Modeling and Tracking Complexly Moving Objects in Location-Based

JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 20, 517-534 (2004)

Modeling and Tracking Complexly Moving Objects in Location-Based Services* MOONBAE SONG, KWANGJIN PARK, JEHYOK RYU AND CHONG-SUN HWANG Department of Computer Science and Engineering Korea University Seoul 136-701, Korea E-mail: {mbsong, kjpark, jhryu, hwang}@disys.korea.ac.kr One of the most important issues in location-based services is tracking moving objects efficiently. To achieve this goal, an efficient protocol which updates location information in a location server is primarily needed. In fact, the performance of a location update strategy highly depends on the assumed mobility pattern. In most existing studies, however, the mobility issue has been disregarded and oversimplified as a linear function of time. In this paper, we propose a new mobility model, called state-based mobility model (SMM) to provide a more generalized framework for describing both the mobility and updating location information of complexly moving objects. We also introduce the state-based location update protocol (SLUP) based on this mobility model. Keywords: mobility modeling, location tracking, moving objects, location-based services, location update protocol

1. INTRODUCTION In mobile computing environments, mobile terminals (MTs) are emerging in many forms and applications, such as databases, networks and so on. MTs, like cellular phones, PDAs, and mobile PCs, can dynamically change their locations over time. Objects which continuously change their location and extent are called moving objects. Thus, what is important in the mobile computing environment is how to model the location and movement of moving objects efficiently. Therefore, a software infrastructure providing location-based services, called a moving objects database (MOD), is greatly needed. Recently, many studies has been done on the representation and management of moving objects [5, 13, 14]. Wolfson et al. presented the well-known data model called Moving Object Spatio-Temporal (MOST) for representing moving objects [18]. In the MOST model, the location of a moving object is simply given as a linear function of time, which is specified by two parameters: the position and velocity vector of the object. Thus, without frequent update messages, the location server can compute the location of a moving object at a given time t through linear interpolation: y (t ) = y0 + v (t - t 0 ) at time

Received October 15, 2003; accepted November 15, 2003. Communicated by Ten-Hwang Lai, P. Sadayappan, Yu-Chee Tseng and Yi-Bing Lin. * This work was supported by grant No. R01-2002-000-00235-0 from the Basic Research Program of the Korea Science & Engineering Foundation.

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t > t0. An update message is only issued when the parameter of the linear function, e.g. v , is changes. In general, we call this update approach dead-reckonin. It offers a great performance benefit in linear mobility patterns, but performance suffers when the randomness of the mobility pattern increases. Thus, this approach suffers greatly from performance degradation in non-linear mobility patterns. In this paper, we examine a mobility model for MOD and an appropriate location update protocol. The purpose of our scheme is to model the overall movement patterns in a probabilistic manner. Depending on the temporal locality of the mobility patterns, the proposed scheme can greatly reduce the number of update messages. The rest of this paper is structured as follows: In section 2, we introduce the characteristics of mobility patterns of real-life objects. Section 3 covers our proposed architecture for managing location information. The proposed mobility model, called the state-based mobility model (SMM), is described in section 4. In section 5, we present a new location update protocol called the state-based location update protocol (SLUP), which considers mobility patterns on a per-user basis. Extensive performance evaluation and comparison of the proposed scheme with traditional update strategies are also included in section 6. Finally, a summary and future works are presented in section 7.

2. MOTIVATION Consider a traveling salesman who travels to several cities to sell commodities. He starts at his company and moves along an expressway. When he reaches his destination, he strolls around the city selling commodities, and then finds a new destination. We anticipate that this model will be able to capture a large part of a real-life object’s movements. Furthermore, it will include the essential elements of mobility patterns, such as linear movement, random movement, and the stationary state. On the other hand, existing mobility models do not express the realistic movements of real-life objects. Thus, it is inevitable that the update cost of a moving object and the average error in accuracy will increase. In our work, we divide the whole trajectory of a user into three basic movements: ‘pause’, ‘linear movement’, and ‘random movement’ (see Fig. 1). mobility patterns

move

linear movement

pause

random movement

Fig. 1. The classification of mobility patterns of real-life objects.

