC is only used for the executionof handovers and standard call procedures, since registration and location update functionalitylie inside the location agent entity.4. LAMPS DescriptionIn a network, like the one presented in Section 3, the number of switches and mobile users istoo large for PNNI ooding of information to advertise the extended addresses of the MTs, sinceit would create huge routing tables in the switching nodes. Thus, a special location managementtechnique is needed. In our proposed mechanism, the network is logically divided into LocationPeer-Groups (LPG). A LPG is de�ned as the set of switches that when a MT moves between

them does not need to acquire a new address. In terms of PNNI peer groups, a LPG containsthe same area of a PNNI peer-group of a level de�ned by the network administrator. One RImay consists of one or more LPGs. Every LPG may contain one or more PNNI peer-groups.Once a PNNI group of level i is de�ned as a LPG, then no other LPG of a higher or lower levelcan be de�ned.In Figure 3, four LPGs are illustrated. LPG1 consists of all A.1 switching nodes, LPG2 andLPG3 consist of switches A.2.1 and A.2.2 respectively, and LPG4 consists of all B switchingnodes. Nodes A and B are considered to be of PNNI level 1, nodes A.1, A.2, B.1, B.2 of level 2,and all other nodes are considered to be of level 3. If for example, a MT with permanent addressA.1.1.z moves from node A.1.1 to node A.1.2, the ooding of information will contain thisaddress expanded only inside the A.1 PNNI peer-group. Outside A.1 , the routing informationwill be of the form: A.1.* through A.1, due to the PNNI summarization of routing information.If however, the MT moves from A.1 to A.2 PNNI peer-groups, it will acquire a temporaryaddress that will be native to the EMS it associates with. The new EMS will not advertise thenewly arrived MT, since its new address is a native address of the switch. However there willbe some extra ooding of information inside PNNI peer-group A.1, to notify the switches thatthe MT is no longer inside their LPG.Each MT is related to an EMS that usually uses to register to the network. This switchis called the home switch - HEMS for that particular MT and it is identi�ed by the pre�x ofthe \permanent"ATM address of the MT, (called the Mobile Home Address, MHA). Whileroaming in another LPG, the mobile terminal acquires a \temporary"ATM address, called theMobile Foreign Address (MFA). The pre�x of the MFA identi�es the visited EMS (VEMS).The HEMS is responsible for keeping the mapping between the MHA and MFA. Whenever aMT registers in a di�erent LPG, a MFA is assigned to it, and its HEMS is noti�ed about itsnew location. The HEMS also manages user pro�les and security information for all the MTsthat use this switch as their HEMS. The HEMS can be considered to perform similar actions asthe GSM HLR. The VEMS keeps similar information about the MT, but locally. The VEMSfor a MT executes similar functions as the GSM/VLR.The PNNI ooding is used inside the LPGs for routing all incoming connections to theVEMS the MT is currently attached to. In other words, the VEMS announces, using the PNNI ooding, that the MT is connected to it. All switches of the LPG (EMSs and standard switches)route incoming connections to the speci�c VEMS. The ooding is limited to the LPG area asthe addresses used (MHA/MFA) are native addresses in the address summarization inside thepeer group.To summarize:1. HEMS knows the LPG the MT is located in and acts as GSM/HLR.2. VEMS provides the MT with a MFA, and acts as GSM/VLR.3. All nodes of the LPG know the currently used serving EMS for a MT.

An example of the routing information that exists in a EMS is illustrated in Figure 4. Inthis example, each RI consists of one LPG. Inside each LPG there are however more than onePNNI peer groups.The PNNI routing table of EMS A.1.2.1 contains the necessary informationfor routing connections in neighboring EMSs. In this example, all setup messages for the MTsA.1.1.*, A.1.2.2.* and A.1.2.3.* are routed to A.1.1, A.1.2.2 and A.1.2.3 respectively. For theMTs A.1.2.3.5 and A.1.2.3.6 the calls will be routed to the EMS A.1.2.2 where they are currentlylocated. The location agent routing table of the EMS A.1.2.1 has the mapping between theMHA and MFA for all MTs with an address A.1.2.1.x. In this example, inquires about thelocation of the MT A.1.2.1.7 will receive as a reply the MFA C.1.1.1.5. All incoming calls tothe MT A.1.2.1.7 will be routed to the serving EMS of the MT (C.1.1.1). The serving EMSwill forward the setups to the MT using its MFA.4.1 Registration and location updateDepending on which LPG a MT uses to enter to the network, two types of registrationprocedures exist. The �rst one takes place when the MT registers to the HLPG, while thesecond situation arises when the MT registers in a Visited LPG (VLPG).4.1.1 Registration in the Home Location Peer-GroupWhen a MT registers in its HLPG, either in its HEMS or not, only its MHA is used. Afterthe registration procedure is completed, the PNNI ooding is used to notify the appropriatenumber of switches inside the LPG about the entrance of the MT in the network. The exactnumber of switches that are noti�ed depends on the the relative position of the HEMS andthe newly associated EMS. For example in Figure 5, if the MT A.1.3.4 registers in its HEMS(A.1.3), then no unsummarized information is ooded inside the HLPG, since the MHA is anative address of the HEMS. If however, the same MT registers in EMS A.1.1, then all switchesA.1.* will receive the unsummarized information about the exact location of the MT.4.1.2 Registration in a Visiting Location Peer-GroupWhenever a MT registers in a LPG di�erent from its home, it initially informs the newswitch about its MHA. The pre�x of the MHA identi�es the HEMS of the MT. The HEMSis then noti�ed about the entrance of the MT in the network and security and authenticationprocedures will take place. Upon successful completion of these procedures, the MT receives aMFA. This address is also stored in its HEMS.Note that since the MFA is a native address of the VEMS, the registration of the MT willnot cause any additional PNNI ooding of information inside the VLPG. In other words nativeMFA addresses are used instead of the MHA to cut down the number of PNNI routing updates.For example consider the network of Figure 5 that consists of three RIs. In RI I, thereare two LPGs, the �rst of them containing two PNNI peer groups while the second containsonly one. Whenever the MT A.1.3.4 registers to a VEMS (e.g., A.3.3) of the same RI or toa VEMS of a di�erent RI (e.g., B.1.2), then the MT will acquire a temporary MFA, and theHEMS is noti�ed. Since the MFA, is a native address of the switch the MT has registered to,no additional PNNI ooding is done. The MFA reachability information is ooded with the

