A Dynamic Location Tracking Strategy for PCS Using Hierarchical Location Databases

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(1)A Dynamic Location Tracking Strategy for PCS Using Hierarchical Location Databases Chi-Chih Lee. Hwa-Chuan Lin. SingLing Lee. Department of Computer Science and Information Engineering National Chung Cheng University, Chiayi 62107, Taiwan, Republic of China Abstract In this paper, we propose a dynamic location tracking strategy for the hierarchical location database architecture in personal communication service systems (PCS). In our strategy, a user’s current location is stored at a specific location database, called the local anchor (LA). We focus on studying the problem how to decide the best position for the LA to get a great benefit in location registration. The LA periodically collects the user’s mobility and calling patterns and dynamically changes its position according to his/her behavior after a period of time. When a user has a small call-to-mobility ratio (CMR), our strategy efficiently reduces registration costs. Besides, we use caching bypass pointers for call delivery procedures but avoid cache miss which happens in the caching strategy. Thus our strategy has the same performance as the caching strategy in reducing call delivery costs when the CMR is large, but performs much better than the caching strategy when the CMR is small. Our simulation result shows that our strategy produces 30% performance improvement than the basic strategy and 20% performance improvement than the caching strategy..

(2) 1 1.1. Introduction Background Personal Communication Service (PCS) system provides people to communicate with. each other within the network coverage. Location management is a key component in the operation of PCS [2, 14]. It is an important problem to design an efficient location management strategy to reduce database access and signaling traffic for the system. Location management contains two main operations — location registration (or called Move) and call delivery (or called Find). There are two commonly standards in the current two-level location database architecture: IS-41 [1, 12] and GSM [12, 13]. Two types of databases are used to record the location information of the mobile terminal (MT), they are the Home Location Register (HLR) and the Visitor Location Register (VLR), respectively. The HLR is a centralized database containing user profiles of subscribers. These user profiles record information such as the type of services subscribed, the billing information, the quality-ofservice (QoS) requirements, and the current locations of the MTs. There are several VLRs distributed throughout the PCS network, and each one stores replication of the user profiles of the registered subscribers and the information of the MTs currently residing in its associated area. Figure 1 shows the basic architecture of the current PCS network in the two-level archtecture. The PCS service area is divided into cells. All MTs within a cell communicate with a base station through wireless links. Several cells are grouped together to form a contiguous geographical region called registration area (RA). All base stations within a giving RA are conected to a mobile switch center (MSC). The MSC provides switching function for the MTs in their associated area. Each VLR may associate with one or several MSCs. In this paper we assume each VLR associates with one MSC. The MSCs, VLRs, and the HLR are interconnected through the public switch telephone network (PSTN). Location registration is the procedure that an MT explicitly reports its new location to the network while the MT crosses RA boundies. When an MT enters a new RA, a location registration request is sent to its serving MSC, which relays the location registration request to the MT’s HLR. The HLR updates the MT’s profile to record the location of the VLR associated with its serving MSC and sends the service profile to the VLR. Furthermore, the.

(3) HLR. PSTN. VLR. MSC. Base station. Cell. Figure 1: PCS network architecture. HLR sends a deregistration message to the VLR associated with the old RA. The old VLR removes the MT’s profile. When a call arrives, the call delivery procedure is used to locate the callee’s current location. The caller’s MSC sends a query message to the callee’s HLR to retrieve the location of his/her VLR. Then the callee’s HLR sends a query message to his/her VLR. The VLR relays this request to the serving MSC of the callee. If the callee can receive a call, a Temporary Local Directory Number (TLDN) is associated to the callee and the TLDN is sent to the callee’s HLR, which forwards the TLDN to the caller’s MSC. The caller then setups a connection. As the PCS subscribers keep increasing, the requirements of database access and signaling transimission also increase dramatically [2, 14, 17, 18]. The traffic load of the HLR will become system bottleneck. To accommodate the increased traffic for the future PCS systems, it is necessary to use a scalable architecture. And the hierarchical distributed location architecture is a possible solution among different approaches. In this architecture, location databases are interconnected by a Common Channel Signaling (CSS) network. The hierarchical location database architecture greatly reduces network signaling traffic while most calls received by users and most RA crossings are geographically localized [2, 3, 5, 10, 11, 18]. However, a major drawback of the hierarchical location architecture is that the number of.