As we already know, great diversity among the mobility patterns of real-life objects is quite natural. However, there are some specific repeated patterns in these movements.

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For example, in linear movements, the trajectory of an object is almost a line in d-dimensional space. Meanwhile, if we can not find the implicit knowledge of a specific pattern, we will identify the portion of that trajectory as random walk or Brownian movement. Also, of course, we consider the temporal patterns of movements as a Markovian process. Our approach to the problem of mobility modeling is primarily motivated by the following observations [4, 10, 16, 18]: • A mobile subscriber will mainly switch between two states: stop and move. A traveling salesman has a tendency to remain in the same state rather than to switch states [16]. • The majority of objects in the real world do not move according to statistical parameters but, rather, move intentionally [10, 15, 16]. • Moving objects belong to a class. This class restricts the maximum speed of the object. Different groups of moving objects exhibit different kinds of behavior [4, 10]. • Motion has a random part and a regular part, and the regular part has a periodic pattern [17].

The above properties are distilled from dozens of papers on both the Personal Communication System (PCS) and MOD. Despite these observations, most of the existing works have disregarded and have oversimplified the mobility issue as a linear function of time. Mobility models and their applications have been widely studied with regard to location management in PCS environments. Many existing location management schemes use some version of a random mobility model that is performed typically one-dimensional [8]. Modeling the random-walk as a mathematical formula is a simple process without difficulty. However, such mobility patterns no longer reflect reality. On the contrary, most of the previous works on spatiotemporal databases have assumed that the movement pattern of a user closely approximated a line. For example, the MOST data model assumes that the movement patterns of real-life objects are very close to being 1 dimensional. That is, objects move in the plane, but their movement is restricted to a given set of routes on the finite terrain [11]. This was called the 1.5 dimensional problem in [7]. As noted above, researches on both MOD and PCS have studied the movement patterns of real-life objects. Yet there are differences in their assumptions, approaches, and environments. Therefore, a more flexible and realistic model for real-life mobility patterns is needed. In the literature, real spatio-temporal datasets of real-life mobile users are very hard to find. Our approach is based on the concept of mobility-awareness of a location update protocol that splits the overall movement of moving objects into simple movement states (or, simply, states). Furthermore, by applying a corresponding update policy with movement states dynamically minimizes the overall cost of location management.

3. SYSTEM MODEL The crucial issue in mobile computing environments is how to organize the location databases, which store information on the locations of moving objects. Important factors

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such as location update, database access time, availability, and scalability depend significantly on the organization of location databases. The simplest approach to location database organization is to store all location information in a single physical storage site, called a centralized database. For large numbers of moving objects, however, such a solution results in a single point of failure and a potential bottleneck. Instead, there is an architectural alternative in which the whole space is decomposed into regions or cells, and this is called a distributed database. Thus, this approach may not only be able to overcome the above-mentioned drawbacks of a centralized database, but also enhance the availability and scalability of various location services. Our architecture is based on a general model described in [2] (see Fig. 2) and can be developed into a hierarchical architecture. Its components and their functionality are shown in Fig. 2.

Fig. 2. System model and the organization of location databases.

• Moving objects (MOs). The mobile clients are the subjective entities of the location-aware application. We assume that every moving object registered to LS is equipped with a positioning device, such as GPS, and must be capable of recognizing its mobility from obtained information about where it is located. Additionally, while performing multiple update policies, it may choose the optimal one which provides the minimum cost of updating its location information to LS for a certain location uncertainty δ1. The remainder update policies, on the other hand, carry out a self-initiated “pseudo-update” of their own local memory. 1

The term “uncertainty” is used as the threshold of location imprecision which is a difference between the actual location and database location.

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• Region processors (RPs). As a lightweight server, each RP only monitors a small set of objects, and RPs work in parallel. Moreover, each RP transmits the information of its region to LS via CCP (coherency control protocol), which stores replicas of the location information of all RPs. The CCP protocol is an application layer protocol that is responsible for moving, caching, and updating the location information of all RPs synchronously or asynchronously. • Location server (LS). The LS is a fixed host that directly communicates with RPs over fixed networks. In order to provide scalable location-based services for mobile users, the LS should maintain per-user profiles and the RP information as well as location information of all moving objects. Hence, the efficient processing of location-based queries greatly requires well-formed structures of location databases.