summarized native addresses of the serving EMS.4.1.3 Location UpdateLocation update takes place each time a MT moves either inside a LPG or through LPGs.In the �rst case the PNNI ooding of routing information is used to update all nodes aboutthe current location of a MT. For example in Figure 5, if the MT A.1.3.4 moves to A.1.1 thenall switches A.1.* are noti�ed by the PNNI. Again the exact number of switches that receivesuch information depends on the relative positions between the old VEMS and the new one. IfA.1.3.4 moves from the PNNI Peer Group 1 (PG1) to a switch of PG2 (e.g., A.2.1), then allA.* switches will be noti�ed.If a MT moves between LPGs then the registration procedure takes place (i.e., the MTreceives a MFA), and the switches of the old LPG are also noti�ed that the MT is no longer intheir area. For example if MT A.1.3.4 moves from A.2.1 to A.3.3 (e.g., inside LPG2), then allswitches of LPG1 (e.g., switches A.*) will be noti�ed that this MT is no longer inside LPG1.The HEMS does not need to be informed when the serving/visited EMS is changed insidethe same LPG. The identity of the new EMS is ooded inside the LPG and security, servicepro�le and charging information can optionally be transferred to the new serving EMS.4.2 Location Inquiring - TrackingLocation inquiring is performed whenever a call setup towards a MT is executed. The �rstEMS that receives a setup message for a MT interrogates the HEMS of the MT about the exactlocation of the MT. The protocol used for this interrogation can be a proprietary protocol, orthe evolution of a standard one such as GSM/MAP. The HEMS to be interrogated is derivedby the MHA pre�x. The routing of these signaling messages is done via the LCCs, based onthe information stored inside the PNNI routing tables.In case there are no EMSs on the route of the setup message, the setup will eventually reachthe HEMS of the MT and will be routed to the current location of the MT. The same scenariocan be used in other cases, where for example location con�dentiality is required.For location tracking to work properly in LAMPS two modi�cations are needed [ACH97].Firstly, there is a need for separating the address space for MTs and Fixed Terminals (FTs).This is necessary since no location inquiry phase is necessary when the called terminal is aFT. Furthermore, since a call setup is further processed in an inquiring EMS, the standardfunctionality of the PNNI Designated Transit List (DTL) has to be altered.In PNNI source routing is used. This means that the �rst node of a peer-group that receivesa setup message calculates the most appropriate path for the connection inside the peer-group,and stores it inside the DTL. In LAMPS, the inquiring EMS becomes aware of the exactlocation of a MT (i.e., receives its MFA), the DTL must be re-calculated. The di�erence withthe standard use of DTLs, is that the inquiring EMS will not always be the �rst node thatreceives the setup message inside a PNNI peer group. Thus, all EMSs, even if they are locatedin the core of a PNNI peer group, need to be able to alter the existing DTLs for a setup message.4.3 Call Setup

