Location Database Clustering to Achieve Location Management Time Cost Reduction in A Mobile Computing System

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1 Location Database Clustering to Achieve Location Management Time Cost Reduction in A Mobile Computing ystem Chen Jixiong, Li Guohui, Xu Huajie, Cai Xia*, Yang Bing chool of Computer cience & Technology, Huazhong University of cience & Technology Department of Computer cience, Huazhong Normal University* Wuhan, P.R.China, Abstract-An important issue in the design of a mobile computing system is how to manage the location information of mobile clients. In the existing commercial cellular mobile computing systems, a two-tier architecture is adopted. However, the two-tier architecture is not scalable. In the literatures, a hierarchical database structure is proposed in which the location information of mobile clients within a cell is managed by the location database responsible for the cell. The location databases of different cells are organized into a tree-like structure to facilitate the search of mobile clients. This architecture can distribute the workload amongst the location databases in the system. The location database organization has much impact on the total location management cost. However, non of previous work touches upon this problem. In this paper, considering the mobility patterns of mobile clients in different cells, we give a heuristic algorithm to cluster the location databases with the objective to reduce the location management cost. Extensive experiments are designed to evaluate the performance. The comparison shows that our location database clustering method can result in location update cost reduction. Index Terms- Mobile computing system, location management time cost, location database, location database clustering, set cover I. INTRODUCTION One of the most important issues in the design of the mobile computing systems is the location management of mobile clients [1, 2, 3, 4]. This is not only essential for providing efficient mobile communication services among mobile clients but also important to many new mobile computing applications, such as systems to support location dependent queries [5]. In the existing cellular mobile networks, a two-tier location database architecture is adopted to manage the locations of mobile clients [6]. This two-tier architecture is simple and easy to implement. However, it has two serious performance problems, which makes it unsuitable for many new mobile computing applications. Firstly, the number of mobile clients in a mobile computing system can be very large, and the system may need to maintain a large amount of location information for its mobile clients. It is obvious that the two-tier architecture is not scalable. econdly, because a mobile client is permanently associated with a Home Location Register (HLR), the overheads for maintaining the locations of mobile clients can be very heavy if the mobility of clients is high. It is obvious that the cost for locating a mobile client greatly depends on the locations of the calling mobile client and the called mobile client. If a called mobile client is far away from its HLR, the cost for locating the mobile client could be very expensive. In order to improve the system performance and to reduce the total cost for locating a mobile client, various strategies have been proposed. One of the efficient methods is to organize the location databases in a hierarchical structure [1, 7]. Although the hierarchical structure of the location databases can improve the performance of searching for mobile clients, the total location update overheads for maintaining the locations of mobile clients can also be heavy. In the organization of the hierarchical databases, it is important to consider the update cost as well as the movements of mobile clients, i.e., the mobility patterns. ince in the system, different mobile clients can have very different mobility patterns, the location database organization has much impact on the location management cost. However, to our best knowledge, it still lacks any detailed study on the relationship between the location database organization and the location management cost. In this paper, we study the location database (LDB) organization problem in hierarchical databases for mobile computing systems over cellular networks. Our objective is to design a nearly-ideal location database topology structure to achieve the location management cost reduction. It is NP-hard to design an ideal LDB topology structure. In this paper, we give a heuristic algorithm to design a nearly ideal topology structure for the LDB organization based on the set covering theory. The remaining parts of this paper are organized as follows. ection II defines the system model. ection III proposes the basic definitions applied in the paper. ection IV presents a heuristic LDB organization method based on the set covering theory. ection V includes the performance evaluation of the algorithm and section VI is the conclusion. II. CELLUAR MOBILE NETWORK AND LOCATION DATABAE MODEL X/05/$ IEEE 1328

