The Predictive User Mobility ProfileFramework for Wireless Multimedia Networks

Ian F. Akyildiz Wenye WangBroadband and Wireless Networking Laboratory Department of Electrical and Computer EngineeringGeorgia Institute of Technology, Atlanta, GA 30332 North Carolina State University, Raleigh, NC 27695

Email: ian@ece.gatech.edu Email: wwang@eos.ncsu.edu

Abstract – User Mobility Profile (UMP) is a combinationof historic records and predictive patterns of mobile termi-nals, which serves as fundamental information for mobilitymanagement and enhancement of Quality of Service (QoS) inwireless multimedia networks. In this paper, a UMP frame-work is developed for estimating service patterns and track-ing mobile users, including descriptions of location, mobility,and service requirements. For each mobile user, the servicerequirement is estimated using a mean square error method.Moreover, a new mobility model is designed to characterizenot only stochastic behaviors, but historical records and pre-dictive future locations of mobile users as well. Therefore, itincorporates aggregate history and current system parame-ters to acquire UMP. In particular, an adaptive algorithm isdesigned to predict the future positions of mobile terminalsin terms of location probabilities based on moving directionsand residence time in a cell. Simulation results are shown toindicate that the proposed schemes are effective on mobilityand resource management by evaluating blocking/droppingprobabilities and location tracking costs.

Keywords—Wireless Network, User Mobility Profile, Quality of Service,Mobility and Resource Management.

I. INTRODUCTION

Diverse mobile services and development in wireless net-works have stimulated an enormous number of people to employmobile devices such as cellular phones and portable laptops astheir communications means. The most salient feature of wire-less networks is mobility support, which enables mobile usersto communicate with others regardless of location. It is also thevery source of many challenging issues, relating to the mobil-ity and service patterns of mobile terminals (MTs), namely usermobility profile (UMP). For each mobile user, a UMP consists ofdetailed information of service requirements and mobility mod-els that is essential to Quality of Service (QoS) and roaming sup-port. In general, the applications of UMP can be categorized asfollows: Development and analysis of handoff algorithms. One of themost important QoS issues is to design efficient hanfoff algo-rithms to reduce handoff dropping probability caused by band-width shortage and mobility when mobile users move from onecell to another [13], [29].

This work is supported by NSF under grant ANI-0117840.

Call admission control (CAC) and resource management. Anefficient CAC algorithm demands the knowledge of UMP in or-der to accommodate the maximum number of users or to yieldmaximum system throughput [23]. Routing optimization. User mobility information can also beused to assist traffic routing in wireless networks to ease the bot-tleneck effect in overloaded base stations or access points [25]. Location update and paging. Many mobility managementschemes utilize UMP to improve system performance with re-gards to reducing signaling costs and call loss rates [8], [14].

Since mobility and resource management are critical to sup-porting mobility and providing QoS in wireless networks, it isvery important to describe movement patterns of mobile objectsaccurately. Moreover, the development of UMP frameworkswill benefit the evaluation of many design issues, such as rout-ing protocols and handoff algorithms. Consequently, there havebeen some efforts in predicting future locations of mobile users.In [2], the location probability at the time of a call arrival is cal-culated by assuming that the MTs take the shortest paths whenthey move from one cell to another with four possible directions.Another prediction method is proposed in [7] in which the nextprobable cell is determined based on path information. In [25], ahierarchical location prediction algorithm is described in whicha two-level user mobility model, global and local, is used to rep-resent the movement behavior of a mobile user. The next cell ispredicted by considering speed and direction of a user’s trajec-tory.

In [13], a bandwidth reservation scheme for handoff in QoS-sensitive cellular networks is introduced by using the estima-tion of user mobility. The authors focused their efforts on thepremise that handoff behavior of an MT is expected to be prob-abilistically similar to the users coming from the same pre-vious cell. Therefore, this estimation is based on statisticalmeasurement. A movement-based location management mech-anism based on historical records is proposed, assuming thateach terminal is equipped with a path length counter storingthe length of a user’s records and IDs of most recently visitedcells [18]. In [6], the authors proposed a model of mobilityprofiles that included the trajectory estimation of mobile usersand arrival/departure times in each cell along a terminal’s path.These cells constitute the most likely cluster into which a termi-nal will move.

As for the estimation of resource demands, two methods areproposed in [47]. One of them is based on the Wiener Process

which predicts the bandwidth requirement according to currentbandwidth usage. The other method is to use time series analysison the premise that future demand increments are related to pastvariations.

To summarize, most of the existing methods are aimed at find-ing the most probable cell [7], [25], [13], [18]. Also, there arevery limited efforts on estimating a group of probable cells ora cluster of cells without considering the historical records [2],[6], [9]. Oftentimes, the demand for multimedia services is nottaken into account, which is critical for efficient resource man-agement. Furthermore, UMP is not well defined, which shouldconsider the characteristics of users’ mobility and service pat-terns. In addition, most of the existing solutions do not providethe flexibility of prediction and quality demands.

Therefore, a framework for UMP is proposed in this paper,which includes the following contributions: A zone concept is proposed to add an additional level of lo-cation description for more accurate location prediction becausea zone is a subset of a location area (LA). The zone partitionis used to differentiate varying future locations of a mobile userdepending on its moving direction, thus reducing computationoverhead. A new framework of user mobility profile is designed to incor-porate service requirements and the mobility model. Based onthe valid time of each factor, the user information is categorizedinto quasi-stationary and dynamic UMP, which corresponds tolong-term and short-term information, respectively. By using an order-

Markov predictor, the service require-

ments of a mobile user are predicted based on the most recent records, aiming to minimize the mean square error. An adaptive prediction algorithm is developed to predict agroup of cells into which an MT will move by considering his-torical records, path information, moving direction and speed,cell residence time, and tradeoff of computation overhead. The implementation of the proposed scheme in third genera-tion (3G) wireless systems is discussed with respect to real-timemonitoring, measurement, and computation. The performance of the proposed scheme is evaluated byshowing its effect on mobility and resource management suchas location tracking costs and blocking/dropping probabilities.

The rest of this paper is organized as follows. In Section II, asystem model with cellular infrastructure is presented. Also inthis section, a new concept of zone is introduced for fine granu-larity of location description. A mobility model, which includesstochastic model, historical records, and predictive trajectory ofmobile terminals is also shown. In Section III, the framework ofUMP is defined, and it is categorized into quasi-stationary anddynamic UMP, in accordance with long-term and short-term in-formation. The estimation and prediction algorithms of servicerequirements and future location probabilities are presented inSection IV. A new algorithm is proposed to estimate the ser-vice pattern based on mean square error; and an adaptive ap-proach is established for prediction and management of UMP.This scheme is expected to derive location probabilities for agroup of cells instead of choosing the most probable cell. Thediscussion of implementation in real systems and other relatedissues is presented in Section V. In Section VI, we describe the

simulation model and the parameters used in our experiments.The effectiveness of the proposed schemes and application onmobility and resource management are shown in Section VII,followed by conclusions in Section VIII.

II. SYSTEM MODEL, LOCATION DESCRIPTION, ANDMOBILITY MODEL

With regard to different service coverage and infrastructure,such as wireless wide area networks (WWANs) and wireless lo-cal area networks (WLANs), a variety of wireless networks ex-ist. In this section, we describe the cellular infrastructure of awireless network based on which proposed schemes will be im-plemented. Then we present a new concept, zone partition for amore precise location description, followed by a mobility model,including stochastic behavior, historical records, and predictivefuture locations.

A. System Model

Consider a mobile wireless network with a cellular infrastruc-ture; e.g., General Packet Radio System (GPRS), which may beone of several macro-, micro-, and pico-cell systems. This wire-less mobile network provides diverse service applications suchas voice, audio, data, and video. A typical network is composedof a wired backbone and a number of base stations (BSs). EachBS is in control of a cell, and a group of BSs are managed bya mobile switching center (MSC) in circuit-switch domain anda serving GPRS supporting node (SGSN) in packet-switch do-main as shown in Fig. 1. Each BS is responsible for deliveringincoming and outgoing calls for the MTs residing in its coveragearea. If an MT is moving from one cell to another cell belongingto another MSC, location registration and identity authorizationneed to be carried out.

MSCMSC

BS

Cell

Fig. 1. System Architecture.

It is envisioned that in the future, mobile users will be able toroam between wired and wireless networks, with the expectationof the same QoS as they can expect in wired networks. How-ever, when an MT moves into an adjacent cell with an activeconnection, it must experience handoff or location registration,which may degrade QoS parameters such as connection delays,call dropping and packet losses. Thus, bandwidth needs to bereserved in advance so that mobile users do not have to wait forthe release or allocation of channels when they are in new cells.This requires the advance knowledge of service requirementsbecause either over- or under- reserved bandwidth will cause areduction in system throughput. Thus, it is necessary to predictservice requirements prior to the arrival of a request.

Here, we extend the shadowing cluster concept, which wasintroduced in [23]. The basic idea of the shadow cluster is that

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each MT with an active wireless connection will affect the band-width reservation in the cells along its moving direction. Asthis MT travels from one cell to another, the influenced cellsalso change over time. The home base station that is servingthe MT’s ongoing connection may estimate the probability thatthis MT will migrate to other cells, sending the respective up-dates with equivalent bandwidth requirements to the cells in theshadow cluster. Usually, in case of two-dimensional topology,hexagons are used to denote the cells; thus, each cell has sixneighbors, and the probability of an MT leaving along one sideis assumed as . However, this is not true for the MTs with anactive connection and a specific destination. Moreover, the orig-inal shadow cluster is proposed in the conceptual level withoutfurther discussion on how to form such a shadow cluster. Thus,we need to formalize shadow cluster in realistic environments.

Due to the process of location registration, which occurswhen an MT crosses the boundary of two LAs, the wireless sys-tem always knows in which LA the MT is located. However, anLA consists of many cells. In this paper, we propose a zone par-tition concept to improve the granularity of location description.A zone is a subset of an LA, which is composed of a group ofadjacent cells. We expect that the MTs in the same zone demon-strate the same, if not similar movement behavior. For example,in Fig. 2, the coverage of an MSC-A is an LA, i.e., MSC-A han-dles incoming and outgoing connections of the MTs who moveinside this LA. There are two MTs, and , which are currentlylocated in the coverage area of MSC-A and may possibly moveinto the area of MSC-B and MSC-C, respectively. The servicearea of each MSC is divided into zones ( ). The estima-tion of future locations of an MT based on its moving directionis presented in Section IV-C.

MSC−B

MSC−A

MSC−C

WZone 0

Zone 1 N

S

Zone 4

Zone 5

S

EW E

N

Zone 2

Zone 3

Zone 6αβ

Location Area

02

01

07

Fig. 2. Zone Partition.

There may be varying numbers of zones in real environments,depending on geographical circumstances and network architec-tures. For the sake of simplicity, we divide an LA into sevenzones in this context. If the radius of the coverage area of anMSC is , then zone is a region, which has the same centeras the whole area within the MSC with a radius of . The re-maining part is then divided uniformly by six, which results insix other zones. This can be implemented through grouping cellIDs based on the coverage area of each cell. For instance, cell 01and cell 02 may be assigned to zone 3, while cell 07 is assignedto zone 5. When the MT receives broadcast ID from the servingBS via down-link, the MT knows in which cell and zone it is

currently residing. Note that the zone partition is a geographi-cal sub-layer of a location area for micro- or pico-cell systems,providing a more accurate description of an MT’s position thanLAs because a zone partition has much less cells than those thatare included in an LA.