For the call setup procedure to be executed, the MHA is initially used. If the called MThas moved in a new LPG, its MFA is required for the call setup to be properly routed. The�rst EMS that intercepts this setup message will use the location inquiring procedure describedin the previous section, to obtain this information. The next step is for the inquiring EMS tosend a call setup towards the called terminal in its current LPG. Inside the LPG the setupwill eventually reach the VEMS with which the MT is currently associated. In order for thisto take place, the PNNI ooding of routing information is used inside the target LPG as wellas the crankback and alternate routing. Note again that each time the MT moves inside thesame LPG, PNNI signals update the routing tables of all nodes about the current location ofthe MT.In Figure 6, an example of a Call Setup is presented. In this scenario it is assumed thatthe calling terminal (CT - B.1.4.7), �xed in this example, is attached to B.1.4. This terminalissues a call setup (step 1) for the MT A.1.3.4 The setup message reaches EMS B.1.2 (step 2),that recognize the called address to be the one of a MT. In order to �nd the current locationof the MT it inquires its HEMS (step 3-4). The HEMS address is derived from the pre�x ofthe MT's MHA (A.1.3). When location inquiry is completed, B.1.2 has the MFA of the MT(A.3.3.9), and issues a call setup towards the serving EMS of the MT (B.3.3 - steps 5-8).With this mechanism, if the number of EMSs in the network is small, there is a possibilitythat the established connections may have non-optimum paths. For example if there was noEMS inside LPG3, then the setup message would be forwarded in the HLPG of the MT,even though the MT is not currently located there. The �rst EMS inside the LPG1 that wouldintercept the setup message, would inquire about the MFA of the MT, and the connection wouldbe established from the inquiring EMS, to the current location of the MT. The advantage ofLAMPS is that when the percentage of EMSs increases the probability of having misroutedconnections drops signi�cantly, as it will be shown by the analysis.5. Evaluation of LAMPS5.1 Short comparison with other schemesIn this section, we discuss the main di�erences (and advantages) of LAMPS in comparisonto the mechanisms described in Section 2.One of the major advantages is that no location registers are used (only location agents thatstore the mapping between the MHA and the MFA). This means that there is no need for de-ploying new routing algorithms or components for exchanging location management messages.Secondly, by separating call setup from location inquiry, connections with optimal routing canbe achieved. Thus, there is no need for route optimization mechanisms. This is especially truewhen the number of EMS inside the network is large.Furthermore, since the PNNI functionality is used during call setup, the route to a MT,even if it has moved from its previous location, is done automatically, thus, eliminating theneed for forwarding pointers. Another major advantage is that since location inquiry is anautonomous operation, the primitives used by the location agents can be identical to the ones

Switching Node TypesNotation Descriptiono; n Old and New node due to a MT moveh; v Home and Visited node of a MTr Registration node of a MTs Standard switch (SW) node from which a call is initiatede The �rst EMS node that intercepts a call set-upTable 1: Node types used in the analysisused in existing standards (e.g., GSM/MAP)and their future modi�cations. This feature canbe very useful if the MTs of the CPN can call, or be called by terminals that roam in otherprivate or public networks.Location management in LAMPS requires less bandwidth and processing requirements thanthe other Mobile PNNI proposals, since the signaling messages of LAMPS are lighter than thecall-setup message of PNNI. Moreover, this approach presents the need for minimummodi�ca-tions in the PNNI functionality, and the functionality of the location agents seems to be easyto implement.The major drawbacks of LAMPS is the required separation of the address space and thealteration of the standard procedure of the DTLs calculations.5.2 Cost AnalysisThe cost analysis of LAMPS will be based on the work described in [VEE97]. A frequentlyused term is the ancestors-are-siblings level aij, that is the level at which the ancestors of twonodes i and j belong to the same PNNI peer group. Figure 7, shows aij for three nodes x, y, zin the PNNI hierarchy. The enumeration of PNNI levels starts from the topmost hierarchicallevel downwards. For the example of Figure 7, axy > axz = ayz. Also the following relationsare true for the ancestors-are-siblings of any three nodes:axy < axz =) ayz = axy (1)axy = axz =) ayz � axz (2)The parameters x; y and z take one of the values in Table 1.There are three di�erent functionalities involved in LAMPS, that is power-on/o�, locationupdate due to a MT's move and location tracking to serve new calls. The performance ofLAMPS will be studied separately for these functionalities due to di�erent �gures of meritinvolved. For power-on/o� and location update the cost used to evaluate LAMPS' performanceis based on the number of switching nodes that receive new reachability information and thecost for notifying the HEMS, each time a MT enters the network, or moves between switchesrespectively. For location tracking the cost is based on the number of misrouting switches, acall has to traverse to reach the called MT plus the cost for the interrogation of the HEMS. We

Cost TypesNotation DescriptionUaij The cost for updating, using the PNNI procedures, the reachabilityinformation sent by node i to all nodes k such that: aik � aijt The cost for transferring the user pro�le and notifying the HEMS� The cost for interrogating the HEMS by an EMS of the HLPG� The cost for interrogating the HEMS by an EMS outside the HLPGDse +Dev �Dsv The number of the misrouted switching nodes on the route froma standard switch (from which a call is initiated) to the called MTDse is the number of the switching nodes on the route froma standard switch to the �rst intercepting EMS.Dev is the number of the switching nodes between the�rst EMS that intercepts the call set-up messageto the EMS that is currently serving the called MTDsv is the number of nodes between the standardswitch and the serving EMS of the called MTTable 2: Node types used in the analysisassume that the MT-serving EMS communication cost is 0. The costs for the aforementionedoperations are summarized in Table 2.We further de�ne the \Radius"R of a LPG as the level in the PNNI peer-group hierarchywhich explicitly determines the speci�c LPG. For simplicity, we assume that all LPGs radii arethe same. We remind the reader that a MT that moves between nodes in the same LPG doesnot acquire a new address.5.2.1 Power-on/o� and Location Update CostsThe cost of distributing the reachability information (Uaij ) is calculated as in [VEE97] i.e.,Uaij = LYk=aij nk � 1where nk is the number of switching nodes in a PNNI peer group at level k. In other words thecost Uaij expresses the number of physical nodes that are under the area de�ned by the PNNIgroup of level aij and receive reachability information.For the power-on and power-o� cases we need only to consider the relation of R and ahr.This is because the location update cost di�erentiates in two cases.� If ahr < R then the MT registers inside a FLPG (Foreign LPG) and consequently it willget a new MFA from the new serving EMS. In this case the \PNNI summary address"isused and no extra ooding is necessary. The only cost is due to transferring the userpro�le and notifying the HEMS of the MT that is t.