2 A cellular mobile network is based on the concept of frequency reuse. The whole service area is divided into a number of connected cells with a base supporting station (B) in each cell. The limited wireless bandwidth is partitioned into channels. The mobile clients within a cell communicate with the B of the cell through a wireless channel. Each B maintains a location database. The location databases of different neighboring B s are organized into a hierarchical tree structure, as shown in Figure 1. Note that in an existing GM mobile network, the location databases are managed by mobile switching centers. There are a large number of mobile clients in the system. They may make a call or submit a query on the locations of other mobile clients. It is assumed that different mobile clients can have different mobility patterns. Cell 1 Cell 2 Cell 3 Cell 4 Cell 5 Cell 6 Cell 7 Cell 8 Cell 9 Figure 1. Hierarchical databases to store the mobile clients locations III. PRINCIPLE AND DEFINITION A. Terminology ince the location databases are organized into a tree like structure, we define the least common ancestor of (leaf) location databases DB i and DB j as LCA(DB i, DB j ). The height of LCA(DB i, DB j ) to the leaf nodes of the tree is denoted as lca(db i, DB j ). (We assume that all of the leaf nodes of the location databases are at the same level in the hierarchical location database tree). Let the leaf location database responsible for the cell i be LDB(i). Definition 1: The distance between cells i and j, termed as dis(i, j), is defined as the height of the least common ancestor of the responsible leaf the location databases, that is dis(i,j) = lca(ldb(i),ldb(j)) If i = j then dis(i, j) = 0. Let cur_cell(x) be the cell in which mobile client x is now residing. Definition 2: The distance between mobile clients x and y, termed dis(x, y), is defined as the distance of the two cells in which x and y is now residing, namely dis(x, y) = dis(cur_cell(x), cur_cell(y)). The above definition captures the locality of two mobile clients. It can be seen easily that a mobile client takes a smaller cost to find the location information of another mobile client if the distance between them is smaller[1]. When calculating the location management cost, as in [1,2], we consider the following related time costs in location update and the lookup procedure: t L : The time cost of following a link in the tree of the location databases, i.e., sending a message to the parent or the child node of a location database; t U : The time cost of a database update; t Q : The time cost of a database query; B. Problem When a mobile client crosses the boundary between two cells and moves from its formerly residing cell, old_cell(x),into the currently residing cell, cur_cell(x), the total location update cost is: Update_cost=2dis(old_cell(x), cur_cell(x)) t L + (2dis(old_cell(x), cur_cell(x))+1) t U eqn. (1) As can be seen from the above equation, the location update time cost is proportional to the distance between the starting and destination cells of a mobile client. However, the distance between two cells in a location database hierarchical tree is not necessarily the same under different LDB topological structure. The hierarchical structure of the location databases can have a significant impact on the location management cost. Before constructing the location database tree, we should consider the mobility patterns of all the mobile clients to optimize the total location management cost. Cell 1 Cell 5 Cell 8 Cell 2 Cell 4 Cell 6 Cell 3 Cell 7 Cell 9 Figure 2. A mobile computing system consisting of 9 cells Let us consider a more detailed example to illustrate the problem. uppose in the systems, there are 9 cells as in Figure 2 and the 9 location databases responsible for the 9 cells are organized as in Figure 1. During a time period, there are 200 times of border-crossings between Cell 3 and Cell 4, and 50 times of border-crossings between Cell 2 and Cell 3. According to Equation (1), the total time cost to update the 200 times of border-crossings between the Cell 3 and Cell 4 is: 200 (2 dis t L + 2 dis t U + t U ) = 200 (2 2 t L t U + t U ) = 800t L t U where dis is the distance (see Definition 1) between the two leaf location databases responsible for Cell 3 and Cell 4, namely 2. The location update time cost to update the 50 times of X/05/$ IEEE 1329

3 border-crossings between Cell 2 and Cell 3 is: 100t L +150t U Therefore, the total location update time cost is 900t L +1150t U. If we reorganize the location databases by switching the positions of DB5 and DB7 with each other in the hierarchical tree, the total time cost to update the 200 times of border-crossings between Cell 3 and Cell 4 becomes: 200 (2 dis t L + 2 dis t U + t U ) = 200 (2 1 t L t U + t U ) = 400t L + 600t U The total time cost to update the 50 times of border-crossings between Cell 2 and Cell3 becomes: 50 (2 dis t L + 2 dis t U + t U ) = 50 (2 2 t L t U + t U ) = 200t L + 250t U The total location update time cost in the reorganized case will be 600t L +850t U and the location update time saving is 300t L +300t U. o the LDB topology structure has a great impact on the location management cost. IV. LOCATION DATABAE ORAGINZATION Before the LDB organization, we construct a mobility matrix, M, in which M ij is the number of boundary crossings between the cell i and cell j during a time period. Table 1 is an example mobility matrix. TABLE I AN EXAMPLE OF MOBILITY MATRIX C1 C2 C3 C4 C5 C6 C7 C8 C9 C C C C C C C C C In the following sections, we give a set-covering algorithm to organize the location databases with the objective to minimize the total location management time cost. Definition 3 A set of sets 1, 2,, n is called a