B. Location Description

Before we describe detailed mobility model, let us look atlocation description first because the ultimate goal of mobilitymodeling is to predict locations. In fact, the locations of mobileusers can be part of the mobility model, whereas traditionally,mobility models are focused on stochastic behaviors of mobileusers. Based on our description in Section II-A, locations can bespecified at three levels. In other words, a mobile user’s currentposition can be represented as follows: Location Area: In cellular networks [3], an MSC controlsa group of base stations as shown in Fig. 1. When an MTmoves from one MSC to another, location registration processis triggered so that the MT’s update location information is de-scribed by a new location area ID. This information is availablein both home location register (HLR) and visitor location regis-ter (VLR). The former is a centralized database that maintainspermanent information of mobile users that subscribe servicesin a system; whereas, the latter is a relatively small database,which keeps the up-to-date locations of those visiting mobileterminals. Therefore, there is no additional memory or cost as-sociated with this information. Zone Partition: The location area gives information of a highlevel because an LA includes many cells. This granularity isnot sufficient to predict future locations. Thus, we use the zoneconcept proposed in the previous section to take into account anMT’s current position as the MT’s current position is closely re-lated to its next position due to the continuity of movement. Asshown in Fig. 2, if an MT is currently in zone 2, it is likely tomove into zone 0,1,3 and even into the coverage area of MSC-Cwithin the next moment. Or, if we know that MT is mov-ing south, it is most likely that it is going to move into zone 3.Therefore, we incorporate an MT’s movement direction and po-sition (zone) to provide a more accurate prediction of the MT’smobility pattern than simply using the LA information. The de-tails of collecting position information are beyond the scope ofthis paper, and they are currently undergoing further research. Cell ID: In order to maintain an active connection for a mo-bile user, it is most important to know in which cell the mobileuser is located. This information is especially useful in resourceand mobility management as explained in Section I. The net-work knows in which cell an MT resides by sending pollingmessages, which can be acquired without additional cost duringcall origination/termination, or through location services (LCS)management. The details of implementation are introduced inSection V.

Among these three levels of location information, the ulti-mate goal of this work is to estimate the next cells into which amobile user will possibly move. The prediction of future LAsis beyond the scope of this paper, and more information can befound in [43]. In this work, we focus on how to use the informa-tion at the zone levels and other parameters to predict possible

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future cells.It is worth mentioning that much information of mobile users

is subscriptive and aggregate information collected and storedin current wireless systems. In the standards such as 3GPP [41],the following parameters are defined for each user. For exam-ple, destination address and originating address must be storedin the VLR or SGSN and HLR before the connection is estab-lished. In addition, each user is allocated a local mobile sta-tion identity (LMSI) by the VLR/SGSN to a given subscriberfor internal management of data in the VLR/SGSN. It is alsosuggested that the previous location area ID and stored loca-tion area ID be specified as user profiles. The former refers tothe identity of the location area from which the subscriber hasroamed, while the latter refers to the identity of the location areain which the subscriber is assumed to be located.

C. Mobility Model

Since mobility models are designed to mimic the movementof mobile users in real life, many parameters need to be con-sidered. Most existing mobility models present the behaviors ofmobile objects without considering previous historical records.There are many mobility models [10], [42], depending on pa-rameters or stochastic characteristics. These models can be cat-egorized into different groups based on the following criteria: 1)macro- or micro-mobility scale; 2) 1-D, 2-D, or 3-D dimensions;3) randomness (since the movement of an MT is random, whichdepends on many unpredictable factors, it is helpful to describethe movement by varying randomness in different parameterssuch as direction, speed, and residence time); 4) geographicalconstraints, which can be very specific for particular scenariossuch as indoor, outdoor pedestrian, and vehicles.

In this paper, we propose a mobility model that considersstochastic behavior of mobile users, e.g., residence time within acell, historical records, and predictive location patterns in termsof location probabilities. There are five components in thismodel to characterize the movement of a mobile user: The MT’s residence time in a cell is represented by a randomvariable, , which has a Gamma distribution with probabilitydensity function (pdf) [4], [26], [27], [30]. Gamma distributionis selected for its flexibility because given different parameters,a Gamma distribution can be an Exponential, an Erlang or aChi-square distribution. The pdf of an MT’s residence time withGamma distribution in [24] has Laplace transform withthe mean value and the variance . Then, ! " $#&%'$#)(+* , where #, -/.021 (1)

The mean residence time of this distribution (1) is 3465 879 . .We assume that the residence time of an MT in each cell is in-dependent throughout this paper. Even considering pdf of resi-dence time enables us to predict the probability that an MT willmove out of a cell or a location area; however, it is unlikely toestimate into which cells an MT will move. We need additionalparameters for this purpose. The MT’s current direction, : <;= is collected through real-time monitoring, which can be initiated by the serving BS. The

MT’s current direction is defined as the direction from its previ-ous position to the current position. Here we denote :>6?;= as themoving direction of the MT @ , which is defined as the degreefrom the current direction clockwise or counter clockwise; i.e.,A8BDC : CEB . Fig. 3 shows the probable cells in the shadowcluster for :FD5 AHG JI G 7 when the current direction is from Westto East. It is reasonable to consider that the cells along theMT’s moving direction will have higher location probabilitiesthan those which are not, as shown in Fig. 3. This emphasizesthe importance of direction in predicting future cells.

The collection of an MT’s dynamic information is related toreal-time monitoring in wireless networks [11], [28], [32]. Themajor issue is how to define the safe regions for monitoring andprocessing queries with respect to the processing capability ofmobile terminals and BSs. If the safe region is too small, thenthe MTs being monitored must update queries very often sincethere is no query boundary inside a safe region.

xθ =π2

θ =− π2

Moving DirectionMoving Direction

Current Direction

Current Cell

Highest Probability Cells

Higher Probability Cells

Low Probability Cells

Fig. 3. Moving Direction.

Moving speed: We also consider the MT’s speed in its mov-ing direction [17], [46]. The MT is allowed to move away fromits current position in any direction, and variation of the MT’sdirection based on its previous direction is a uniform distribu-tion limited in the range of K G . The initial velocity of an MT isassumed to be a random variable with Gaussian probability den-sity function truncated in the range of 5 I ML8NO>QPRST7 , and thevelocity increment is taken to be a uniformly distributed randomvariable in the range of UVXW of the average velocity, FS . Historical records: In this context, we use historical recordsto specify a mobile user’s previous trajectory, e.g., the cells havetraversed during the observation time. The historical records arethe statistical information accumulated by maintaining a list ineach MT or in the servers of location client services (LCS). Thedetails of LCS is presented in Section V. We can trace the histor-ical records of an MT by using a trace records matrix (TRM) ofZY\[

, where

is the total number of records and[

is the totalnumber of cells that an MT has traversed in the period of obser-vation. The element ]_^a` ( bc IedTI 1f1g1 I ; hi IedTI 1f1g1 I [ ),of the TRM, denotes whether the MT has traversed a cell. The

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matrix j can be written as

jklmmmmmmn ] e ] ogofo ] =p...

. . ....

...ofogo ofogo ] ^a` ofofo...

.... . .

...]q ]q ogofo ]q prfsssssst I (2)

and ]>^a` is given by]>^a`uwv if the MT has entered this cell otherwise 1 (3) Predictive future locations: In most of the existing work, thefuture location is estimated as next cell. However there are sev-eral disadvantages for predicting only one cell. First, when anMT moves quickly through in micro-cell networks, the short res-idence time in a cell does not allow computations in every cell.In other words, there will be tremendous computations alongthe path of an MT’s movement. Second, next cell predictioncannot be integrated with bandwidth reservation schemes verywell with the intention of improving QoS. Therefore, we are in-terested in the probabilities that an MT will be in other cells attime ; , which is denoted as xy z <;= given the current servingBS of the MT @ , is . The serving BS of an MT is expected todetermine location probabilities and notify other BSs with thisestimation. Then,xy a z|?;=!D5 9a z< ~Q?;= z? ?;= z< ?;= ofogo 9a z< ?;=7 I (4)

where is the total number of cells for the estimation. Thisnumber is closely related to the scope of location prediction.Theoretically, we can think that it is possible that an MT is likelyto move into every cell, does not limit the number of future prob-able cells. In reality, the prediction is valid for a specific timeperiod. Given the moving speed of an object, the maximumdistance that an object can travel within a time period can bedetermined. Thus, the maximum number of cells that cover themaximum distance can also be decided accordingly.

III. THE USER MOBILITY PROFILE (UMP) FRAMEWORK

In this section, we present the UMP framework for the man-agement of service patterns and mobility characteristics. TheUMP maintains a mobile user’s information, which is associ-ated with the information of a user’s velocity, moving direction,current position, and service requirements. In order for wirelessnetworks to support different bandwidth reservation and mobil-ity management strategies, the networks must be able to dynam-ically and adaptively maintain historical records and predictivelocations of mobile users online.

The historical records can be collected from the user’s sub-scription such as entire information stored in home location reg-ister (HLR) for cellular wireless systems or during the origina-tion or termination of a session for the purpose of quality moni-toring and billing. On the contrary, future positions must be pre-dicted based on historical records and mobility-related parame-ters such as current position, direction, and speed [17], [46]. Inthe proposed framework, the predictive records are referred to as

the location probabilities of the cells in the shadow cluster andthe estimated service type during an MT’s roaming into othercells.

User Mobility Profile

Network Configuration

Location ProbabilitiesService Description

Calling Pattern

Quasi−Stationary UMP

Time Period

Service Type

UMPDynamic

Fig. 4. The User Mobility Profile (UMP) Framework.

There are two types of data in the new UMP frameworkas shown in Fig. 4. The first type is called quasi-stationaryUMP, which represents the MT’s information that changes in-frequently or that can be obtained from network databases. Thisincludes both subscriptive and historical information. The othertype is called dynamic UMP, which changes over time or can-not be obtained from network databases. The quasi-stationaryUMP, long-term information, is used to find the dynamic UMP,short-term information. The following two subsections presentthe details of the framework.

A. Quasi-Stationary UMP

An MT’s quasi-stationary information includes an MT’s cur-rent serving system description, calling pattern, and service re-quirements. In wireless networks, a mobile user receives its mo-bile services by subscribing to a home network. For example, auser can subscribe to a service package, which is the combi-nation of different service classes. Such information will re-main unchanged for a long time until the mobile users explic-itly change their services. Moreover, the communication recordsand location information of mobile users will be updated fromtime to time during the connection establishment and connectionrelease phases. In other words, this information may remain un-changed for a certain period of time.

For instance, each user has an individual record in the HLRof its home network. When a user roams from one locationarea to another, the location update process is triggered. Ac-cordingly, the mobile user’s current location at the level of lo-cation areas is updated in the HLR and visitor location register(VLR) or SGSN. Therefore, such information can be referred toas quasi-stationary UMP. We denote this long-term informationas a quadruple, D<J Ie I IO > for an MT, @ . Here, weconsider that each element of is a component of a vector,which indicates a specific character. Thus, Ie I IO arethe elements of vectors , , , and , respectively, which areelaborated as follows: Network Configuration I I ofofo I . This is a vec-tor that identifies different network architectures such as pico-cell, micro-cell, macro-cell, and satellite systems. Since the ra-

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dius of each cell, the service description, and the signaling for-mats may be different from system to system, each componentis associated with only one type of network. is the numberof the registered networks among which an MT is allowed forseamless roaming. At a specific time instant, an MT must belocated in a network, e.g., 9 . This information is not requiredfrom users; instead, it is recorded in the network entities such asHLR, VLR, and SGSN [41]. Time Period c Ie I ofogo Ie8 . This set identifies dif-ferent time periods of one day. is the cardinality of the set, i.e.,the maximum number of time segments divided within d hours.We do not differentiate weekdays and weekends because anMT’s movement during a time period on a weekday may be sim-ilar to another time period on a weekend [36]. How to divide thetime period is more related to traffic load and mobility patterns.In current cellular networks, time segments relating to account-ing are categorized into peak time, non-peak time, weekends,weekdays, and are decided by service providers. These timesegments sometimes overlap for different service plans. How-ever, each service operator has its proprietary statistics abouttraffic loads and handoff rates for each local area for networkplanning [22]. Service Description I I ofofo I¡ . This set repre-sents service requirements such as bandwidth requirement andend-to-end delay. ¢ is the total number of service patterns al-lowed in the network. Each element in this set provides the prob-ability mass function (PMF) over a particular sampling spaceof service types as described in Section III-B. For example, ¤£ is used to represent the probability mass function(PMF) of an MT, @ and its corresponding sample space ¥¦ .A mobile terminal may have the same service requirement indifferent networks if this customer subscribes its service as a“fixed” rate service, or it may need different services in somenetworks because some networks may provide various services. Calling Pattern ¤§ I I ofogo I - , where is the car-dinality of the set. Each element is related to the description ofcalling events, which can be different from one user to another.However, in most of the existing networks, the calling patternsare defined based on a group of mobile users so that compu-tation complexity can be simplified and scalable. According tocurrent service providers, each user has a personal record, whichis typically kept for a certain period such as three months or sixmonths, depending on local regulations and operators’ capabil-ity. This data may include the probability distribution of callingarrival time, call holding time, and call origination rate.