Power-on/o� ProcedureRelative Location MLAMPS Cost MPNNI Costahr < R t Uahv + 1ahr � R Uahr US + tTable 3: Location Update Costs for the Power-on/o� procedure� If ahr � R then the cost depends on whether the MT registers in the HEMS or not. Ifthe MT registers in the HEMS then the location update cost is 0 since no extra oodingis necessary (i.e., the MHA is a native address of the HEMS). The only case of interestis when the MT registers inside its HLPG (Home Location Peer Group) but not at itsHEMS. Then reachability data have to be sent by the registration node r to all nodes jsuch that ajr � ahr.Exactly the same analysis applies for the power-o� procedures. The aforementioned cases aresummarized in Table 3, where the relative costs from [VEE97] are also shown. For comparisonpurposes it is assumed that the are de�ned by the radius R of an LPG and the area de�ned bythe PNNI scope parameter S are the same.Their major di�erence is that whenever a MT registers in a di�erent home area, in LAMPSit will acquire a native address and only the HEMS will be noti�ed. In [VEE97] however, sincethe MT does not receive a MFA, all the switches of the new area will have to be informed. Inthis comparison, it is assumed that the cost of setting forwarding pointers in the home switchand The cost for notifying the HEMS are the same (i.e., t).In the case of Location Update costs due to a move of the MT we have to consider whetherthe move is between two nodes in the same LPG or not. In the �rst case (aon � R), the cost isonly Uaon. If however the mobile moves outside a LPG, then we have to di�erentiate whetherthe move is towards/from the HLPG of the mobile or not.� In case a MT enters its HLPG (ahn � R) there is a cost of updating reachability data,sent by the new switching node to all nodes j of the HLPG, such that ajn � ahn. Weshould also consider the cost of updating reachability data sent by the old node to allnodes i, of the old LPG, such that aio � aor. In summary, the total cost for this case isUaro + Uahn.� In case where the MT moves to a new node which is outside the HLPG (ahn < R), therelative location between the old serving EMS and the HEMS is of importance.1. If the home and the old node are in the same LPG (aho � R), the total locationupdate cost is Uaho + t. The �rst term caters for the updating reachability data sentby the old node to all nodes j such that ajo � aho, whereas the second term catersfor transferring the user pro�le from the MT's HEMS to the new serving EMS. Thistask is necessary, since the new node and the home node belong to di�erent LPGs.

Move ProcedureRelative Location MLAMPS Cost MPNNI Cost (S = R)aon � R Uaon Uaon + 1aon < R ahn � R Uaro + Uahn US + Uahn + t+ 1aon < R ahn < R aho � R Uaho + t US + Uaho + 2taon < R ahn < R aho < R Uaro + t 2US + 2tTable 4: Location Update Costs for the Move procedure2. If the old node resides in a LPG di�erent than that of the home node, the total costis Uaro + t. This is because, there is only a cost of updating reachability data sentby the old switch to all nodes j such that aoj � aro plus the cost of transferring theuser pro�le and notifying HEMS.Table 4 summarizes the cases described previously. This table also contains the correspond-ing costs of [VEE97]. In all rows, the areas where ooding of routing information takes place,denoted by S (i.e., PNNI scope) and R (i.e., LAMPS radius of a LPG), have been assumed thesame for both mechanisms (i.e., S = R). The main di�erence of the two mechanisms appears inthe three last rows of Table 4. In LAMPS, whenever a MT changes LPGs only those switchesthat lie between the old location and the registration switch will have to be informed. This isnot the case in [VEE97] where the movement between di�erent areas causes all of the switchesin the previous/new PNNI group to be informed.For simplicity sake we will upper bound the cost Uaro by UR. Thus, assuming that we knowthe probabilities Pfaon = ig; Pfahn = ig, Pfaho = ig, and that the number of peer group levelsin the network is L, the average update cost per move is given byMLAMPS =LXi=RPfaon = igUaon + R�1Xi=1 Pfaon = ig �8<: LXj=RPfahn = jg (UR + Uahn) + R�1Xj=1;j 6=iPfahn = jg (UR + t)+Pfahn = ig8<:R�1Xj=i Pfaoh = jjahn = aon = ig (UR + t)+ LXj=RPfaoh = jjahn = aon = ig (Uaoh + t)9=;9=; (3)5.2.2 Location Searching CostsFor the computation of the location searching cost we further de�ne:

� q: the probability that the call is initiated by a terminal attached to an EMS and,� p: the fraction of the EMSs to the total number of nodes in the network.The location searching cost is computed based on the number of the additional nodes thatthe call set-up message has to traverse. The reason for having misrouted connections is that,a call is heading to the HEMS of the called MT, until the current location of this terminal isresolved. In case the call setup is initiated from a MT, or a �xed terminal attached to an EMS,then we have no misrouted calls since the serving EMS will resolve the exact location of thecalled MT before establishing a connection.To the number of misrouted nodes we also add the cost of performing the inquiry to theHEMS of the called MT. Thus, if for example, the calling terminal is attached to a standardswitch and the �rst EMS that intercepts the call set up resides in the HLPG of the called MT,the total searching cost is: Dse +Dev �Dsv + �If however, the �rst EMS that intercepts the call set up is outside the HLPG of the calledMT, the total searching cost is: Dse +Dev �Dsv + �Assuming an average length of the shortest path between nodes of a peer group at level iequal to pi, the costs Dij are calculated byDij = LYk=aij pk (4)Note that if the calling terminal is attached to an EMS, then the inquiring EMS is theserving EMS thus, Dse = 0 and Dsv = Dev so that the cost is only due to performing theinquiry (� or �). This suggests the incorporation of the probability q in our analysis.Various cases arise depending on the relative location of the calling terminal, the called MTand the home EMS of the called MT. These cases along with their accompanying costs forthe cases of calling terminal attached to a standard switch (SS) and to a EMS are depictedin Table 5. The �rst three rows of Table 5 are explained as follows. When ahv � R the callset-up message, which is targeted towards the home node of the called mobile, follows the rightdirection, and there is no misrouting. If the �rst EMS that intercepts the call setup is outsidethe LPG of the called mobile the cost is only due to performing an inquiry in which case is�. If however, the �rst intercepting EMS has the exact routing information of the MT (i.e.,aeh � ahv), the inquiring cost is 0; otherwise (i.e., aeh < ahv), the intercepting EMS will haveto interrogate the HEMS of the MT, and the cost is �.The contribution of these rows (rows 1 to 3 of Table 5) to the average searching cost isA(�; �; q; p) = LXi=RPfahv = ig �8<: i�1Xj=RPfaeh = jg � �+ R�1Xj=1 Pfaeh = jg � �9=; (5)

Location Searching Costs: SLAMPSRelative Location Cost (SS) Cost (EMS)ahv � R aeh � R aeh � ahv 0 0aeh < ahv � �aeh < R � �ahv < R aeh � R ase > aev Dse + � �ase < aev Dev + � �ase = aev 2Dse �Dsv + � �aeh < R ase > aev Dse + � �ase < aev Dev + � �ase = aev 2Dse �Dsv + � �Table 5: Location Searching Costs SLAMPSFor the next three rows of Table 5 (rows 4 to 6) we argue as follows. Consider �rst the case ofa call initiated by a terminal attached to a standard switch. This event has probability 1 � q.If ase > aev (row 4) then by using (1) we obtain asv = aev and therefore Dse+Dev �Dsv = Dse.To this misrouting cost we have to add the inquiry cost, which is � due to the fact aeh � R.Similarly, if ase < aev (row 5) we obtain asv = ase and therefore Dse +Dev �Dsv = Dev. Thetotal cost in this case is equal to Dev + �. For row 6 we have ase = aev with a correspondingtotal cost equal to 2 �Dse �Dsv + �. If the call is initiated by a terminal attached to a EMS(probability q) the cost is simply �. The contribution of rows 4 to 6 of Table 5 to the averagesearching cost isB(�; �; q; p) =R�1Xi=1 Pfahv = ig LXj=RPfaeh = jg0@(1� q) � 24 LXm=i+1Pfase = mg(Dse + �) + i�1Xm=1Pfase = mg(Dev + �)+Pfase = ig � LXm=iPfasv = mjaev = ase = ig � (2Dev �Dsv + �)#+q � LXj=RPfaeh = jg�1A (6)Note that we have expressed this cost as a function of four parameters �; �; q and p. Al-though, the role of �; � and q is clear, the in uence of the parameter p is hidden, as we will seelater, in the calculation of the used probabilities.Similar arguments hold for the last three rows of Table 5. The contribution of these termsto the averaging searching cost isC(�; �; q; p) =

R�1Xi=1 Pfahv = ig( (1� q)�"i�1Xj=1Pfaeh = jg �8<: LXm=j+1 Pfase = mg(Dse + �) + j�1Xm=1Pfase = mg(Dev + �)+Pfase = jg � LXm=j Pfasv = mjaev = ase = jg(2 �Dse �Dsv + �)9=;+R�1Xj=i+1Pfaeh = jg �8<: LXm=i+1Pfase = mg(Dse + �) + i�1Xm=1Pfase = mg(Dev + �)+Pfase = ig LXm=iPfasv = mjaev = ase = ig(2 �Dse �Dsv + �)!) +Pfaeh = ig � LXm=iPfaev = mg �24m�1Xn=1 Pfase = ng(Dev + �) + LXn=m+1 Pfase = ng(Dse + �)+Pfase = mg � LXn=mPfasv = njaev = ase = mg(2 �Dse �Dsv + �)##q � R�1Xj=1 Pfaeh = jg�9=; (7)Note that in the third line of the previous equation it holds that aeh < ahv and thereforeaev = aeh. This means that Dev = Deh. Similarly in �fth line we have Dev = Dhv . Summingequations (4) - (6) we obtain the total average searching cost.SLAMPS = A(�; �; q; p) +B(�; �; q; p) + C(�; �; q; p) (8)The required probabilities for the calculation of the average move and searching cost aregiven in the appendix.For comparison purposes, Table 6 gives the corresponding search cost of [VEE97]. The maindi�erence of the two mechanisms is that in LAMPS even if the calling terminal and the calledterminal are inside the same LPG (di�erent from the HLPG), the HEMS has to be contactedin order to resolve the MFA. This is not the case in [VEE97], where, in this case, the callingterminal knows (in most of the cases) the exact location of the called MT. On the other hand,in situations (Figure 8) where the calling terminal knows nothing about the current location ofthe called terminal, LAMPS results in shorter misrouted paths than the mechanism of [VEE97].This is because, the �rst EMS that intercepts the call setup will start forwarding the call setuptowards the current location of the called terminal. The relative gain of the two mechanismswill become apparent in the following section.5.3 Analysis ResultsThe parameters used for the analysis are given in Table 7. In Figure 9, we illustrate the