4. STATE-BASED MOBILITY MODEL (SMM) A mobility model, in the context of location management, understands the daily movements of a user [8], and describes this understanding. Thus, various mobility models have been developed for mobile computing environments [8, 16]. Mobility modeling in MOD is difficult because the higher location resolution compare to PCS. Moreover, a matter of concern in MOD is not a logical/symbolic location, like cell-id, but the very physical/geographical location of a moving object obtained by a location-sensing device, such as GPS. As noted above, it is necessary to consider a complex movement containing both random and linear movement patterns. 4.1 Basic Definitions

We propose the state-based mobility model (SMM) that understands a complex mobility pattern as a set of simple movement components using a finite state Markov chain based on the classification scheme discussed in section 2. Definition 1 A movement state si is a 3-tuple (vmin, vmax, φ), where vmin and vmax are the minimum and maximum speeds of a moving object, respectively. φ is a function of movement and is either probabilistic or non-probabilistic. S is a finite set of movement states (called the state space). Definition 2 The state-based mobility model (SMM) describes user mobility patterns using a finite state Markov Chain {staten}, where staten denotes the movement state at step n, staten ∈ S. Furthermore, the chain can be described completely by its transition probability as

pij ≡ Pr{staten+1 = j | staten = i} for all i, j ∈ S.

(1)

These probabilities can be grouped together into a transition matrix as follows: P ≡ (pij)i,j∈S.

(2)

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An important question is why such a general mobility model is not as popular as the restrictive models so abundant in the literature [3]. The most important reason is that the generalized model has nothing to be assumed to start the analysis. In this paper, we assume only that the mobility patterns are divided into three basic movement states: pause, linear, and random. Each state has a self-transition probability iii. In the SMM model, we also assume that a moving object has a tendency to remain in the same state rather than to switch states [16]. This is generally called temporal locality. The self-transition probability vector (STPV) is obtained by taking all of the self-transition probabilities, which is equivalent to an 1 × |S| matrix. Definition 3 The self-transition probability vector (STPV) p~ of a transition probability matrix is defined as

p~ = ( pii ) i ŒS .

(3)

And the temporal locality (or locality) τ is defined as

t =(

’p ) ii

1/|S |

.

(4)

i ŒS

4.2 A Practical Instance of the SMM Model As we noted above, complex mobility patterns in the real world can be interpreted as a set of basic movement states (Fig. 1). In this section, we present a practical instance of the proposed SMM model based on the three states described above, S0 = {P, L, R}. Fig. 3 shows a state transition diagram for this instance. Intuitively, the instance S0 can be extended with additional states, for example, a Manhattan walk. Let us define three measurements that estimate how much influence each state on the whole movement pattern in this instance.

Fig. 3. An instance of SMM model: S0 = {P ≡ pause, L ≡ linear, R ≡ random}.

MODELING AND TRACKING COMPLEXLY MOVING OBJECTS

Linearity l is defined as

Definition 4

l=

523

 Â

i ŒS

piL

i , j ŒS , j π L

.

pij

(5)

Randomness γ is defined as

g =

 Â

i ŒS

piR

i , j ŒS , j π R

pij

.

(6)

Also, stationarity ρ is defined as

r=

 Â

i ŒS

piP

i , j ŒS , j π P

pij

.

(7)

For practical purposes, the above parameters are quite important for describing the various features of mobility patterns. 4.3 Determining the Transition Matrix One of the most important tasks in the SMM model is to determine the transition matrix P. The matrix can be determined using the user profile, the spatiotemporal data mining process, or in an ad hoc manner. The simplest way to determine the transition matrix P is to set pij = |S1 | for all i, j ∈ S. A more reasonable solution is to use statistical techniques to infer the values of the transition probabilities empirically based on past data [3, 9]. For example, suppose the optimal state for each time unit is a Markov chain having state space S0 (see Fig. 3). Furthermore, assuming that the optimal state for 36 time units has been PPPLLLLRRLPLLLRRRPPPRLLRLLLLRPPRRRRP. Counting the number of transitions Nij2 from state i to state j gives P

[ N ij ]i , j ŒS =

2

P L R

F5 GG 1 H3

L

R

I JJ K

2 2 9 4 . 3 6

We only assume first-order Markov chain model.