B. Dynamic UMP

The quasi-stationary UMP provides long-term information ofmobile users. In order to satisfy real-time prediction require-ments, we also need to consider data that changes from time totime such as moving direction, speed, and service type. Thistype of information is referred to as dynamic UMP. Our objec-tive is to derive or estimate dynamic UMP information based onquasi-stationary UMP. We focus on the predictive records thatare derived from the mobile user’s previous service and mobilityinformation. We assume that locations are independent of ser-vices in this context because they can be reflected in the network

configuration. In particular, we examine location probabilitiesand service type in the future cells because these two metricsare the most often used parameters for mobility and resourcemanagement.

Let ¨ ©5 ª I xy a z|?;=«7 denote the dynamic UMP for the MT,@ at time ; . The first element ª is the service type that @ will re-quest, and the second item, xy z <;= , represents the estimation oflocation probabilities given that the MT, @ is currently in cell .Location probabilities are used to represent the likelihood of anMT’s presence in a cell. For single cell location estimation, thereare only two possibilities: 1 or 0, in accordance with whether anMT will be in a cell or not, respectively. Since it is unrealisticto represent an MT’s movement by a single random variable, weuse location probabilities to describe the result of many factorssuch as mobility models, changing directions, and geographicconditions. This method is widely used in the research of hand-off, location tracking, and mobility management [13], [35], [44].

In this context, we use PMF to describe different service re-quirements, which are offered to subscribers in terms of servicepackages, covering the most popular service requirements ofmobile users. In other words, each service pattern has a spe-cific PMF with regard to each service type. For a discrete ran-dom variable, service type Y, the PMF ¬\<­T of ® over a samplespace ¥ is defined by [33]¬4<­T!¯±°²a³®©´­2 and µN¶· ¬4<­T! 1 (5)

For a particular MT, @ , the service pattern is denoted by .The PMF can be decided either by the network administratorsor by accumulating the mobile user’s records. The algorithmfor estimating ª will be illustrated in Section IV-B. One ofthe main tasks of predicting and computing UMP is to deter-mine xy z=<;= . The sequence of cells that will be visited by theMT constitutes a random process, with location probabilities, a z< ¸ ?;= , which is the probability that an MT, @ , residing in cell , will be in cell ¹ at time ; . The location probabilities, xy ze?;= ,are calculated by the serving BS based on the MT’s historicalrecords, current position, velocity, and moving direction.

IV. MEASUREMENT AND PREDICTION ALGORITHMS

A block diagram of the algorithms proposed for service andmobility prediction is illustrated in Fig. 5. The objective of thesealgorithms is to determine dynamic UMP, ¨ , using quasi-stationary UMP, , and other parameters. We start with theaccount of UMP framework by explaining the parameters usedfor prediction. Then, we discuss the description and predictionof service requirements. Afterwards, we present the predictionalgorithm of location probabilities.

A. Flowchart of the Algorithm

As shown in Fig. 4, the generic UMP is composed of quasi-stationary UMP and dynamic UMP, where the former one is ob-tained during the MT’s interaction with the network, such asincoming and outgoing calling requests as shown in box º inFig. 5. First of all, given the network infrastructure by , thecell radius and network configuration are then available. Sec-ond, the time period £ is one element in . The direct

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information corresponding to a particular timing period is themoving velocity and the pdf of an MT’s residence time in a cell,which depend upon traffic conditions, such as congestion in rushhours. Then, the service description is given by £ , withPMF ¬»6­T and its corresponding sample space ¥, . Finally,the calling pattern of the MT is described by £ , relatingto the incoming/outgoing call distribution and call holding time.This information will be used for resource allocation in possiblefuture cells.

In addition to predicting location probabilities, we estimatethe next service request based on the PMF of service patternsas well as historical records shown in box C of Fig. 5. The his-tory of service requirements is known to the network becauseof billing and service management. Thus, this information doesnot require extra effort and can be utilized efficiently. It is worthnoticing that the network does not need to specify bandwidth foreach particular MT; rather, it manages resource based on statisti-cal summation of all possible requirements so that the resourcesare used effectively and the throughput can be maximized [23].

B. Service Description, Measurement, and Estimation

The aim of our algorithm is to minimize the estimation errorbetween the estimated service type and the real value. The futureservice pattern is estimated based on a priori PMF of servicepatterns, ¬6<­T . First, we assume that the service pattern ofan MT can be represented by a random variable ® . The PMFof this random variable is ¬ <­T , which is the probability forvalue ®¤©­ . The sample space of service types is denoted byº¼ . For example, there are four samples in º4 , i.e., there are4 different services which may be requested by an MT, such asvoice, data, audio, and video, corresponding to values 1, 2, 3,and 4, respectively. We define a PMF vector x½ > as½ _!5 ¬»6= I ¬»6 d I ofogo I ¬2<¾¿7 (6)

where ¬»2 o is the probability of each service type for ­ £ ¥,and ¾©À ¥Z2À relating to .

Then, we consider an order-L Markov predictor, which as-sumes that the service can be predicted from the most recentvalues in the service history, which isxÁ 6 ©5 S2X<; 9S66?; ofogo S26<; q 7 I (7)

where

is the length of historical records and S$6?;= is theservice that the MT, @ has requested at time ;e .

If we think of the user’s service requirement as a random vari-able ® , and ®Z? I ¹Q is a string ® z ® zÄà 1g1f1 ® ¸ representing the se-quence of values that ® takes for any C C ¹ C , then theMarkov assumption is that Y behaves as follows, for all ­ £ ¥±°²a³®2Åà h­$À ®Æ= I J xÁ 6 = (8)h±°²a³a<® Åaà h­ÇÀ ®Æ< A %´ I JhÈf´±°²a³® zÄà q à ´­ÇÀ ®Æ?/%´ I $%ÉXhÈf

(9)

where the notation ±°²a³a<® Åaà ­ z À 1f1f1 denotes the probabil-ity that ®Mz takes the value ­Qz . The first two lines indicate that the

probability depends on only the most recent

records, while thelatter two lines indicate the assumption of a stationary distribu-tion.

Since we do not know the next service type, we can generatean estimate Ê from the current history. We denote the probabil-ity that the next service type takes the value ­ as ʬ\­Q ,ʬ4<­ÇÀ xÁ |!ËÊu®2q à ´­ÇÀ xÁ 1 (10)

We also notice that history records xÁ and the new esti-mate ­ will result in an estimate PMF,

ʬ\<ÌzÀ ® q à h­ I xÁ X =!wÍ \ÎÐÏÑÒ q à ÔÓ Ã \ÎÐÏÑÒ q à =Ó if Ì z ´­\ÎÐÏ Ñ q à ÔÓ\ÎÐÏ Ñ q à ÔÓ if Ì z)Õ´­ (11)

where Ì>z for \¤ Ied ogofo I ¾ is one of the values in the samplespace, ¥ , and ÖÈ I|× denotes the number of times that valueÈ occurs in the number × historic records.

As a result, we can generate an estimate PMF vector, whichshows the frequency of each service request for ­ £ ¥¦ . Wedenote this PMF as ʽ > :ʽ Ø 5 ʬ\?Ì QÀ ®Mq à h­ I xÁ = I (12)ʬ4?Ì z d À ®Mq à h­ I xÁ | ofogoʬ\<ÌÙÚh¾À ®Mq à ¯­ I xÁ |Ç7 1

We predict the next service requirement by minimizing themean square error between the prior PMF and the estimate PMF.Considering that the mean square estimation of the random vari-able ® is to find an optimal constant ­ that minimizes Û ,Û4´3_® A ­T \ÚÜÉÝÞ Ý ® A ­T gß ?ÌX × Ì I (13)

whereß <ÌT is the pdf of a continuous random variable ® . For

the discrete random variable ® , which follows the PMF, , theabove equation is rewritten asÛ\ µÏ Ñ ¶·à ?Ì z A ­T ¬ ?Ì z (14)

where ­ is one of the values of Ì I Ì I ofofo I Ìz I ofogo I Ì Ù .However, this definition cannot indicate the relationship be-

tween the history and the selection of an optimal value, showingthat an optimal value is selected independently of the previousrecords of the random variable. When we consider historicalrecords in our estimation, it is necessary to take into accountthe historical effect on finding an optimal value. In this con-text, this effect is represented by the estimate PMF for an es-timate value. Accordingly, the objective of the estimation isto find an optimal value ª that can minimize the differencebetween the prior PMF vector, x½ in (6) and the empiri-cal PMF, ʽ ³aÀ xÁ = , in (12). Therefore, we define meansquare error between these two vectors, á <­ÇÀ xÁ <â&| asá <­ÇÀ xÁ <â&| ¾ Ùµ zÄã À¬ ?Ì z A ʬ\<Ì z À ®Mq à h­ I xÁ |+À

(15)

7

Service Estimation Eq. (16)

Γx

Ωx

Φx

Ψx

A

B

Dynamic UMP

C

Σ UMPQx

ΛDx

Velocity

Quasi−Stationary UMP

Cell Radius

Network Configuration

Residence TimeTraffic Condition

Call Arrival/Outgoing

Call Holding Time

Computing Mobile

Previous Service

Prediction Order

Moving DirectionCurrent Position

Records

Λ

PMF of Service

Probabilities Eq. (4)

Fig. 5. Flowchart of Computing User Mobility Profile.

where ¾ is the cardinality of ¥ . By applying the minimumsquare error for the estimation, the estimated result of the nextservice type is: ª À xÁ häaåeæ>çRèÄéê ëíì î·Øï fá ­$À xÁ âØe 1 (16)

Therefore, the estimation is determined by both the service PMFand historical records.

...Historic Sample

Sample

Records Space

Space

Error Calculator

Decision Maker

0. . .

1 h2 . . . h

1 2 3 U

hL U 0321

Fig. 6. The Estimation of Service Type.

During the implementation, we consider that an MT’s his-torical records will be updated in VLR/SGSN and HLR dur-ing the connection origination stage. Then, we can proceed toestimate the future service type ª by examining each servicetype ­ £ ¥Z . Each service type in the sample space ¥, isselected sequentially and input to the square error calculator to-gether with the historical records as shown in Fig. 6. The resultsof this calculation are then input into a decision maker to obtainthe most probable service type with the minimum error. Finally,the corresponding service type »ª is chosen as the estimated

service pattern. This method guarantees that the estimated ser-vice pattern fits well with the known PMF. If an MT is not inthe progress of a call and its next probable service request is es-timated as ª , then the bandwidth that needs to be reserved canbe determined by substituting »ª in (16) for ­ in (31).

C. Prediction Algorithm of Location Probabilities

In Section II-C, we introduced a mobility model that de-scribes the movement of an MT by considering the cell resi-dence time, historical records, and future location probabilities.Note that the prediction of location probabilities involves manyparameters. In this work, we develop an algorithm which takesseveral important factors into account, while providing a sub-optimal maximum likelihood estimation.

C.1 Assumptions and Parameters

We assume that the MT’s residence time in a cell is repre-sented by a random variable, , which has a Gamma distribu-tion with probability density function (pdf). First of all, we needto assume and measure the following parameters described inSection II-C: The pdf of the residence time is described by Laplace trans-form, a in (1), with a mean of ( ) and variance of . The MT’s current position is represented at three levels as de-scribed in Section II-B. The zone partition can be obtained byknowing the cell ID. The MT’s current direction, : ?;= , and speed, VM<@M , are col-lected through real-time monitoring, which can be initiated bythe serving BS as explained in Section V. The initial velocity ofan MT is assumed to be a random variable with Gaussian proba-bility density function truncated in the range of 5 I L8NO QPðaSX7 . Historical records are available in the form of trace recordsmatrix (TRM) of

ñYR[as in (2).