Location Searching Costs: SPNNIRelative Location Costahv � S 0acv � S 0ahv < S acv < S ahv < ach Dchahv < S acv < S ach < ahv Dhvahv < S acv < S ach < S ach = ahv 2 �Dch �DcvTable 6: Location Searching Costs in SPNNIParameter ValueL 10pi; 1 � i < L 2pL 5ni; 1 � i < L 5nL 10� 1Table 7: Parameters used in the analysisaverage move cost (MPNNI, MLAMPS ), as a parameter of t (i.e., the cost of updating theHEMS and transferring the user pro�le) for various values of S and R. As can be seen from this�gure MLAMPS cost is always lower than MPNNI. This is expected since in LAMPS fewernetwork components need to store and update the information of the current location of a MT(i.e., no need for forwarding pointers). This di�erence is expected to grow if Uaro is calculatedappropriately instead of using its upper bound UR.In Figure 10, we plot the average move cost di�erence vs. the values of S (PNNI scopeparameter) and R (LPG Radius). These parameters de�ne speci�c reachability update areas,and for comparison purposes they take the same values. For large values of R and S, the e�ectof the parameter t on the total cost is noticeable. This is because for large values of S and R thePNNI ooding of reachability information will reach fewer nodes. In these cases, the MTs willcross more frequently the boundaries of PNNI groups (or LPGs), necessitating the updating(e.g., forwarding pointers, transferring of user pro�le) more often. Since this updating dependson t, that has smaller weight in LAMPS, the cost di�erence of the two algorithms increases.In Figure 11, we present the average search cost di�erences vs �. The parameters p and qwere set equal to 0:5. As can be seen from this �gure when the value of � increases, SPNNIoutperforms LAMPS. For example for R = S = L � 3 and for � > 15, SPNNI < SLAMPS.This means that if the communication cost is not large compared to the misrouting cost thenLAMPS is preferable.Also observe that the relative cost di�erence decreases, when the parameters S and R

decrease. This is because SPNNI cost decreases dramatically when the area of nodes thatreceive reachability updates increases (i.e., more nodes know the exact location of a MT). InLAMPS however, the cost decreases smoothly, because during searching, the area of a LPGdoes not a�ect the operation the mechanism (i.e, the �rst EMS that intercepts a call setup,forwards it in the right direction).In Figure 12, we plot the average search cost di�erence as a parameter of the total number ofphysical nodes (i.e., the nodes presented in the lowest hierarchical level). The parameters usedare � = 10, p = q = 0:5, and � = 1. The average shortest path length pL was set depending onnL, according to (nL=5) � 2. In the aforementioned �gure, it is clear that when the number ofswitches (and the relative average shortest path) increases, LAMPS outperforms SPNNI. Thereason for this is that in LAMPS, the intercepting EMS will correct the heading of a call setupearlier avoiding in this way large misrouting loops.The average search cost for LAMPS vs. the fraction of EMSs to the total number of switchesin the network, is presented in Figure 13. As p increases the cost is stabilized due to the factthat an intercepting EMS is found in the neighborhood of the calling terminal with probabilityclose to 1. Also as the LPG area increases (more EMSs belong to the same LPG, thus higherthe probability of intercepting a call setup earlier), the average search cost decreases.Finally, the average search cost for LAMPS vs. q is presented in Figure 14. As q increases,more call are initiated by terminals attached to EMSs avoiding misrouted paths. The purposeof this test was to show the e�ciency of LAMPS in a network topology where standard switchesare simply used in the backbone. 6 ConclusionsIn this paper we have presented a new location mechanism (LAMPS) that combines thecharacteristics from the location register and mobile PNNI schemes. For this mechanism towork, minor modi�cations are needed in the PNNI functionality (modi�cation of the DTLfunctionality and addressing issues). LAMPS however inherits the advantages of the MobilePNNI schemes and the Location Register schemes, such as the usage of the PNNI routingprotocol, the light messages for location inquires, and the short misrouted paths.We have also presented the protocol stack and the the functional entities of the networkelements that can use LAMPS. Our protocol was designed in a way to take in considerationthe existence of switches that are unaware of any mobility procedures.LAMPS was compared to another Mobile PNNI scheme. In terms of location update costs ,LAMPS performs always better than the algorithm proposed in [VEE97]. Concerning Locationsearching costs, the relative performance depends on the communication cost between remotenodes. If this cost is small compared to the number nodes that form a misrouted path (i.e.management of network resources in terms of processing power and bandwidth), then LAMPShas a better performance.One of its major advantages is that the performance of LAMPS improves, when the numberof the EMS increases in the network, as well as when the majority of calls is initiated from