(8)

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The transition probability pij can now be estimated as p$ ij =

Â

N ij k ŒS

(9)

N ik

giving the following estimation of P:

P$ =

P L R

F GG H

P

P

P = L R

L

R

5 / (5 + 2 + 2) 2 / (5 + 2 + 2) 2 / (5 + 2 + 2) 1 / (1 + 9 + 4) 9 / (1 + 9 + 4) 4 / (1 + 9 + 4) 3 / (3 + 3 + 6) 3 / (3 + 3 + 6) 6 / (3 + 3 + 6)

F 0.5556 GG 0.0714 H 0.2500

L

R

I JJ K

I JJ K

0.2222 0.2222 0.6429 0.2857 . 0.2500 0.5000

(10)

From this estimated matrix, we can calculate the movement parameters, such as l = 0.59160, γ = 0.50595, and τ = 0.56320, by means of Definitions 3 and 4. Let π = (πP, πL, πR) be the steady-state probability vector or equilibrium [9]. Solving for π = π × P, we obtain πP = 0.257, πL = 0.4, and πR = 0.343 as estimates of the residence probabilities of each movement state [9].

5. STATE-BASED LOCATION UPDATE PROTOCOL (SLUP) 5.1 The Basic Idea Suppose that there are a huge number of moving objects in d-dimensional space »d = [0, 1]d. For any time t, the position of the ith object is given by oi(t), which is a point in d-dimensional space. Then, the movement history of the object oi is described as a trajectory in (d + 1)-dimensional space, which consists of 〈oi(0), oi(1), …, oi(now)〉. For location-dependent query processing, the LS should track the trajectories of network-registered moving objects. Thus, an efficient protocol which updates location information in the location server is highly needed. The goal of a location update protocol is to provide more accurate location information with fewer update messages to LS. Clearly, there is a tradeoff between accuracy and efficiency. Location update protocols are divided into four major types based on when an update message is transmitted: time-based, movement-based, distance-based, and dead-reckoning [1]. Each update protocol has its own characteristics and performance, depending on its underlying mobility model. In other words, these algorithms need different numbers of update messages to achieve the same location precision. We introduce here a new criterion to compare the efficiency of update protocols using a simple formula that measures the update cost and the imprecision cost for a certain amount of time. This criterion is called UITR (update-and-imprecision to time ratio) (see Eq. (11)). Naturally,

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it is preferable to keep the value of UITR small while achieving the same degree of location accuracy.

CUITR =

update cost (CU ) + imprecision cost (Cε ) monitoring time

 =

wndsize k =1

( wU U k + we e k )

wndsize

(11)

To compute the value of UITR efficiently, we employ an update window (UWin) and imprecision window (IWin) in the form of a circular queue. Each update flag (Uk) in UWin is true if an update message is transmitted, or false if it is not. Each item εk of IWin is the Euclidean distance between the actual location and the estimated location by an update policy. Both UWin and IWin contain wndsize cost items for the time ti and the current time (ti+wndsize). Therefore, the value of UITR is defined as the average cost of update and imprecision cost to the size of UWin and IWin. Fig. 4 shows a comparison of the distance-based approach and the dead-reckoning approach in terms of CUITR. In this comparison, the movement of whole objects is random or linear by turns with a fixed time interval 100.

Fig. 4. A example showing variation of CUITR.