8

Path database (PD), which is a part of the digital mapdatabase. The digital map is obtained by discretizing a mapinto small segments and each segment has many routes alongwith their relationship to others [12]. This information is avail-able for many applications, such as finding directions from onelocation to another. We also assume that an aggregate historical path database òuóis retrievable in the network administration center. Each recordin this database is the previous path that the MT, @ , has traversed.We assume that the movement of an MT have similar patternssuch as traveling between home and work sites.

Note that the path database ò ó is different from trace matrixj . The former shows the cells in the sequence of an MT’s trav-els, while the latter may not follow the same order. Another dis-tinction is that the path database maintains an MT’s past travelinformation, which may be considerable than the TRM becauseTRM is more related to dynamic information in short term. Theobjective of TRM is to determine future cells given the trajec-tory of an MT; whereas, the path database objective is to find thesimilarity of an MT’s movement.

C.2 Prediction Algorithm

In a wireless network, the BSs are the entities which canfetch and transfer the users’ information and provide terminalservices. They also allocate bandwidth and maintain the QoSrequirements of a connection. In this section, we show howto identify those cells into which an MT will probably moveand how to determine their location probabilities. There hasbeen some success of varying degrees on this problem, whichis mainly focused on determining the next cell [25]. In [16],[34], it is assumed that the MT’s direction is a uniform distribu-tion in a range of 5 Ied B 7 or that relies on the signaling measure-ment without considering road conditions and an MT’s histori-cal behavior. The most challenging work is to distinguish thoseprobable cells based on an MT’s moving behavior including itsvelocity and direction.

In this work, we consider the following constraints in our pre-diction: The maximum distance that an MT can travel in the estimationinterval: For a certain time period, UF , the maximum distanceof an MT’s traveling is UF Y 2L8NO , where 2L)Ní is the upperlimit of moving speed. Therefore, given the cell radius, we canobtain the maximum number of cells that an MT can traverse,i.e., the maximum number of cells to be considered in the pre-diction. The future zones: By considering the maximum distance, wecan determine a group of cells into which an MT can possiblymove into. However, this set can be further reduced when weconsider moving direction and the MT’s current position. The prediction level: Similar to all the prediction-basedschemes, our algorithm inevitably involves overhead for com-putations and communications. Therefore, we introduce a newconcept called prediction level to reflect the effect of this over-head. The higher the prediction levels, the more complicatedthe computations, which result in more accurate predictions be-cause more cells are considered. The details of prediction levelare described in Section IV-C.2.b.

The self-similarity of movement: We assume that an MT hasa self-similar moving pattern. Therefore, if a route in a cell hasbeen traversed by an MT before, which is shown in ò ó , thenwe consider this cell to have higher location probabilities, i.e.,the MT is more likely to move into this cell. The path information: To be realistic, we take the path infor-mation into account. For a given part of the digital map, weassume that it is covered by a number of cells. Each cell hasa set of routes. If a cell consists of a route that is continuedfrom the current cell in which an MT resides, then this cell hasa higher location probability. In this way, we combine the effectof historical records as well as path information.

The prediction of location probabilities involves many param-eters, which cannot be simply represented by a mathematicalpredictor. By considering the above constraints, we will achievea sub-optimal estimation with maximum likelihood. In our pre-diction, first we will find the most probable cells, based on theMT’s 1) current position, 2) moving speed, 3) prediction level,and 4) direction. Then, we will examine each cell in accordancewith the last two elements. The cells which satisfy all four willhave the highest probabilities.

C.2.a Estimation of Zones. For the sake of simplicity in pre-sentation, we consider a wireless network with hexagonal con-figuration for the remaining of this paper, although arbitraryshape configurations can also be covered by our solution. Wenotice that most people travel along a route to a destination,which means that their movement can be traced and predicted.In order to take the MT’s direction into consideration, we firstdetermine the possible zones defined in Section II. In otherwords, the region of an MT’s future position is constrained toa set of specific cells relating to its direction variation. The mostcommonly used method is to denote the position of an MT bycoordinates at a specific time. Here, we use the example of sevenzones described in Fig. 2. In Fig. 7, let ô <;=!hõ ~ represent theMT currently in zone , and : ?;= be the current moving direc-tion of the MT, which is the direction variation derived from theprevious direction. This coordinate system is defined with itsorigin at the current location of the MT; i.e., the MT is always inits origin, and its previous direction is the positive direction ofthe @ axis. The Ì axis can be obtained by turning ö Tª counter-clock wise from the @ axis. Thus, the MT’s position can berepresented by ÷É?ø <;= I : ?;== as shown in Fig. 7. This coor-dinate system is dynamic in the sense that its origin and axes’orientation change over time.

Assume an MT is moving from point ù toward º ; thus, itsnext position may be in zone 1, õ . In general, the future zone,Case k ( C C A ) can be determined asõ!ÂúEÍËûfü ï Îþý Óü=ÿ if : <;= A A û ü ï Îþý Ó ü ÿ if : <;= (17) Case 1 to n-1 õ to õ Å Þ Iwhere is the total number of zones, and : ~ is the angle of eachzone. By default, we always consider õ ~ to be included in theUMP. It is possible that more than one zone is involved in esti-mating location probabilities since it is difficult to differentiate

9

CurrentDirection

DirectionPrevious

θ (t)x

( ρx θx (t), (t) )

XZone 1

Zone 2

Zone 5

Y

A

O

π

π

98

9− 8

Zone 0

Zone 6

Zone 3

Zone 4

Mobile Terminal

Previous Direction

Current Direction

Mutiple Zones

Fig. 7. Coordinate System with Zone Partition.

an MT’s position around the boundary of zones. Thus, we ex-tend possible zones for Case k ? C C d A as in thefollowing expression: À:6<;=8À B C o :~ (18) Case õ Å Þ and õ À: ?;= A : ~ À B C o : ~ Case Æ%´ õ and õ À:6<;= A d o :~À B C o :~ Case Æ% d õ and õ

...À: ?;= A < A d o : ~ À B C o : ~ Case d A õ»Å Þ and õÅ Þ In the example shown in Fig. 7, Ö is the number of zones,and :~ G is the angle of each zone. Although the selectedzones can shrink the number of probable cells, it is not sufficientto identify the probable cells. Next, we will further approachthose probable cells by considering velocity V>2?;= and residencetime distribution.

C.2.b Prediction Level. Apparently, the prediction of loca-tion probabilities may involve many cells as well as computa-tion complexity, which is incurred mostly from the number ofcells to be considered. Basically, the more cells or larger areasconsidered in the prediction, the better approximation can bereached, requiring more computations. To balance the computa-tion and estimation accuracy, we introduce a new concept calledprediction level to describe the influenced region of the shadowcluster of an MT. According to the concept of shadow cluster,the influenced cells are a group of cells surrounding the cell inwhich the MT is residing. Thus, we always start from a currentcell, which is the center of a shadow cluster. The vicinity of thecurrent cell can be denoted according to its distance away fromthe center cell. If a cell is adjacent to the current cell, then it is

in the first layer of the current cell. The cells adjacent to the firstlayer cells form the second layer of the current cell. If the esti-mated cells cover only the cells of the first layer, then it is calledfirst level prediction. Similarly, the second level prediction isassociated with both first and second layer cells. Fig. 8 showsan example of the probable cells with first and second levels ofprediction.

(a) First−Order Prediction (b) Second−Order Prediction

Fig. 8. Prediction Levels.

The definition of the prediction level is related to the accuracyof a prediction and can also be used as a QoS constraint, as well.For the first level of prediction, only six cells are considered; i.e.,the computation is not very complicated. On the other hand, ifthe network should provide location probabilities with secondlevel of prediction, there are eighteen cells, including the firstlayer and second layer cells. Correspondingly, the complexityof computation increases, which is demonstrated in Section IV-C. Note that some second layer cells may have higher locationprobabilities than some cells in the first layer, based on an MT’smovement pattern. One example is that an MT traveling on ahighway, is more likely to be in the second layer cells along itsmovement direction than the first layer cells behind its trajectoryor off the highway.

C.2.c Calculation of the Number of Cells. Mobile users’ ve-locity can be influenced by circumstances including geographi-cal condition and timing period. For example, in an urban areain which there are many buildings, MTs are forced to travel ata low speed with diverse direction changes. On the contrary, inrural areas, MTs can travel at a higher speed and change direc-tion infrequently. The maximum distance traveled by an MT canbe determined by a knowledge of the upper and lower velocitybounds of an MT.

We compute the number of cells that an MT could have trav-eled during the time window UF . We consider that the MT goesthrough a cell with the mean residence time in a cell. The aver-age distance, × 6?;= , that an MT may travel along one direction,in terms of number of cells, is obtained by× ?;=! û UF3+25 +7 1 (19)

Note that × ?;= may be greater or less than the required pre-diction level ù46?;= at time ; for a terminal @ . If the formeris the case, the ù\M?;= will not affect the computation of prob-able cells, which means the estimated region covers the areaspecified by ù <;= . However, if the latter is the case, then thecomputed region cannot cover the area that is required by theprediction level. In this scenario, it is necessary to enlarge the

10

calculation range to meet the requirement of ù±6<;= . We de-note <°Ç;¡uä$ × <;= I ù ?;= I X , which is rewritten as ?°; I X in short, as the number of probable cells in the mo-bility profiles with order ° at time ; for Case . The simplestscenario is × 2?;=!bù\6?;=D , the number of the probable cellsfor Case 1 in (17), ?°ð/; I , can be calculated by thefollowing formula as there are six cells in the first layer:F6<°¡a; I û o À: <;=8Àd B 1 (20)

The second layer includes two parts, one of which is the firstlayer cells and the other is the second layer cells which fall intothe zone, that is ?° d a; I ÔØ% û o À:2?;=+Àd B %Ô!% û d o o À: ?;=¼Àd B 1 (21)

One additional cell is added to each item in (21) because we con-sider the worst case scenario to be two incomplete cells fallinginto the probable zones. Similarly, we can have a general formfor calculating the number of probable cells in the mobility pro-files, 2?°a; I 6 , that is

?°; I X A Ø% û o ü ïÎþý Ó G % û d o o ü ïÎþý Ó G % ofogo % û o o ü ï Îþý Ó G if C C A d o A Ø% û o ü ïÎþý Ó G % û d o o ü ïÎþý Ó G % ofogo % û o o ü ïÎþý Ó G if C C d A

(22)For the !±­TÛ of C C d A , the number of cells is doubledsince there are two possible zones resulting from the movingdirection. Notice that the cells included in our illustration arethose that fall into the zone partitions and within the averageorder, × <;= or prediction level ù ?;= . The set or sample spaceof the mobility profiles is denoted as "¦2?°; I X , and each cellthat belongs to this set is denoted by ÷ £ " ?°a; I 6 .C.2.d Prediction of Location Probabilities. Thus far, wehave determined the total number of probable cells and the setof those cells. Now, we must estimate the location probabilityfor each cell. We observed that for a particular cell, the numberof paths or travel routes is finite, i.e., the MT is moving amongfinite states. The a z< ¸ ?;= for ¹Æ IdTI ofofo I ?°#T; I X , whichis the probability that an MT, @ , currently in cell , will be in cell¹ during the timing window UF , is computed by performing thefollowing procedures: Step 1: Select a value from %$ ~ Ú as the initial point forcomputing the location probabilities. Step 2: Start from the bottom line of TRM and take the lasttwo non-zero elements of the TRM to make a temporary path &as shown in Fig. 9(a). Step 3: Compare the path & to the equal or close segment inPD as shown in Fig. 9(b). There may be a set of cells that canbe the next cell along with path & , which is represented by a set

...

...

......

...

...

...

1X X2 XMX3

...

...... ... ...

......

...

......

... ... ...

...

......

...

1

2

3

L

L−1

L−2

0 0 0 0 0 0 1

0 0 0 0 1 0 0

1 0 0 0 0 0 0

0 1 0 0 0 0 0

0 0 1 0 0 0 0

0 0 0 0 1 0 0

0 0 0 1 0 0 0

1 0 0 0 0 0 0

0 1 0 0 0 0 0

0 0 0 0 1 0 0 0

0 0 0 1 0 0 0

1 0 0 0 0 0 0

0 1 0 0 0 0 0

0 0 0 1 0 0 0 0

(b)(a)

(c)

Segment of Path Database

Probable Cell

Trace \Records Matrix G

Aggregate Historic Path

Probable Cell

Fig. 9. Prediction of Location Probabilities.