cover of a set if and only if = n i=1 i Definition 4 A set of sets 1, 2,, n is called a non-overlapping cover of a set if and only if (1) n = i i=1 (2) i, j,1 i, j n, i j, i j = φ In general, a (non-overlapping) cover of a set is associated with a cost and we try to find an algorithm to get a cover of a set with the minimum cost. Actually, to find a (non-overlapping) cover of a set with the optimal cost is NP-hard [8]. Under different circumstances, heuristic algorithms are given to get the nearly ideal result. In the following, the problem of location database structuring is transformed to the problem of getting a non-overlapping cover of the set of location databases (the associated cost is explained later) where (1) et is the set of leaf location databases in the system; (2) The objective function is the total location update time cost in the given location database topological structure. To get a location database organization with a nearly ideal location update time cost, a set of sets is constructed as follows: (1) For i, 1 i n, i =Cell i (2) For each Cell j, if the number of border-crossings between Cell i and Cell j (denoted as M ij ) is larger than 0, then i = i Cell j Obviously, 1, 2,, n is a cover (with overlapping) of the set =Cell 1, Cell 2,., Cell n. Here n is the total number of cells in the system. Based on this cover of, we get a non-overlapping cover of. Note that here the cost with the set covering of the n leaf location databases corresponding to the n cells in the systems is the total number of boundary crossing between two cells in two different sets. That is num-crossing= M p q p q Cell i Cell j p ij,,, q p and q are two different set in a covering of Where the set of the n cells. After the construction of the above objective function, we give a heuristic algorithm to get a nearly-ideal covering of the set of n cells ( leaf location databases corresponding to the n cells) with the objective to get the minimal value of num-crossing. Then each component (a leaf location database set which is composed of d(explained later) location databases) of the cover forms a cluster. The following is the procedure to get the non-overlapping cover. In the following section, the number of elements in a set is denoted as. d is the number of sub-location databases in the hierarchical tree. In figure1, d is 3. PROCEDURE LDB-structuring INPUT: M ij, 1, 2,., n OUTPUT: A topology structure for the location database tree =1; REPEAT UNTIL i i = φ X/05/$ IEEE 1330

4 (1) uppose that the M ij is maximal value in the set M ab r,s, 1 r,s n, (Cell a r Cell b s ) (2) =Cell i, Cell j (3) Delete Cell i/cell j from any k (1 k n) which includes Cell i/cell j (4) WHILE <d DO 1 Compose the temporary set T as follows:t=φ; 2 For Cell p in the system If ( k, 1 k n (Cell p k )) (Cell p ) ( Cell q (M pq >0)) T= T Cell p IF T φ 3 For Cell m in T, according to the following equation, calculate total-num m where total-num m = Mim Cell i i 4 elect the Cell x from T with the maximal value of total-num m defined as above. ELE elect a Cell x randomly from any i (1 i n) 5 = Cell x 6 For all the set i, (1 i n) i = i -Cell x =+1; After the above procedure terminates, the leaf location databases corresponding to the sets (=1,2,..., n/d) forms a cluster. The clusters of the leaf location databases are organized recursively in the same way to achieve the total location update time cost reduction. Due to the limitation of space, the detailed procedure is omitted. V. IMULATION PERFORMANCE EVALUATION As can be seen from the construction of the covering of the n location databases, for the location databases between which there are a larger number of boundary-crossings, they are clustered to reduce the distance between the location databases. This can obviously result in the location update cost reduction. To see to what extent the algorithm can reduce the location update cost, first we give an algorithm under which the location databases are connected with their randomly chosen neighboring location databases (We call this method Randomly Clustering: RC). Then we design simulation experiments and compare the performance of the algorithm with that of the algorithm proposed in this paper (Clustering based on et Covering: CC). In the simulation experiment, there are 6561(=38) cells (corresponding to 6561 leaf location databases) in the system and all the location databases are organized into a hierarchical tree. There are 100,000 mobile clients scattering in the 6561 cells randomly. In the location database tree, each inner location database has 3 sub-location databases and the depth of the location database tree is 8. In other words, the maximal distance between any two leaf location databases is 8. The number of boundary-crossings per time unit for all the mobile clients follow a normal distribution. We argue that even if in a real application, the number of boundary-crossings for mobile clients may not follow a normal distribution, these experiments can show that we can achieve the total location management cost reduction by structuring the location databases deliberately. As can be seen from Equation (1), the location update cost is proportional to the distance between two leaf location databases responsible for the corresponding two cells. In the experiments, when comparing the location update costs, we only need to count the total distance for all the boundary-crossings. The following table