We can identify the behavioral difference of the two update policies in Fig. 4. Exhibiting complementarity with respect to mobility patterns, different − mutually complement − update policies can be applied to the aforementioned states. Under the pause mode, we adopt the time-based approach to minimize communication with the base station. Reducing the average number of update messages can have a significant impact in the power consumption of MT. Thus, it is important to find a reasonable threshold T,

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which is quite greater than that in the traditional approach. In the linear mode, the dead-reckoning approach offers a great performance benefit, especially under a constant speed. In [18], the authors report that the update costs can be reduced by 83% compared to other protocols. A comprehensive study of dead-reckoning was reported in [18]. Finally, under the random mode, the movement patterns of an object have the special property of spatial locality. In this case, we employ the distance-based update protocol [6]. 5.2 Overview of the SLUP Protocol During the life of a SLUP connection, the SLUP protocol running in each moving object executes transitions through various SLUP states. The behavior of a moving object is modeled as a state-transition diagram (Fig. 5). Each moving object begins in the INITIAL state. The initialization process starts with the bootstrapping phase, then processes to a self-test, performs RP discovery by means of network layer functionality, and then enters the WARMUP state. While in the WARMUP state, each moving object chooses a beginning update policy according to its current mobility pattern. In terms of the temporal locality of user movement, the update policy phase is decomposed into a small number of update states, such as UP_PAUSE, UP_LINEAR, and UP_RANDOM. Each update state consists of an update policy, that indicates how the location information of an object is reflected in the location databases, the state-transition function determining the next states of the object, and information related to the state. The DISCONNECTED state is the place where a disconnection occurs between an object and the current RP. In this state, the last update policy with a timestamp should be saved to the local memory of an object. Upon reconnection, the state transition from DISCONNECTED to the saved update state is legal only if the time interval between the timestamp of the saved update state and the reconnection time is smaller than a given threshold Tdiscon. If not, the destination of the state-transition will be the WARMUP state.

Fig. 5. The state transition diagram for the SLUP protocol.

As mentioned previously, each moving object implements not only the current update policy but also the others. The optimal update policy with the minimum UITR can be decided without any difficulty. We believe that the additional cost of a small amount

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of memory and a small number of operations is acceptable owing to its reflective effectiveness in the small number of update messages and the development of hardware technology. Definition 5 The SLUP Protocol is based on the SMM model, and is represented by a finite set of update policies called the update policy list UPL = {µ1, µ2, …, µN} and the optimal update policy index opt. Definition 6 An update policy µ is a 6-tuple (l$, f , C , UWin, IWin, d ) consisting of the estimated location l$ by f, a location estimation function f, the cost function C, the update window UWin, the imprecision window IWin, and a predefined location uncertainty δ. Algorithm State-based Location Update Protocol Input: A set of update policies UPL = {µP, µL, …, µR} 1. t ← 0 2. repeat 3. do for each state µi ∈ UPL 4. do l$i ← fi(t) if d (l$i , lnow ) > d i 5. 6. then UWini[t mod wndsizei] ← true 7. l$i ← lnow //pseudo-update 8. else UWini[t mod wndsizei] ← false 9. IWini[t mod wndsizei] ← d (l$i , lnow ) 10. Ci ← computeCost(UWini, IWini) 11. opt ← arg min1≤i≤N Ci if µopt is pseudo-updated 12. then SendUpdateMsg(opt, l$opt , f opt, δopt) to LS. 13. 14. t←t+1 15. until the termination condition is satisfied Fig. 6. Algorithm for the SLUP protocol.

We provide the algorithm in detail in Fig. 6. Furthermore, the main contributions of the SLUP protocol are summarized as follows. • Reducing the location update cost. The movement states are divided into two major classes: linear movements and random movements (Fig. 1). The linear components can be abstracted as a linear function of time, which is specified by two parameters: the position and velocity vector for the object. Consequently, this approach could minimize the location update cost, peculiarly under a constant velocity. Meanwhile, we regard all other movements, including random walk and ping-pong movements, as random components. This is because it is difficult to discover knowledge or relevant information for further classification. This classification scheme can be interpreted as a process for ex-

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tracting the low-cost movement component from the whole trajectory in terms of its movement patterns. Though simple, the proposed approach is very efficient in the case of complex movements and quite new in terms of the moving objects database. • Energy-efficiency with consideration of the stationary state. The simplest movement is ‘don’t move’; we called this the ‘pause’ mode. Under the pause mode, the moving object is perhaps located at the person’s home, office, or meeting room for a long time. It is quite reasonable to consider a location update policy for a stationary state as well as a moving state. This idea has been adopted in the location management of PCS, called the Stop-or-Move mobility model [16]. We can assume that an object is in a stationary state if it remains still at its location for a certain time. Then, in this “doze mode”, it is a great benefit in term of power consumptions, the update cost for location databases, and network cost by minimizing communication with BS.