& . Each element of this set, ÷ ¸ £ & is a probable cell inFig. 9(c), and which provides a possible path, '&Æ<÷¸ . Step 4: Estimate location probabilities, z< ¸ ?;= , by perform-ing the process shown in Fig. 10. This algorithm starts by ex-amining each cell in the set of possible cells, ÷ ¸É£ & , andthe total number of cells in this set is "¦6<°(»; I X from (22).If a probable cell, ÷ ¸ , is in the first order of prediction and itscorresponding path, '&H<÷ ¸ , can be found in the historical pathdatabase, ò ó , then this cell, ÷F¸ has the highest location prob-abilities. This emphasizes the importance of prediction con-straints and user history. Additionally, as the probable cellsget further away from the MT’s current position, and they arenot relevant to the historical paths, the location probabilities de-crease. This examination continues until all cells in the possibleset are scrutinized.

As a result, a sequence of location probabilities is obtained interms of $2~ , where $2~ can be solved by applying the followingexpression: µêëíìî¸í¶TÎ*),+ï-/. ïaÎ1032 ý  Ó<Ó 9 z? ¸><;=! (23)

V. DISCUSSIONS ON IMPLEMENTATION AND OVERHEAD

We describe how to implement the proposed schemes withinthe existing cellular network specifications [1]. Like all pre-diction related schemes, our scheme is also inevitably involvedwith overhead for computation and communications, which isworthy of discussion.

A. Implementation in Existing Wireless Networks

In our proposed framework in Fig. 4, we consider system pa-rameters, such as radius size, time segments, and service de-scription, which are available in the network databases. The im-plementation of prediction algorithms is completed in the basestation which currently serves an MT, and does not affect theentire system design, but is related to the overhead described inSection V-B. The three aspects relating to the implementation

11

465 := initial value of the highest probability7:= temporary path of TRM798: := set of probable cells in PD along path

7;7=<?>,@BA:= possible path of cell

>9@DCE7F8:G : <?H9IKJMLONPA :=G : <?Q9RMSPT U : <VJABLOW : <VJAXZYHFI[JMLMN\A] :M^ _ ^ @ < JA := location probability at cell ` given an MT a

is currently in cell b] 5 := threshold of probability computationwhile cedf : <?H9IKJMLONPA do

for all>9@DCE7 8: do

if> @ C G : <hgiIKJMLMN\A and

;7=<?> @ AjCEkml: then] :M^ _ ^ @ <VJAnI Y 4 5else

case :> @ C G : <?o,IKJMLONPA and

;7<V> @ AjCpkml:] :M^ _ ^ @ < JAnI Yqr 4 5case :

> @ C G : <?o,IKJMLONPA and;7<V> @ AZsCpkml:] :M^ _ ^ @ < JAnI Yqt 4 5

case :> @ sCu< G : <hgiIKJMLONPAwv G : <*oxIyJOLMN\AzA and

;7=<?> @ AnCkml:] :M^ _ ^ @ < JAnI Y qt 4 5others :for all

HF|odo

while] :M^ _ ^ @ <VJA d ] 5 do

case :> @ C G : <?H9IKJMLMN\A] :M^ _ ^ @ < JAnI Y<qr A~z q 4 5

case :> @ sC G : <?H9IKJMLMN\A] :M^ _ ^ @[< JAjI Y<qr A~ 45

end whileend for

end ifend for

end while

Fig. 10. Estimation of Location Probabilities (Step 4).

and incorporation within existing networks are location descrip-tion, real-time monitoring of speed and velocity, and collectionof historical records.

A.1 Location Information

In wireless networks, mobile devices are required to updatetheir locations when they cross the boundaries of two locationareas. Therefore, new location area ID will be stored in the MT’shome HLR as well as its current VLR. Therefore, the locationdescription at the level of location area is already available in thesystem, and no extra effort is required to obtain this information.

We recognize the effort in the updated specifications [1]that the user profiles are being required so that the location-dependent services can be provided by the third parties besidesthe vendors and service operators. The new parameters includecurrent location area ID and target location area ID. The cur-rent location area ID indicates the location in which the sub-scriber is currently served, while the target location area IDindicates the location into which the mobile user intends to

roam. Note that the LCS (Local Client Service) is a new fea-ture in 3G wireless systems, as specified in Universal MobileTelecommunications System (UMTS) standards, to provide lo-cation information, which can be accessed through a gatewayLCS. The proposed user profile framework can be used as anaccess point to user profile data for the service providers. Ofcourse, the service-specific user preferences may be stored in alocal database owned by a service provider. The implementationof this capability is the home subscriber server (HSS) [1].

The second level of our location description is at the zonelevel, which is a new concept introduced in this paper. The ob-jective of this zone partition is to reduce the granularity of the lo-cation description at the LA level, combining information aboutan MT’s current position and moving direction. Therefore, wecan reduce the overhead of prediction. Note that, as in the de-sign of LAs, each zone consists of a group of cells, which arerepresented by cell IDs. Therefore, given a cell ID, we knowto which zone a cell belongs, i.e., the zone level information oflocation description.

The remaining issues are whether the system knows an MT’smoving direction and its cell ID. The former one involves real-time monitoring, which is discussed in detail in Section V-A.2.As for the collection of cell IDs, there are several ways for wire-less systems to collect location information at the level of cell. When an MT initiates a call, it sends a routing request to theserving MSC through its BS, and MSC may convey this requestto the HLR for call delivery. As a result, the network knows inwhich cell the calling MT is located. If the MT moves during thecall connection, the updated position of an MT can be obtainedthrough the call release procedure [40]. When an incoming call arrives at an MT, the network firstlocates the MT in an MSC that is serving the called MT. Thenthe MSC pages the BSs in its controlling area in order to findthe serving BS of a called MT. The serving BS responds witha confirmation message to the MSC, indicating that the calledMT is in its coverage area. Next, the call connection can beestablished between the calling and called MTs. Therefore, thecalled MT’s current cell is known to the network [38]. The MT’s location can also be obtained through locationclient services (LCS) management provided by wireless sys-tems [37]. LCS is supported by serving mobile location cen-ter (SMLC), which may be call independent. Each SMLC con-trols a number of location measurement units (LMUs), whichintervenes with MTs and BSs via air interface ¢!L (Type A)or º\³O« (Type B). The LCS provides the geographical estima-tion about an MT in terms of universal latitudinal and longitu-dinal data [39]. Mapping between the MT’s position in termsof latitude and longitude and local coordinate system is finishedthrough location client co-ordinate transformation function (LC-CTF).

A.2 Measurement and Real-Time Monitoring

In the proposed framework, collection or measurement ofhistorical records, including moving direction, speed, and cur-rent positions, is an important step to predict future locations.The user profiles that are quasi-stationary are stored in theHLR and VLR/SGSN because they are considered to be rela-

12

tive long-term information compared to parameters that changefrequently, such as moving direction and speed. This informa-tion can be updated in three processes: location update, callorigination, and call termination. During the location update,the current location area in which the mobile user is located, isupdated with the serving VLR and the HLR. In the Third Gen-eration Partnership Project (3GPP) specifications, three locationupdate schemes are suggested: distance-based, time-based, andmovement-based. No matter which scheme is used for wirelessnetworks, the location area ID will be changed upon locationregistration [3], [4]. For each mobile user, the serving BS andthe corresponding VLR/SGSN will update the user profiles forany incoming and outgoing calls due to billing purposes. There-fore, the mobile users’ current position with respect to locationareas and cells are maintained in the HLR and VLR/SGSN bymobility application part (MAP) protocol during the call man-agement process.

The measurement of directions and velocity is an issue ofreal-time monitoring. In wireless cellular systems, there havebeen a few recognized algorithms for mobile velocity and direc-tion estimations [17], [31], [46]. The velocity information canbe collected during the handoff process. When an MT movesfrom one cell to another, the velocity estimation is required tokeep handoff delay acceptable. These methods include the es-timation of maximum Doppler frequency because of the fad-ing process during the movement [21], [45]. The detailed al-gorithms about velocity estimation can be found in [17], [31],[45], [46], which is beyond the scope of this paper. According tothe 3GPP specifications, both the velocity and the location of anMT in a cell can be provided through the LMUs and LCS [39].Each cell is associated with at least one LMU. Therefore, the lo-cation and speed information can be requested through BSs andthe LMUs.

In [11], the safe region is designed according to the least ca-pable MTs and BSs by assuming that each entity can process thesame maximum number of queries. In [28], a variable thresh-old scheme is proposed to process location-dependent queriesso that a base station will not update the user profile if the queryresults are unlikely to affect the BS records. In [32], the per-formance of how to efficiently process the querying records ofmobile terminals is evaluated. Other related work also addressesthe scalability issue of monitoring and collecting mobile users’information by carefully constructing the databases that main-tain the querying records [19]. This work has demonstrated thatthe BSs, LMUs, and VLRs are able to support discrete informa-tion monitoring and collecting. For the continuous monitoringin which the mobile objects are monitored continuously over atime period until the MTs or BSs interrupt, simulation resultsshowed that the existing BSs and MTs are capable of handlingeven continuous monitoring if the databases and safe regions aredesigned appropriately. The more details about real-time mon-itoring and information processing in wireless networks can befound in [11], [19], [28], [32].

B. Overhead of Prediction Algorithms

The overhead that will be incurred by the proposed schemeconsists of three parts: 1) buffer space to store historical records;

2) communication cost to send prediction results to probablecells for bandwidth reservation; and 3) computation time re-quired to perform the algorithms to obtain prediction results.

As described in Section III-A, the quasi-stationary, UMPwill be updated during the procedures of location update, callorigination and termination. This information is stored in theVLR/SGSN and HLR, i.e., the network core entities; therefore,there are no extra requirements for storing quasi-stationary in-formation. On the other hand, the dynamic UMP can be deter-mined according to the information maintained in the servingBS and the MTs. In the proposed framework, each MT keeps alist that stores the cell IDs that it has traversed and the servicesthat it has requested compared to scheme that do not require his-torical records [2], [25]. This list is refreshed when the MT ex-periences a handoff, incoming, or outgoing service. Accordingto the specifications of cellular handsets, each one can store 50to 100 records of calls and an additional 50 to 100 frequent call-ing users. Each of these records can accommodate 180 charac-ters, which results in a total storage of P> Y Y g > 4D >6I > bits to 576,000 bits. Considering each cell ID is 15 bits [5], 50-cell IDs will take just 750 bits. The historical records of cellIDs take up to 1 W auxiliary storage space in a cellular hand-set, which is a very small amount. Thus, historical records areconsidered in many schemes [7], [13], [18]. Note that the histor-ical records can also be stored in the serving base station ratherthan in the terminals, and the processing capability of a BS ismuch more powerful than a terminal. Therefore, using histori-cal records will not cause significant overhead in storage.

During the handoff process, this information can be tailoredto the signaling exchanged between the mobile terminals and thebase stations. Another way to deal with the information changeis that the previous BS forwards the information to the currentserving BS. We consider that this is a better method because theinformation can be transmitted via the wired interface betweenBSs. Therefore, the radio resource used to communicate be-tween the MTs and BSs will not be consumed while deliveringuser information.

We consider three conditions for triggering the update processof location probabilities: the average residence time in a cell, thetermination of a service, and the origination of a service. Whena mobile user moves to a new cell, a timer is established for thisMT. If one of the above three events occurs, the update processof location probabilities is initiated and the timer is reset to zero.For example, if an MT does not have any incoming or outgoingcalls after it moves to a cell, the location probabilities will becalculated after the average residence time in a cell accordingto the stochastic mobility model. If an incoming call arrivesbefore the average residence time has elapsed, the user profile inthe HLR and VLR/SGSN will be updated for connection setupand accounting. Therefore, the computation and communicationcosts can be reduced.