describes the key parameters in the experiments. TABLE II THE KEY PARAMETER IN THE EXPERIMENT The parameters The value Number of cells 6561 Number of sub-ldb for an inner LDB 3 Depth of the LDB hierarchical tree 8 Number of mobile clients 100,000 We design two sets of experiments. In one set of experiments, we assign a static number (=4) to the mean value (for the normal distribution) of the number of boundary-crossings (NBC) per time unit for a mobile client and change the deviation (for the normal distribution) of the number of boundary-crossings. Then we compare the location update cost per time unit in the two location database tree organization method: RC and CC. The performance comparison is shown in Figure 3. Location update cost per time unit The deviation of the NBC Figure 3. Location update comparison(nbc=4) RC CC X/05/$ IEEE 1331

5 As can be seen from Figure 3, when the deviation of the NBC becomes larger, this means that there is more difference in the actual number of boundary-crossings per time unit for different mobile clients. In other words, there is more difference in the mobility patterns for different mobile clients. By using the CRC method, we can achieve a significant location update cost reduction. Contrary to the RC method in which the total location update cost remains almost the same, in the CRC case, the total location update cost decreases gradually. This is because even though the total number of boundary-crossings remains stable (because the mean value of NBC remains the same), the distances for the frequent boundary-crossings are reduced by using CRC method. Thus this results in total location update cost reduction. In the other set of experiments, we change the mean value of the NBC for a mobile client and the deviation of the NBC is set as half of the mean value. The performance comparison is shown in Figure 4. In both cases, we can see that with the increase of mean value of NBC, the total location update cost increases. But the location update cost increases more slowly in CRC method than that RC method. Furthermore, location management cost in the CRC method is much less than that in the RC method. This is because that with the increase of the NBC mean value, the NBC deviation also increases (it is half of the NBC mean value) which means greater different among the mobility patterns for mobile clients. This gives more space for the CRC method to organize the location databases which means more location update cost reduction. The more location update cost reduction is reflected as more difference in location update cost between the RC method and CRC method in Figure 4. Location update cost time unit The Mean Value of NBC RC CC patterns of the mobile clients. This paper focuses on this problem with the objective to achieve the location management cost reduction. Actually, when organizing the location databases, we should not only consider the number of boundary-crossings between different cells but also the number of calls between them. Furthermore, a mobile client can change its mobility pattern after the location database tree has been constructed. o the performance of an ideal location database topological structure can deteriorate with the time. A location database re-organization procedure is needed to accommodate the mobility pattern variation. We are currently concentrating on these research topics to achieve a better location management performance. REFERENCE [1] Evaggelia Pitoura and George amaras, Locating Objects in Mobile Computing, IEEE Transactions on Knowledge and Data Engineering, VOL. 13, NO.4, 2001 [2] ajak K. Das and anjoy K. en, Adaptive Location Prediction trategies Based On a Hierarchical Network Model in a Cellular Mobile Environment, The Computer Journal, vol. 42, no.6, [3] Xie, H., Tabbane,. and Goodman, D., Dynamic Location Area Management and Performance analysis, in Proceeding of 43rd IEEE Vehicular Technology Conference, May [4] Plassmann, D., Location Management trategies for Mobile Cellular Networks of 3rd Generation, in Proceedings of 44th IEEE Vehicular Technology Conf., June [5] Hüseyin Gökmen Gök and Özgür Ulusoy, Transmission of Continuous Query Results in Mobile Computing ystems, Information ciences, vol. 125, no. 1-4, pages 37-63, [6] M. Mouly and M.B. Pautet, The GM ystem for Mobile Communication, Cell and ys, [7] E. Pitoura and I. Fudos, An Efficient Hierarchical cheme for Locating Highly Mobile Users, in Proceedings of the 6th ACM International Conference on Information and Knowledge Management (CIKM98), November 1998, pp [8] V. Chvatal, A greedy heuristic for the set-covering problem, Mathematics. Operations. Research (1975) Figure 4. Location update cost comparison (Variable Mean Value) VI. CONCLUION Maintaining the real-time locations of mobile clients is essential to many new mobile computing systems. The traditional two-tier location database architecture is not scalable and unsuitable for the new applications in which there are a very large number of mobile clients. A hierarchical location database architecture is proposed to distribute the location update and search workload among different location databases. However, if the location databases are not properly organized, the total location management cost can be very high. When organizing the location databases, we should take into account the mobility X/05/$ IEEE 1332

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