EMSs (i.e., MTs). The �rst feature will be proved a valuable asset in the evolution towardsthe wireless ATM era, whereas the second feature is useful in topologies where EMSs are usedin the access network and conventional ATM switches are used in the backbone.AppendixIn this section we present the probability distributions used in the analysis. Assuming auniform distribution of calls to a mobile, the probability Pfash = ig is simply the fraction ofthe standard switches for which ash = i. Thus,Pfash = ig = 8>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>:0; i = L+ 1nLLYk=1nk ; i = L(ni � 1) � LYk=i+1 nkLYk=1nk ; 1 � i < L (9)Note that Pfash = L+1g = 0 since h denotes the HEMS of the called mobile which cannot be astandard switch. The probabilities in the above relation do not depend on p since this parameterappears as a factor in the numerator and denominator and it is canceled out. Similarly, thedistribution Pfaehg is given byPfaeh = ig = 8>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>:1p � LYk=1 nk ; i = L+ 1p � nL � 1p � LYk=1 nk ; i = L(ni � 1) � LYk=i+1 nkLYk=1nk ; 1 � i < L (10)For aev and asv, we assume that they follow the same distributions as aeh and ash, respectively.The probabilities Pfahng, Pfahog and Pfahvg are as in [Vee97]:Pfahn = ig = Pfaho = ig = Pfahv = ig = fL�i+2 (11)with f suitably chosen to satisfy Pi Pfahn = ig = 1.Pfaong is assumed the same as in [Vee97]. However, since the number of the EMSs insidethe lowest PNNI group level (physical nodes) is p � nL, the number of base stations in a peernode of level k is N(k) = p �Nb NYi=k+1 ni (12)

with Nb denoting the number of base stations under a switch.The conditional distributions Pfasv = jjaev = ase = kg and Pfaoh = jjahn = aon = kg aregiven by the following relations:Pfasv = jjaev = ase = kg = 8>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>:0; j = L + 1nLL+1Ym=k nm ; j = L(nj � 1) � LYm=j+1 nmL+1Ym=k nm ; 1 � j < L (13)Pfaoh = jjahn = aon = kg = Pfaoh = jgL+1Ym=k Pfaoh = mg (14)We turn now to the calculation of Pfase = ig. This is the probability a standard switch(from where a call setup message originates) and the �rst EMS, that intercepts this message,satisfy ase = i. We �rst assume that a message entering a PNNI group, of the lowest level, willpass pL nodes before leaving this group. The probability of hopping on standard switches and�nally leaving the PNNI group is� = 8>><>>: pL+1Yi=1 (1 � p)nL � (i� 1)nL � (i� 1) !; (1� p) � nL � pL0; otherwise (15)There is a minor modi�cation of the above formula for the �rst PNNI group, containing theoriginating standard switch, but we ignore this optimization. If we further assume that thelength of the \shortest-path"between nodes of a peer group at level i is pi, then the desiredprobability is given byPfase = ig = 8<: �iL; � = 0A � (1 � �) � �QL�1k=i pi; otherwise (16)where �iL is the Kronecker's delta, and A is a constant such that Pi Pfase = ig = 1.References[ATM96a] The ATM Forum Technical Committee, ATM Forum af-pnni-0055.000 PrivateNetwork-Network Interface Speci�cation Version 1.0 (PNNI 1.0), March 1996.[ATM96b] The ATM Forum Technical Committee, ATM Forum af-sig-0061.000 UNI Signal-ing 4.0, July 1996.

[ATM95] The ATM Forum Technical Committee,ATM Forum af-bici-0013.003 B-ISDN InterCarrier Interface (B-ICI) Speci�cation, Version 2.0, December 1996.[ATM94] The ATM Forum Technical Committee,ATM Forum af-sig-0010.002 UNI Signaling3.1, 1994.[ITU94a] ITU-T Recommendation Q.2130, B-ISDN Signaling Adaptation Layer - Service Spe-ci�c Coordination Function for Support of Signaling at the User-to-Network Interface(SSCF at UNI), 1994.[ITU94b] ITU-T Recommendation Q.2110, B-ISDN Adaptation Layer - Service Speci�c Con-nection Oriented Protocol(SSCOP), 1994.[ITU94c] ITU-T Recommendation Q.2761, B-ISDN User Part - Functional Description, Oc-tober 1994.[ITU95] ITU-T Recommendation Q.2931, B-ISDN Digital Subscriber Signaling System No 2(DSS2 - UNI), Layer 3 Speci�cation for Basic Call/Connection Control, 1995.[Rau97] K. Rauhala, Baseline Text for Wireless ATM speci�cations, ATM Forum BTD-WATM-01-05, 1997.[Kal98] A. Kaloxylos S. Hadjiefthymiades and L. Merakos, Mobility Management and Con-trol Protocol for Wireless ATM Networks, IEEE Network Special Issue on PCS NetworkManagement, May 1998.[Lin95] Y. B. Lin and S. K. DeVries, PCS Network Signaling using SS7, IEEE Personal Com-munications, June 1995.[Mou92] M. Mouly and M. B. Pautet, The GSM system for mobile communications, 49 rueLouise Bruneau, Palaiseau, France 1992.[EIA95] EIA/TIA IS-41 Rev C., Cellular Radio Telecommunications Intersystem Operations,November 1995, TIA/EIA PN-2991.[Kri96] B. Krishna, N. H. Vaidya and D. K. Pradhan, E�cient Location Management inMobile Wireless Networks, Department of Computer Sciences, Texas A&M University,Technical Report #96-030.[Noy94] A. Bar Noy and I. Kessler, Mobile Users: To Update or not to update?, Proceedingsof IEEE INFOCOM'94, pp 570-576, 1994.[Ho96] J. Ho and I. Akyildiz, Local Anchor Scheme for Reducing Location Costs in PCNs,IEEE/ACM transactions in Networking Vol. 4, No 5, October 1996.