Compared to other algorithms introduced in Section I, theproposed scheme will incur extra communication costs for dis-tribution prediction results to other cells. Except for the selectivepaging algorithm in [2], [23], all other schemes on the mobilityprediction are instructed to find the next cell instead of multiplecells. Let us consider that the maximum number of cells to be

13

predicted in our algorithm is F2?°#T; I X in (22) for terminal @given that the MT is currently in zone , and the prediction levelis ° . Then, the total communication cost of informing other cellsis obtained as ?°M; I X Y ! , where ! is the communica-tion cost for one cell, i.e., the cost for all algorithms of next-cellprediction. Therefore, the overhead of the proposed scheme isclosely dependent on the number of cells in the mobility profiles,which is also the number we need to reduce as much as possi-ble. However, this communication cost does not take any radioresources; instead, it uses dedicated wirelines between base sta-tions. With the transmission speed in fiber optics at 10Gbps,this communication overhead is trivial. But, we obtain bene-fits in terms of QoS improvement and decreased tracking cost.In fact, this information can also be used for advanced routingalgorithms which require reservation and estimation [14], [23].

We can further reduce the overhead by grouping users. Al-though we describe the prediction scheme based on per-user ba-sis, it is possible that the same results can be applied to differentmobile users who follow the same mobility pattern. If a group ofmobile users in one cell are moving along the same path withinthe time interval for records updating, then the location prob-abilities in the adjacent cells may be the same. However, weneed to differentiate two mobile terminals that are in the samecell, but may result in different prediction results. For instance,there are two users that are both traveling on a highway, whichis covered by a BS in the downtown area of a city. One of usersis a local commuter, and the other user is passing on his way toanother city. In other words, they are in the same cell, probablyeven move moving very close to the same speed, but they havedifferent destinations. The system is not aware of these mo-bile users’ destinations, but it is possible to have their recordsthrough the HLRs of their home networks. Moreover, in themacrocell systems, the location probabilities and service typescan be estimated for adjacent cells only rather than a group ofcells. For micro-cell systems, which are now being used in manyurban and suburban areas, the estimation for only one cell is notenough as the mobile users may pass through that cell in a shortamount of time. The challenge is how to identify these cells,which is being addressed in this paper.

VI. SIMULATION MODEL

In this section, assumptions and specifications used in thesimulation are described. Instead of assuming in many previousstudies, that an MT travels along a highway or one-dimensionalenvironment, we consider random behavior in our simulation,which involves much more complicated computation. We con-sider two scenarios in our service estimation: uniform and non-uniform distributions. As described in Section III-A, i.e., theservice description of quasi-stationary UMP is able to providethe PMF of services as shown in (5).

Suppose there are five types of services supported by theMT’s current wireless network, which are audio, video, voice,data, and voice mail. When the uniform PMF is the case, i.e.,¬ ­Qد 1 d , the probability of each type of service is equal. Asfor the non-uniform PMF, we use the same example as in Sec-tion III. Each MT is allowed to request any type of service at aparticular moment. We will predict the service pattern by using

(10) to (16) in Section IV-B.

Fig. 11. MAP for Simulation.

The time is quantized in intervals UF _ , which is apreset time window. This interval is chosen based on cell resi-dence time for each mobile terminal. In reality, different usersmay have different moving speeds and different mean residencetimes. However, for a specific cell, the average velocity canbe determined for the mobile users in its coverage area. Ac-cordingly, the cell residence time can be calculated by dividingthe cell diameter by the average velocity. The calculation timewindow is much smaller than the cell residence time except inpico-cell systems. In our simulation, the service request froman MT is generated according to a Bernoulli process in each celland each moment.

We also consider the MT’s speed and changes in its movingdirection [17], [46]. The MT is allowed to move away from itscurrent position in any direction, and variation from its previousdirection is a uniform distribution limited in the range of K G .The initial velocity of an MT is assumed to be a random vari-able with Gaussian probability density function truncated in therange of 5 I d QPðaSX7 and the velocity increment is taken to bea uniformly distributed random variable in the range of K _Wof the average velocity, > >QPðaS . As for the residence time dis-tribution in (1), the values of is taken with 1 [48].

The most important feature of this simulation is that we usean actual digital map for computing the mobile location proba-bilities. In the selected segmentation of the MAP as shown inFig. 11, there is an Interstate Highway I-85 and a toll freeway400 on which most of the city traffic travels. We deliberatelychose this segment, 7km by 5km, because it is a combinationof diverse environments that provides a number of choices for atraveling MT, thus generating different location probabilities. Ifwe only consider highways, then the location probability predic-tion is only related to the next cell in a one-dimensional model.By establishing a grid model, this area is covered by 30 cellscovering the area. We find that the maximum number of routesfor each cell is 10. Thus, the maximum number of routes in oursimulation is 300. Based on the geographical condition of thisarea, we generate a path database (PD), which will be used forpredicting location probabilities in Section IV-C.2.

14

A. Effect on Mobility Management

In current personal communication service (PCS) systems, lo-cation update and paging are two fundamental operations for lo-cating a mobile terminal (MT). As the demand for wireless ser-vices grows rapidly, the signaling traffic caused by location up-date and paging increases accordingly, which consumes limitedavailable radio resources. Location update is concerned reportscurrent locations of the MTs. In a paging process, the systemsearches for the MT by sending poll messages to the cells closeto the last reported location of the MT at the arrival of an incom-ing call. Delay time and cost are two key factors in the pagingissue. Of the two factors, paging delay is very important as theQoS requirement for multimedia services. Paging cost, whichis measured in terms of cells to be polled before the called MTis found, is related to the efficiency of bandwidth utilization andshould be minimized under delay bound [3], [44].

To evaluate the performance of mobility profiles, we use thepaging costs and paging delays [2], [15] as metrics to demon-strate the effect of the designed schemes on mobility manage-ment. We will also compare the results with the so-called se-lective paging in [2] because the location probabilities are esti-mated. The cell radius is assumed to be d QP in our simulation.The full area of the segmentation map is covered by this type ofcells, and we assume there is one BS in each cell and all of themare controlled by an MSC as in Fig. 1. A highest-probability-first (HPF) scheme is introduced in which the sequential pollingis performed in decreasing order of probabilities to minimize themean number of cells being searched [35].

We assume that each LA consists of the same number[

ofcells in the system. The worst-case paging delay is consideredas delay bound, ò , in terms of polling cycle. When ò is equalto , the system should find the called MT in one polling cycle,requiring all cells within the LA to be polled simultaneously.The paging cost, ! , which is the number of cells polled to findthe called MT, is equal to

[. In this case, the average paging

delay is at its least, which is one polling cycle, and the averagepaging cost is at its highest, ! [ . On the other hand, when òis equal to

[, the system will poll one cell in each polling cycle

and search all cells one by one. Thus, the worst-case scenariooccurs when the called MT is found in the last polling cycle,which means the paging delay is at its maximum and equal to[

polling cycles [44]. However, the average paging cost maybe minimized if the cells are searched in decreasing order oflocation probabilities [35].

We consider the partition of paging areas (PAs) given that C ò C [, which requires grouping cells within an LA

into the smaller PAs under delay bound ò [35], [44]. Sup-pose, at a given time, the initial state P is defined as

y=5 $ I $ I ofogo I $T¸ I ogofo I $2¼7 , where $X¸ is the location probability of¹ ý cell to be searched in decreasing order of probability. We

use triplets ¡ºe? Iy z I z to denote the PAs in which is the se-quence number of the PA; z is the location probability that thecalled MT can be found within the ý PA and Jz is the numberof cells contained in this PA. An LA can be divided into ò PAsbecause the delay bound is assumed to be ò . Thus, the worstcase delay is guaranteed to be ò polling cycles. The systemsearches the PAs one after another until the called MT is found.

Accordingly, the location probability z of the ý PA is: zJ µ¸í¶ifÎÐz Ó $T¸ 1 (24)

If the called MT is found in the ý PA, the average pagingcost under delay bound ò , 3Æ5 ! ò«7 , is computed as follows:3Æ5 ! ò«7ǵ zÐã z o zµÂOã  I (25)

and the average delay, 3Æ5 ð ò«7 is:3Æ5 ð ò«7ǵ zÄã o z 1 (26)

B. Effect on Resource Management

When the estimation of service type is applied to resourcemanagement, we define the probability vector, x a z <­ I ;= , asx z ­ I ;=©5 z? ~ <­ I ;=, a z< ­ I ;= ogofo a z< ­ I ;=7 I (27)

where z? ~ <­ I ;= is the probability that an MT, @ remains in acell given that the MT initiates a call in cell while this call isa ­ type of service and it is not over by ; . ¡a z< ¸><­ I ;= for ¹ð Id ofogo I , is the probability that a call is still active in cell ¹given that this call is initiated in cell . We also consider the pdf,]Ç<­ I ;= , which represents the distribution of call holding time ofservice type ­ . With the above consideration and recalling thedefinition of xy a z of (4) in Section III-B, for an MT, @ that isinitiating a call of service ­ in cell , the probability a ~ <­ I ;=can be determined by the following expression:

4 ~<­ I ;=D5Ð A% ­ I ;=7 o 5Ð A µ¸|ã 9a z< ¸?;=«7 (28)

where <­ I ;= is the cumulative distribution functions for ]$­ I ;=and z? ¸ <;= for ¹Z IdTI ogofo I is the probability that the MTwill be in cell ¹ in (28) which is the product of two probabilitiesbecause we assume the calling pattern is independent of an MT’smovement. 5Ð Ae ­ I ;=7 is the probability that the call is not overby time ; , and 5þ A ¸|ã 9a z< ¸>?;=«7 is the probability that the MTis still in cell at time ; given that there are probable cells.

For the other cells in the shadow cluster, we define the cumu-lative distribution functions for probable cells with service ­as x z=<­ I ;=Ø5 z? <­ I ;= z? <­ I ;= a z< <­ I ;=«7 . Therefore,x a z ?;= is determined byx a z <­ I ;=ê ëOì îzMã/~ 5 x A x a z <­ I ;=«7 o\ (29)

where x is a vector with ones and is a diagonal matrix as:

z? ?;= ogofo 9 z? ?;= ogofo . . . . . . ogofo a z< ?;=

* 1 (30)

15

As a result, each element of x a z|<­ I ;= in (27) is determined.Accordingly, the bandwidth needed in the next probable cellsfor an MT, @ in cell , x¡ z <­ I ;= , can be reserved as:x¡ zÔ­ I ;=!¯­ o x z=<­ I ;= (31)

We consider the stochastic admission control in our simula-tion [20], [23]. For each mobile user, the current serving basestation periodically exchanges information with its adjacent andnon-adjacent neighbors periodically with the equivalent band-width requirement. We assume that the time is quantized inslots of length UF . Also, we assume that new call requests arereported at the beginning of each time slot, and that a decisionregarding an admission request is made sometime before the endof the time slot where the request was received. Every base sta-tion gathers call connection requests from MTs in its cell, andchecks whether its current resources can support the requestedequivalent bandwidth. A call is admitted if the sum of the equiv-alent bandwidth at a link is less than the link capacity, which isalso called semi-resource reservation [20]. We use the metricsof handoff call dropping probability for handoff calls and callblocking probability for new arrivals.

VII. COMPARISON AND EVALUATION

A. Comparison of Single- and Multi-Cell Prediction

In the proposed UMP framework, we consider the followingfactors in predicting future locations of mobile users: 1) histori-cal records; 2) path information; 3) statistical model; 4) movingdirection and velocity; 5) current position of a mobile object;and 6) shadow cluster, i.e., a set of possible cells. All of thesefactors impact location prediction as described in previous sec-tions. In this section, we evaluate the proposed scheme withregard to the effect on mobility and resource management.

In addition, we compare the proposed scheme with previouswork on location prediction. As described in Section I, manyprevious schemes consider only some of the factors that we con-sider in the proposed UMP framework. This work can be cat-egorized into single-cell prediction [7], [13], [16], [18], [25],[34], [48] and multi-cell prediction [2], [6], [23]. In the formercategory, each of them considers only two or three factors com-pared to six factors covered in our proposed scheme. Moreover,location estimation is focused on the next cell instead of a groupof cells. Therefore, the impact of other factors is ignored andmay also overlook the possibilities in other cells.