6. PERFORMANCE EVALUATION 6.1 Simulation Model and Workload Generation

The workload for a scenario of moving objects can be either real, that is, extracted from a real-life application, or synthetic, that is, a mathematical model (e.g., probability theory). Artificially synthesized datasets are normally used to evaluate the impact of specific parameters or in some cases when real datasets are not available. Since real datasets in spatio-temporal databases are very hard to obtain, the method of synthesizing data is widely used in various fields [4, 10, 12]. First of all, we suppose the use of a centralized database for the evaluation of the proposed protocol with traditional update protocols. Thus, we only observe the number of sending the update messages while omitting the update step in the RP layer. To simplify the simulation model, we assume that the delay time for sending messages does not exist. And, we leave out the pause (P) state because it is not relevant to the evaluation. The two state-transition matrices for this assumption are L

T(t ) =

L( l) =

L R

L R

FG t H1 - t

F GH

R

IJ K

1- t , where 0 £ t £ 1. t

L

R

l l +1 l l +1

1 l +1 1 l +1

I , where 0 £ l £ •. JK

(12)

(13)

T(τ) has various characteristics as the locality τ changes from 0 to 1 with linearity l fixed at 1. L(l) has linearity l and the same value for the L and R column. By definition, the locality of these matrices is l / ( l + 1) 2 . The maximum value of their locality is 0.5, where l = 1 with the pause state omitted. For simplicity, we denote the transition matrix of T(τ) with locality τ and the transition matrix of L(l) with linearity l as T(τ) and L(l), respectively.

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During workload generation, we employ parameters consisting of linearity, locality and maximum speed of moving objects, called vmax, for our state transition matrix. The first mobility pattern is a pure random-walk. If the moving objects exist in the dimension »d in this situation, this means that the probability of movement in all directions in dimension d is the same. These workloads may be generated by means of uniform, Zipf or Gaussian distribution as in [10]. If the linearity and locality are 0.0 and 1.0, respectively, in the matrix, L(0), we can generate these workloads. In our simulation, we use the movement vector by means of a real number extracted from a uniform distribution within the range [− vmax, + vmax] in each dimension. On the other hand, we may consider a linear mobility pattern for all moving objects. In this situation, the trajectory of the movements is almost a straight line. We assume a constant speed in this situation, and the movement vector is generated in the same way with a random state. These workloads are generated by the matrix L with linearity ∞, L(∞). But the mobility patterns are more realistic if the two characteristics of the movements − random-walk and linear mobility − are mixed appropriately because the mobility patterns for the real world may be both. Therefore, these mobility patterns are required to approximate the pattern in the real world. We can create the workloads by changing the linearity and locality. Table 1 summarizes the settings for the parameters. Table 1. Simulation parameters.

Parameter #objects vmax vavg

δ

#gen

τ

l

Description Values Used the number of objects 1,000 maximum speed of moving objects 0.005, 0.01 average speed of moving objects E(vmax) = vmax /2 location uncertainty 0.005, 0.01 the simulation time 1,000 the temporal locality 0.0 ~ 1.0 (spacing 0.1) the linearity of movement 0, 0.1, 0.25, 0.5, 0.75, 1, 5, 10, 20, ∞

6.2 Effect of Linearity l In this section, we discuss the effect of linearity l. The experiment was performed on the transition matrix L(0) ~ L(∞), and the maximum speeds vmax of all the objects were 0.005 and 0.01. Thus, the pure random and the pure linear movements were represented as the transition matrices of L(0) and L(∞), respectively. Fig. 7 shows the average number of update messages and the average imprecision for an object with varying linearity l and δ parameters. In the distance-based approach, increasing the linearity gave rise to an increased number of update messages. This is because the displacement of the linear state was comparatively larger than that of the random state for the same amount of time. The average update count of the distance-based approach to the linear movement patterns is

2vavg pd

. Intuitively, the average speed vavg of

all moving objects converges to vmax/2 if uniform distribution is used. The average update v count under uniform distribution of v , thus, is max . On the other hand, the pd

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(a) Location update cost: vmax = 0.005.