[Aky96] B. Akyol and D. Cox, Handling Mobility in a Wireless ATM Networks, Proceedingsof Infocom'96, 1996.[Hac97] A. Hac and Z. Zhiou, Locating Strategies for Personal Communication Networks: ANovel Tracking Strategy, IEEE Journal on Selected Areas in Communications, Vol. 15,No 8, Oct 1997.[Vee96] M. Veeraraghavan and G. Dommety, Location Management in Wireless ATM Net-works, ATMF Contribution 96-1500.[Por96] J. Porter and D. Gilmurray,Tunneled Signaling for the Support of Mobile ATM, ATMFContribution 96-1699.[Ach97] A. Acharya J. Li, B. Rajagopalan and D. Raychaudhuri, Mobility Management inwireless ATM Networks, IEEE Communications Magazine, November 1997.[Ach96] A. Acharya and D. Raychaudhuri, Primitives for Location Management and Hando�in Mobile ATM Networks, ATM Forum contribution 96-1121, August 1996.[Raj97] B. Rajacoplan, H. Mitts, A. Massarella et. all, Reference Con�gurations and anArchitectural Model for Location Management in WATM Networks, ATMF Contribution97-1041, December 1997.[Vee97] M. Veeraraghavan and G. Dommety,Mobile Location Management in ATM Networks,Journal on Selected Areas in Communications, Vol 15, No 8, October 1997.[Bau96] F. Bauchot, G. Marmigere, L. Merakos, N. Passas and S. Decrauzat, MASCARA,A MAC Protocol for Wireless ATM, Proceedings of the ACTS Mobile CommunicationSummit '96, Granada, Spain, November 1996.[Noe97] A.R. Noerpel and Y.-B. Lin, Handover Management for a PCS Network, IEEE Per-sonal Communications Magazine, Vol 4, No 6, 1997.

MT

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I

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BS 1Figure 1: Network Topology

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Mobile Terminal Base Station EMS1 EMS2

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B

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A.1.1A.1.2

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Level 1

Figure 3: De�nition of LPGs

PublicNetwork

A.1.2.1 PNNI Routine Table

MTMHA=A.1.2.1.7MFA=C.1.1.1.5

MT MT

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A.1.1 A.1.2.1.7

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C.1

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2.533.544.555.566.57

0 5 10 15 20 25 30Move Cost t MLAMPS R = LMPNNI R = LMLAMPS R = L� 1MPNNI R = L� 1Figure 9: Average Move Cost vs. t

0.50.60.70.80.911.11.21.31.4

5 6 7 8 9 10S = RMPNNI �MLAMPSt = 6 33 3 3 3 3 3t = 12 ++ + + + + +t = 24 22 2 2 2 2 2

Figure 10: Average Move Cost Di�erence vs. S=R

-15-10-5051015

0 5 10 15 20 25 30�SPNNI � SLAMPS

p = 0:5q = 0:5� = 1nL = 10R = S = L � 5R = S = L � 4R = S = L � 3R = S = L � 2R = S = L � 1R = S = L

Figure 11: SPNNI � SLAMPS vs. �-50510152025

5 10 15 20 25 30nL (pL = (nL=5) � 2)SPNNI � SLAMPSp = 0:5q = 0:5� = 10� = 1 R = S = L � 5 3

3 3 3 3 3 3R = S = L � 4 ++ + + + + +R = S = L � 3 22 2 2 2 2 2R = S = L � 2 �� � � � � �R = S = L � 1 44 4 4 4 4 4R = S = L ?? ? ? ? ? ?

Figure 12: Average Cost Di�erence vs. nL

5.15.25.35.45.55.65.75.85.96

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9SLAMPS p� = 10� = 1q = 0:5 R = L 33 3 3 3 3 3 3 3 3R = L � 1 ++ + + + + + + + +R = L � 2 22 2 2 2 2 2 2 2 2Figure 13: Average Search Cost vs. p

55.25.45.65.866.2

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9SLAMPS q� = 10� = 1p = 0:5 R = L 33 3 3 3 3 3 3 3 3

R = L � 1 ++ + + + + + + + +R = L � 2 22 2 2 2 2 2 2 2 2R = L � 3 �� � � � � � � � �Figure 14: Average Search Cost vs. q