Especially, for micro-cell systems, single-cell prediction notonly can provide advance probabilistic information for resourcereservation, but more importantly, the estimation of locationprobability can be used for location tracking as well. In par-ticular, if there is no new interaction between the system and amobile user since the last update, multi-cell prediction will havean important influence on user tracking. Regardless of the rea-sons causes the interruption of communications, the system canalways initiate searching or testing a mobile object based on itsprofiles in mobile environments. Moreover, if the cell radius isvery small, it may not be efficient to generate dynamic UMPfrequently, e.g., per cell; instead, we can adjust the window timefor calculating UMP to reduce computation and communication

cost. The effect of single-cell prediction and multi-cell predic-tion are shown in Figs. 15 to 18.

For the second category, i.e., multi-cell prediction, it hasbeen very difficult to compare the location probabilities quan-titatively. Thus, most of the literature will elaborate the ratio-nale of the proposed schemes and demonstrate the results by theeffect on either mobility management or resource management.In [23], the shadow cluster idea was proposed, but there is nofurther discussion on how to decide such a cluster and how toestimate location probabilities. To find a group of cells in multi-cell prediction, in [6], the authors propose a prediction methodto find most likely cluster (MLC) based on directional proba-bilities. The method of MLC further approaches and reducesthe number of cells defined in [23]. The location probabilities,therefore, are defined as the fraction of directional probabilityin one cell to all the cells through which a mobile object cantraverse during the window time.

However, there are three major concerns of this method. First,it depends on accurate direction measurements using the GlobalPositioning System (GPS). This assumption is relaxed in ourwork by using zone partition. In our algorithm, as long as thedirection measurement is accurate to ª IV-C.2, no cells will bemissed in the prediction. This is easier to implement in real sys-tems. Second, this paper does not take user history into consid-eration. Although user history may not be important for macro-cell systems, it is critical to micro- and pico-cell systems be-cause mobile objects are very likely to change their directionsfrequently. Considering that mobile users usually follow a cer-tain pattern in their movement, this pattern based on directionalchanges only, is not sufficient for mobility prediction. Third,there was no consideration of path information in [6]. No mat-ter how likely a mobile object can move into a region from theanalysis based on current measurements, it must move into anarea that allows movement continuity, i.e., a path must exist inthe next cell. Therefore, we take the path database into accountby comparing available path with the predictive future path.

In [2], moving direction, current position, and the grid layoutof a cellular architecture are considered for location prediction.Similar to [6], user history and path information are ignored.Location probability is estimated based on cell residence timeinstead of directional changes. Although it is stated that the lo-cation probabilities can be computed, paper [2] is more focusedon how to group those possible cells into subsets for paging pur-poses. The algorithm described in [2] is labeled as ”SelectivePaging” in Fig. 15. More details about the paging algorithmsand comparison can be found in our paper [44].

B. Numerical Results

First, we investigate the convergence of mean square error byusing (15), which is shown in Fig. 12. For the uniform PMF,the first convergence point is approximately

, while it isapproximately

d for non-uniform PMF. Thus, if an MTsubscribes a service package which conforms to a uniform PMF,the next probable service type can be predicted more accuratelycompared to a non-uniform PMF. Accordingly, the bandwidthrequirement can be determined. For example, the bandwidthrequirement for each service type may be normalized by voice

16

0 50 100 150 200 250 3000

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Fig. 12. Convergence of Mean Square Error.

service, such as ­£¢ × «²ñ¥¤ I V> × Û²ñ¥ I VQ²«ÈíÛ I|× ­_;Ô­Ú¤ I V_²«ÈíÛ A P,­_«ô . Then, we estimate service type ª for anMT using the algorithm in Section IV-B. In our experiments,both uniform PMF and non-uniform PMF are considered. Wecompute the mean square errors using (14) and (15). Then, wedetermine the service type according to the scheme in Fig. 6.

2 4 6 8 10 120

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0.3

0.4

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Loca

tion

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babi

litie

s

θx= ± π/3, first−level

θx = ± π/2, first−level

θx= ± π/3, second−level

θx = ± π/2, second−lvel

Fig. 13. Mobile Probabilities.

Then, we predict the probable cells using the algorithm de-scribed in Section IV-C. For : ?;=!bK B ¤ , and : ?;=!bK B d ,we first determine the probable zones using (17) and (18), limit-ing the probable cells in a particular region. Next, the number ofprobable cells is computed using (1), (19) and (22). The com-puted probabilities are shown in Fig. 13 in a decreasing order oflocation probabilities.

It can be seen that the number of probable cells influencedby shadowing effect depends on the variation of the direction ofan MT’s movement as well as the velocity and prediction level.For the first order of prediction, the number of cells is small,indicating that the probability in each cell is higher. For thesecond order of prediction, the location probabilities decreasewith an increase in the number of cells. When the predictionlevel is the same, the variation of direction is the key factor thataffects the number of cells and location probabilities. We notice

that there are fewer high probability cells than low probabilitycells because an MT is most likely to be moving into a few cellsin the next moment rather than uniformly being dispersed in itssurrounding cells.

There are many ways to evaluate the effectiveness of the pre-diction algorithm of computing location probabilities [13], [14],[23], [29] as we introduced in Section I. Here, we show theeffect of these results on paging issues since it involves bothpaging costs and paging delays. Paging is the process by whichthe MSC sends polling message to BSs in its management areato determine the serving cell of the called MT. Paging cost af-fects network resources because the paging message is sent viadown-link channels; thus, it should be reduced as much as pos-sible. Paging delay is part of call delivery delay, and it is relatedto QoS requirement. Thus, it should also be reduced so that thecall connection can be established quickly.

Paging costs resulting from location probabilities of first andsecond levels of prediction are compared to those of uniformdistribution assumed in the existing paging schemes [14], [15].Note that the number of cells is determined by the predictionlevel and moving direction presented in Section IV-C.2, whichhas a strong impact on the performance of the scheme. Increas-ing the prediction level and change in direction, by includingmore cells, increases the likelihood of supporting QoS in futurepossible cells. But, this will cause more computations and com-munications. Therefore, we compare paging cost and delay withregard to change in direction and prediction levels. An extremecase is that the prediction level is zero, i.e., there is no predic-tion at all. We conduct the experiments on the following cases:: B ¤ with first- and second-level prediction; : B ¤without prediction for the cells in one or two layers surroundingthe current cell; :a B d with first- and second-level predictionas shown in Figs 14 and 15.

The numerical results of paging costs are given in Fig. 14(a)and Fig. 14(b), in which paging costs are measured by the num-ber of cells to be searched before finding the MT. Since thelocation probabilities provided in [2] are related to three cells,the paging cost is better than the two-cell prediction, and worse

17

than the 4-cell prediction as shown in Fig. 14(a) and Fig. 15(a).When the variation of moving direction is high, causing moreprobable changes, the improvement of paging costs is more vis-ible in Fig. 14(a). For example, when : wK G , the reductionin paging costs due to the location probabilities is not as largeas that of :Ö K G . This means that it is more important topredict location probabilities if the MTs are moving randomly,i.e., the movement of the MTs is not uniformly distributed in thelocation area.

The paging cost of the proposed scheme is very close to thescheme proposed in [2] for the first level prediction becausethere are a small number of cells in the shadow cluster. There-fore, the benefits of the proposed scheme are not evident com-pared to the scheme for ”Selective Paging” in [2], which alsocovers the cells adjacent to the current cell. If the predictionlevel is higher, the paging costs are significantly reduced com-pared to those without prediction. Specifically, if MTs are mov-ing very fast and are expected to other cells in a short time,there are more probable cells. As a result, location probability ineach cell is smaller. As a result, it is more difficult to locate theMT. Accordingly, the prediction of MTs’ location probabilitiesis more effective and more important.

Paging delays are compared in Fig. 15(a) and 15(b), which aremeasured in terms of polling cycles. Each polling cycle is thetime from sending a paging request to receiving a response. InFig. 15(a), the paging delays are greatly reduced in comparisonto not using prediction. As the delay constraints increase, theaverage paging delays increase while the paging costs decrease.We notice that the delays are reduced even more when the de-lay constraints are greater. Also, the predicted probabilities aremore effective on reducing paging delays when the predictionlevel is higher as shown in Fig. 15(b). This is especially usefulfor those MTs moving in wide areas, where there are many pathsavailable instead of high-way scenarios.

We also conduct simulations of resource management. Thepredicted service type and location probabilities are used to re-serve the equivalent bandwidth for the mobile terminals. In oursimulation, we consider different new call ratio as the numberof requests of new calls to the total number of call requests. Theresults shown in Fig. 16 to Fig. 17 are the statistics of 20,000 callrequests. If the requested bandwidth cannot be allocated, then anew call will be blocked or the handoff call will be dropped.

We consider that handoff calls have higher priority than newcalls. Therefore, call dropping/blocking probabilities are relatedto the new call ratio, which is the fraction of new calls in thetotal number of connections requested. For each of them, wecompare no-reservation, next-cell reservation, two-cell reserva-tion, and 4-cell reservations. In particular, next cell reservationcorresponds to single-cell prediction discussed in Section VII-A. In Fig. 16, we can observe that call dropping probabilitiesincrease as call arrival rates increase, indicating that the band-width release depends on the call departure. Given the fixedcall holding time, the more call arrivals, the higher call drop-ping and blocking probabilities. Meantime, we can see that thecall dropping probabilities decrease as we reserve bandwidth inmore cells, i.e., better than single-cell prediction. The effect ofreservation are obviously on the handoff dropping probabilities

than on the new call blocking probabilities. If major call re-quests come from handoff, then call dropping probabilities arehigher, compared to the case in which the new calls are domi-nant.

1 1.5 2 2.5 3 3.5 4

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Fig. 14. Comparison of Paging Costs.

VIII. CONCLUSIONS

We have explored a fundamental issue of providing high levelQoS in wireless networks. Noticing that the key point to QoS-based mobile networks is the knowledge of service requirementsand future locations prior to the arrival of mobile objects, wefirst proposed a novel framework of UMP, considering many im-portant factors associated with the MTs’ behavior. Then, we cat-egorized the UMP information into quasi-stationary UMP anddynamic UMP, and discussed how to coordinate them for theprediction of services and possible locations. The service re-quirement is estimated by using a mean square error methodbased on the historical records and service probability distribu-tions. Moreover, we introduced the concept of zones and predic-

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1 1.5 2 2.5 3 3.5 41

1.5

2

2.5

Delay Constraints

Pag

ing

Del

ays

θx= ± π/3, first−level prediction

θx = ± π/3, one layer without prediction

θx= ± π/2, first−level prediction

θx = ± π/2, one layer without prediction

Selective Paging

Next cell prediction

(a) First-Level Prediction

2 4 6 8 10 121

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Pag

ing

Del

ays

θx= ± π/3, second−level prediction

θx = ± π/3, two layers without prediction

θx= ± π/2, second−level prediction

θx = ± π/2, two layers without prediction

Delay Constraints

(b) Secon-Level Prediction

Fig. 15. Comparison of Paging Delays.

tion levels to shrink the region of probable cells. In the proposedprediction algorithms, we took several important factors into ac-count, including direction and velocity of mobile objects, histor-ical records, stochastic model of cell residence time, and path in-formation into account. Therefore, the service requirement andfuture locations are predicted more accurately compared to pre-vious schemes because this is the first time that all of these fac-tors are considered. As examples, we provided the simulationresults to demonstrate that the proposed algorithms for mobil-ity and resource management are effective in terms of reducinglocation tracking cost, delays, and call dropping/blocking prob-abilities.

REFERENCES

[1] 3G TS 23.002 v3.6.0 (2002-09), ” ¦\§©¨ Generation Partnerships Project:Technical Specification Group Services and Systems Aspects: NetworkArchitecture/(Release 1999),” September 2002.

[2] A. Abutaleb and V.O.K. Li, “Paging Strategy Optimization in PersonalCommunication System,” ACM-Baltzer Journal of Wireless Networks(WINET), Vol. 3, pp. 195-204, August 1997.