(c) Imprecision cost: vmax = 0.005.

(b) Location update cost: vmax = 0.01.

(d) Imprecision cost: vmax = 0.01.

Fig. 7. Effect of linearity l.

dead-reckoning approach performed very well in the case of increasing linearity. Moreover, the performance improved considerably with a parameter linearity was greater than 1.0. The proposed approach outperformed the dead-reckoning approach in every case with varying linearity. 6.3 Effect of Locality τ In this section, we discuss the impact of varying locality. For example, if the locality is 0.0, the object will change to other states unconditionally. On the other hand, if the locality is 1.0, the object will maintain its current state forever. We expected that this locality would greatly influence the performance of the location update protocol. The experiment was performed on the transition matrix T(0) ~ T(1), and the maximum speeds vmax of the objects were 0.005 and 0.01. The matrix T(τ) was defined as a state-transition matrix with fixed linearity 1.0 and varying locality τ. With respect to the matrix, the number of random movements was identical to that of linear movements, for the linearity was fixed at 1.0. However, a transition matrix with a larger locality would likely have more linear movements than the opposite one. The dead-reckoning approach, therefore, would be advantageous for a larger locality under the same linearity.

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Fig. 8 shows the number of update messages and the average imprecision for an object with varying locality τ and δ parameters. In the case of the distance-based approach, increasing the locality gave rise to an increased number of update messages. Since the linearity was fixed at 1.0, the performance degradation described in the previous section can be avoided. Like the previous results, moreover, the performance of the proposed approach is likely to have the same curve as that of the dead-reckoning approach. The proposed approach outperformed the dead-reckoning approach in every case with varying linearity.

(a) Location update cost: vmax = 0.005.

(b) Location update cost: vmax = 0.01.

(c) Imprecision cost: vmax = 0.005.

(d) Imprecision cost: vmax = 0.01.

Fig. 8. Effect of temporal locality τ.

7. CONCLUSIONS AND FUTURE WORKS We have argued that a generalized mobility model for a moving objects database is crucial for mobile computing environments, especially LBS. However, few studies have focused on this issue. In order to provide an efficient location update strategy, we have proposed a new mobility model called SMM to describe the movement patterns of real-life objects in a probabilistic manner. As we had assumed, the proposed approach outperforms previous studies in the complex situation including linear movements and random movements. Moreover, in every case that we have considered, the proposed approach outperforms the dead-reckoning approach and the distance-based approach.

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MOONBAE SONG, KWANGJIN PARK, JEHYOK RYU AND CHONG-SUN HWANG

Future researches include the following. First, we want to find a hierarchical way to manage moving objects. Second, we plan to investigate the location update policy for stationary objects. Finally, we want to develop a portable software interface for workload generation based on our state-based mobility model.