0.05 0.1 0.15 0.2 0.25 0.30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Call Arrival Rate with 10% New Calls

Cal

l Dro

ppin

g P

roba

bilit

y

No resvNext cell resv2 cell resv4 cell resv8 cell resv

(a) Handoff Dropping Probabilities

0.05 0.1 0.15 0.2 0.25 0.30

0.005

0.01

0.015

0.02

0.025

Arrival Rate with 10% New Calls

Cal

l Blo

ckin

g P

roba

bilit

y

No resvNext cell resv2 cell resv4 cell resv8 cell resv

(b) New Call Blocking Probabilities

Fig. 16. Dropping and Blocking Probabilities with 10% New Calls.

[3] I.F. Akyildiz, J. McNair, J.S.M. Ho, H. Uzunalioglu, and W. Wang”, ”Mo-bility Management in Next-Generation Wireless Systems,” Proceedings ofthe IEEE, Vol. 87, No. 8, pp. 1347-1384, August 1999.

[4] I.F. Akyildiz and W. Wang, ”A Dynamic Location Management Schemefor Next Generation Multi-Tier PCS Systems,” IEEE Transactions onWireless Communications, Vol. 1, no. 1, pp. 2040-2052, January 2002.

[5] D.P. Agrawal and Q-A. Zeng, “Introduction To Wireless and Mobile Sys-tems,” Thomson Brooks/Cole, 2003.

[6] A. Aljadhai and T.F. Znati, ”Predictive Mobility Support for QoS Provi-sioning in Mobile Wireless Environments,” IEEE Journal on Selected Ar-eas in Communications (JSAC), Vol. 19, No. 10, pp. 1915-1931, October2001.

[7] A. Bhattacharya and S. K. Das, “LeZi-Update: An Information-TheoreticApproach to Track Mobile Users in PCS Networks,” ACM/IEEE Mobi-Com’99, August 1999.

[8] E. Cayirci and I.F. Akyildiz, “User Mobility Pattern Scheme for LocationUpdate and Paging in Wireless Systems,” IEEE Transactions on MobileComputing, Vol. 1, No. 3, pp. 236-247, July-September 2002.

[9] E. Cayirci and I.F. Akyildiz, “Optimal Location Area Design to MinimizeRegistration Signaling Traffic in Wireless Systems,” IEEE Transactions onMobile Computing, Vol. 2, No. 1, pp. 76-85, January-March 2003

[10] T. Camp, J. Boleng, and V. Davies, “A Survey of Mobility Modelsfor AdHoc Network Research,” Wireless Communications & Mobile Computing,Vol. 2, no. 5, pp. 483-502, 2002.

[11] Y, Cai and K. A. Hua, ”An Adaptive Query Management Technique for

19

0.05 0.1 0.15 0.2 0.25 0.30

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Call Arrival Rate with 10% New Calls

Cal

l Dro

ppin

g P

roba

bilit

y

No resvNext cell resv2 cell resv4 cell resv8 cell resv

(a) Handoff Dropping Probabilities

0.05 0.1 0.15 0.2 0.25 0.30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Arrival Rate with 90% New Calls

Cal

l Blo

ckin

g P

roba

bilit

y

No resvNext cell resv2 cell resv4 cell resv8 cell resv

(b) New Call Blocking Probabilities

Fig. 17. Dropping and Blocking Probabilities with 90% New Calls.

Efficient Real-Time Monitoring of Spatial Regions in Mobile Environ-ments,” Proc. of the 21st IEEEE Int’l Performance, Computing, and Com-munications Conference (IPCCC), pp. 259-266, April 2002.

[12] K. Choi and W. Jang, “Development of a transit network from a street mapdatabase with spatial analysis and dynamic segmentation,” Transp Res PartC Emerging Technol, Vol. 8, No. 1, pp. 129-146, January 2000.

[13] S. Choi and K.G. Shin, “Predictive and Adaptive Bandwidth Reser-vations for hand-offs in QoS-sensitive Cellular Networks,” ACM SIG-COMM’1998, pp. 155-166. Vancouver, August 1998.

[14] M. Y. Chung and D. K. Sung, “Performance Analysis of a Profile Man-agement Scheme for Incall Registration/ Deregistgration in Wireline UPTNetworks–Part I: Request-Based Scheme,” IEICE Transactions on Com-munications, Vol. E82-B, No. 5, pp. 686-694, May 1999.

[15] D. Gu and S.S. Rappaport, “A Dynamic Location Tracking Strategy forMobile Communication Systems,” IEEE VTC’2000, vol. 1, pp. 259-263,Ottawa, May 1998.

[16] M. Hellebrandt and R. Mathar, “Location Tracking of Mobiles in CellularRadio Networks,” IEEE Transactions on Vehicular Technology, vol. 48,no. 3, pp. 1558-1562, September 1999.

[17] M. Hellebrandt and R. Mathar and M. Scheibenbogen, ”Estimation Posi-tion and Velocity of Mobiles in a Cellular Radio Network,” IEEE Transac-tions on Vehicular Technology, Vol. 46, No. 1, pp. 65-71, February 1997.

[18] J.S.M. Ho and J. Xu, “History-Based Location Tracking for Personal Com-munications Networks,” IEEE VTC’1998, vol. 1, pp. 244-248, Ottawa,May 1998.

[19] C.S. Jensen, A. Friis-Christensen, T.B. Pedersen, D. Pfoser, S. Saltenis,

and N. Tryfona, ”Location-Based Services - A Database Perspective,”Proc. of the Eighth Scandinavian Research Conference on GeographicalInformation Science, pp. 59-68, June 2001.

[20] G.S. Kuo and P-C. Ko and M-L. Kuo, ”A Probabilistic Resource Estima-tion and Semi-Reservation Scheme for Flow-Oriented Multimedia Wire-less Networks,” IEEE Communications Magazine, Vol. 39, No. 2, pp. 135-141, February 2001.

[21] K. Kawabata, T. Nakamura, and E. Fukuda, “Estimating Velocity UsingDiversity Reception”, Proc. IEEE Veh. Tech. Conf., vol. 1, 1994, pp. 371-374.

[22] J. Korhonen, “Introduction to 3G Mobile Communications”, ArtechHouse, 2001.

[23] D.A. Levine, I.F. Akyildiz, and M. Naghshineh, “A Resource Estimationand Call Admission Algorithm for Wireless Multimedia Networks Usingthe Shadow Cluster Concept,” IEEE/ACM Transactions on Networking,Vol. 5, No. 5, pp. 1-12, February 1997.

[24] A. Leon-Garcia, “Probability and Random Processes for Electrical Engi-neering,” Second edition, Addison-Wesley, 1994.

[25] T. Liu, P. Bahl and I. Chlamtac, “Mobility Modeling, Location Tracking,and Trajectory Prediction in Wireless ATM Networks,” IEEE Journal onSelected Areas in Communications (JSAC), Vol. 16, No. 6, pp. 922-936,August 1998.

[26] Y-B. Lin, “Reducing Location Update Cost in a PCS Network,”IEEE/ACM Transactions on Networking, Vol. 5, No. 1, pp. 25-33, Febru-ary 1997.

[27] Y-B. Lin and W-N. Tsai, “Location Tracking with Distributed HLR’s andPointer Forwarding,” IEEE Transactions on Vehicular Technology, Vol. 47,No. 1 , February 1998.

[28] K. Lam, O. Ulusoy, T.S. H. Lee, E. Chan, and G. Li, ”An Efficient Methodfor Generating Location Updates for Processing of Location-DependentContinuous Queries,” Proc. of DASFAA’2001, pp. 218-225, April 2001.

[29] J. Misic and T. Y. Bun, “On Call Level QoS Guarantees under Heteroge-neous User Mobilities in Wireless Multimedia Networks,” IEEE GLOBE-COM’99, Vol. 3, pp. 2730-1769, December 1999.

[30] W. Ma and Y. Fang, ”Two -Level Pointer Forwarding Strategy for LocationManagement in PCS Networks,” IEEE Transactions on Mobile Comput-ing, Vol. 1, No. 1, 32-45, March 2002.

[31] R. Narasimhan and D.C. Cox, ”Speed Estimation in Wireless Systems Us-ing Wavelets,” IEEE Transactions on Communications, Vol. 47, pp. 1357-1364, 1999.

[32] D. Pfoser, C.S. Jensen, and Y. Theodoidis, ”Novel Approaches in QueryProcessing for Moving Objects,” Proc. of Very Large Database (VLDB)Conference 2000, September 2000.

[33] S. Ross, ”A First Course in Probability,” Prentice Hall, Sixth Edition,2002.

[34] X. Shen, J.W. Mark and J. Ye, “User Mobility Profile Prediction: AnAdaptive Fuzzy Inference Approach,” ACM-Baltzer Wireless Networks(WINET), No. 6, pp. 363-374, June 2000.

[35] C. Rose and R. Yates, ”Minimizing the Average Cost of Paging UnderDelay Constraints,” ACM-Baltzer Journal of Wireless Networks (WINET),Vol. 1, pp. 211-219, February 1995.

[36] J. Sun and H.C. Lee, “Mobility Data Pattern Tracking via Multidimen-sional Data View Approach,” IEEE MilCom’97, pp. 1255-1260, Novem-ber 1997.

[37] ETSI TS 101 513 V8.0.1 (2000-11), ”Digital cellular telecommunicationssystem (Phase 2+); Location Services (LCS); Location services manage-ment,” (GSM 12.71 version 8.0.1 Release 1999), November 2000.

[38] ”ETSI TS 123 012 V4.0.0 (2001-03),” Digital cellular telecommunica-tions system (Phase 2+) (GSM); Universal Mobile TelecommunicationsSystem (UMTS); Location Management Procedures, (3GPP TS 23.012version 4.0.0 Release 4), March 2001.

[39] ETSI TS 123 271 V4.1.0 (2001-03), ”Universal Mobile Telecommunica-tions System (UMTS);Functional stage 2 description of location services,”3GPP TS 23.271 version 4.1.0 Release 4, March 2001.

[40] ETSI TS 129 010 V4.0.0 (2001-03), ”Digital cellular telecommunicationssystem (Phase 2+) (GSM); Universal Mobile Telecommunications System(UMTS); Information element mapping between Mobile Station - BaseStation System (MS - BSS) and Base Station System - Mobile-servicesSwitching Center (BSS - MSC); Signaling procedures and the MobileApplication Part (MAP),” (3GPP TS 29.010 version 4.0.0 Release 1999),March 2001.

[41] 3G TS 23.018 v3.5.0 (2000-06), ”3rd Generation Partnership Project;Technical Specification Group Core Network; Basic Call Handling; Tech-nical Realization,” June 2000.

[42] W. Wang, “Modeling and Management of Location and Mobility,” Wire-less Information Highways, To be published in March 2004.

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[43] W. Wang and I.F. Akyildiz, “Intersystem Location Update and PagingSchemes for Multitier Wireless Networks,” ACM/IEEE MobiCom’00, pp.99-109, August 2000.

[44] W. Wang, I.F. Akyildiz, G. Stuber, and B-Y. Chung ”Effective PagingSchemes with Delay Bounds as QoS Constraints in Wireless Systems,”ACM-Baltzer Wireless Networks (WINET), Vol. 7, No. 5, pp. 455-466,September 2001.

[45] C. Xiao, “Estimating Velocity of Mobiles in EDGE Systems,” Proc. 2002IEEE ICC, pp.3240-3244, April 2002.

[46] C. Xiao, K.D. Mann, and J.C. Olivier, ”Mobile Speed Estimation forTDMA-Based Hierarchical Cellular Systems,” IEEE Transactions on Ve-hicular Technology, Vol. 50, No. 4, pp. 981-991, July 2001.

[47] T. Zhang, E.V.D. Berg, J. Chennikara, P. Agrawal, and J-C. Chen and T.Kodama, ”Local Predictive Resource Reservation for Handoffs in Multi-media Wireless IP Networks,” IEEE Journal on Selected Areas in Com-munications (JSAC), Vol. 19, No. 10, pp. 1931-1941, October 2001.

[48] M.M. Zonoozi and P. Dassanayake, “User Mobility Modeling and Charac-terization of Mobility Patterns,” IEEE Journal of Selected Areas in Com-munications, Vol. 15, No. 7, pp. 1239-1252, September 1997.

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