REFERENCES 1. A. Bar-Noy, I. Kessler, and M. Sidi, “Mobile users: to update or not to update?” Wireless Networks, Vol. 1, 1995, pp. 175-186. 2. D. Barbará, “Mobile computing and databases − a survey,” IEEE Transactions on Knowledge and Data Engineering, Vol. 11, 1999, pp. 108-117. 3. A. Bhattacharya and S. K. Das, “LeZi-update: an information-theoretic framework for personal mobility tracking in PCS networks,” Wireless Networks, Vol. 8, 2002, pp. 121-135. 4. T. Brinkhoff, “Generating network-based moving objects,” in Proceedings of the 12th International Conference on Scientific and Statistical Database Management (SSDBM ’00), 2000, pp. 253-255. 5. R. Güting, M. Böhlen, M. Erwig, C. Jensen, L. Schneider, and M. Vazirgianis, “A foundation for representing and querying moving objects,” ACM Transactions on Database Systems, Vol. 25, 2000, pp. 1-42. 6. S.-H. Kim, M.-B. Song, S.-H. Nam, C.-S. Hwang, and J.-G. Shon, “Distance-based indexing strategy for moving objects database,” in Proceedings of Korea Information Science Society Conference, Vol. 29, 2002, pp. 196-198. 7. G. Kollios, D. Gunopulos, and V. J. Tsotras, “On indexing mobile objects,” in Symposium on Principles of Database Systems, 1999, pp. 261-272. 8. T. Kunz, A. A. Siddiqi, and J. Scourias, “The peril of evaluating location management proposals through simulations,” Wireless Networks, Vol. 7, 2001, pp. 635-643. 9. D. L. Minh, Applied Probability Models, Duxbury, 2001. 10. D. Pfoser and Y. Theodoridis, “Generating semantics-based trajectories of moving objects” in Proceedings of International Workshop on Emerging Technologies for Geo-Based Applications, 2000, pp. 59-76. 11. E. Pitoura and G. Samaras, “Locating objects in mobile computing,” IEEE Transactions on Knowledge and Data Engineering, Vol. 13, 2001, pp. 571-592. 12. J. M. Saglio and J. Moreira, “Oporto: A realistic scenario generator for moving objects,” GeoInformatica, Vol. 5, 2001, pp. 71-93. 13. A. P. Sistla, O. Wolfson, S. Chamberlain, and S. Dao, “Modeling and querying moving objects,” in Proceedings of International Conference on Data Engineering, 1997, pp. 422-432. 14. Z. Song and N. Roussopoulos, “Hashing moving objects,” in Proceedings of International Conference on Mobile Data Management, 2001, pp. 161-172. 15. Y. Theodoridis, J. R. O. Silva, and M. A. Nascimento, “On the generation of spatiotemporal datasets,” in Proceedings of International Conference on Large Spatial Databases (SSD ’99), 1999, pp. 147-164. 16. Y. C. Tseng, L. W. Chen, M. H. Yang, and J. J. Wu, “A stop-or-move mobility model for PCS networks and its location-tracking strategies,” Computer Communications, Vol. 26, 2003, pp. 1288-1301.

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17. O. Wolfson, “Moving objects information management: the database challenge,” in Proceedings of Workshop on Next Generation Information Technologies and Systems (NGITS), 2002, pp. 75-89. 18. O. Wolfson, A. P. Sistla, S. Chamberlain, and Y. Yesha, “Updating and querying databases that track mobile units,” Distributed and Parallel Databases, Vol. 7, 1999, pp. 257-387.

MoonBae Song received his B.S. degree in Computer Science from Kunsan National University in 1996, and his M.S. degree in Computer Science from Soongsil University in 1998. He is currently a Ph.D. candidate in Computer Science and Engineering, Korea University, Korea. He is also a researcher in the Research Institute of Computer Information and Communication at Korea University. His research interests include moving objects database, location-aware services, mobility modeling, and data management for mobile computing.

KwangJin Park received his B.S. and M.S. degree in Computer Science from Korea University, Korea in 2000 and 2002, respectively. He is currently a Ph.D. candidate in Computer Science and Engineering and a researcher in the Research Institute of Computer Information and Communication, Korea University, Korea. His research interests include location-dependent information systems, mobile databases, and mobile computing systems.

JeHyok Ryu received his B.S. and M.S. degree in Computer Science from Korea University, Korea in 1997 and 1999, respectively. He is currently a Ph.D. candidate in Computer Science and Engineering from Korea University, Korea. He is also a researcher in the Research Institute of Computer Information and Communication at Korea University. His research interests include location-dependent data management, pervasive and mobile computing.

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MOONBAE SONG, KWANGJIN PARK, JEHYOK RYU AND CHONG-SUN HWANG

Chong-Sun Hwang received his M.S. degree in Mathematics from Korea University, Korea in 1970, and Ph.D. degree in Statics and Computer Science from University of Georgia in 1978. From 1978 to 1980, he was an Associate Professor at South Carolina Lander State University. He is currently a Full Professor in the Department of Computer Science and Engineering at Korea University, Korea. Since 1995, he has been a Dean in the Graduate School of Computer Science and Technology at Korea University. His research interests include distributed systems, distributed algorithms, and mobile computing systems.