(4) database access is more than that of the two-level architecture. A number of auxiliary strategies has been proposed to improve this drawback.. 1.2. Previous work To reduce location registration and call delivery costs further, several auxiliary strategies. have been proposed. They are the user-profile replication, pointer-forwarding, local anchor, and caching strategies, which are described as follows. In the user-profile replication strategy [16], a user’s profile is replicated at one or several selected locations in order to reduce the call delivery cost. On the other hand, the database update cost will be increased potentially since replicas must be maintained consistently whenever the MT moves. The number of replicas of an MT may be limited by system resource, such as the signaling network and the database capacity. Besides, the replication decision is made by a centralized system, which must collect mobility and calling patterns of all users from time to time. This strategy performs well for those users who receive calls frequently relative to the rate at which they cross RAs, i.e., users with large call-to-mobility ratio (CMR). In the pointer-forwarding strategy [7, 9, 15], a pointer is created at the old VLR that points to the location of the new VLR instead of updating the HLR when a user moves across his/her RA boundary. When an incoming call arrives, the callee’s HLR is queried first to find the first VLR which he/she was registered at, and then the signal follows a chain of forwarding pointers to the his/her current serving VLR. This strategy saves the registration cost while users change RAs frequently. However, the cost of the call delivery procedure will increase due to trace the chain of forwarding pointers whose length is too long. The pointer-forwarding strategy performs good while users with small CMR. In the local anchor strategy [4], the MT reports its location change to a specific VLR called the local anchor (LA) which points to the location of the MT’s current RA. The HLR keeps a pointer to the local anchor. This approach reduces the registration cost. While an incoming call arrives, the caller first queries the callee’s HLR to get the location of the local anchor, and then the callee’s HLR queries the local anchor to retrieve the location of his/her current serving VLR. This strategy performs well for users with small CMR. In the caching strategy [8, 10, 11], the callee’s location information is stored at the caller’s database. The main idea is to reuse the information about the user’s location from the previous call to that user. This information consists of bypass pointers kept at a database.

(5) along the path that allows the signaling messages to bypass portions of the path. A pair of bypass pointer will be created between the caller and the called party. They are the forward bypass pointer and the reverse bypass pointer. The forward bypass pointer is created at the database s which is the ancestor of the caller’s RA to reduce the setup time of the call delivery procedure. And the reverse bypass pointer used by the acknowledgement message is created at the database t, the ancestor of the callee’s RA. When the CMR is large, clearly, those saving information will be useful and efficient for locating users. When the CMR is small, the caching strategy must pay an additional cost to maintain the validness of the bypass pointers [6].. 1.3. Motivation of our work In this paper, we propose the dynamic location tracking strategy to reduce database. access and signaling traffic at the same time. This strategy combines the characteristic of the local anchor strategy in registration and that of the caching strategy in call delivery. While a user has a large CMR, the cost of the call delivery will be reduced by using the information of bypass pointers. Besides, the registration cost also can be greatly reduced even when a user has a small CMR. Each user selects a database as the local anchor (LA) to record his/her location information. A user performs the registration procedure only at the current serving VLR and his/her local anchor instead of updating several databases. Besides, each forward bypass pointer records the callee’s LA for call delivery. As long as we find the callee’s LA, then we can find his/her actual location through querying his/her LA. Hence, our strategy can prevent cache miss when a user moves out of the subtree rooted at the database t. Furthermore, we focus on deciding an appropriate position for each LA in the tree-structured location architecture. Each LA periodically collects a user’s mobility and calling patterns, and its position can be dynamically adjusted according to the computing result after a certain time period. When the LA has been adjusted, it implies that several forward bypass pointers which cache this LA need to be updated. If these bypass pointers are updated at once, the update cost will increase dramatically. In order to overcome this problem, we keep a pointer from the old LA to the new LA instead of updating bypass pointers at once. When a call delivery procedure is invoked, the bypass pointer will be updated through call delivery message. First, the reverse bypass pointer will be created at the new LA, then the forward bypass pointer will be updated through the acknowledgement message. In other words, the forward bypass pointer will be updated.

(6) through the acknowledgement message only when it is used by a user to perform a call delivery procedure. Thus we can avoid that several forward bypass pointers are updated at the same time. Finally, the experiment result shows that our strategy gains a great benefit in reducing database access and signaling traffic by dynamically adjusting bypass pointers with LAs. The rest of this paper is organized as follows. In Section 2, we describes the dynamic location tracking strategy and the appropriate position deciding scheme. Section 3 briefly discuss analysis of different strategies. Simulation result shows in Section 4. Finally, Section 5 concludes the thesis..

(7) 2. Dynamic Location Tracking Strategy Our strategy is able to make database access and signaling traffic reduced in the hier-. archical location database architecture for PCS mobility management. Our objects are as follows : • Reduce the cost of location registration operation. • Reduce the cost of call delivery. • Dynamically adjust the position of the LA according to a user’s behavior to make bypass pointers used more efficiently.. LA i. Move. RA x. i. RA y. Figure 2: An example of the local anchor strategy. Our strategy makes use of the local anchor to track users’ location information, and the cost of updating databases for location registration can be reduced. Whenever an MT moves to a new RA, it sends a registration message to the new RA and its current serving LA. Furthermore, an anchoring pointer is created at the MT’s LA. This approach only needs to have two database registrations, hence the registration cost can be reduced efficiently. Figure 2 shows an example of the local anchor strategy. While the MT i moves from the RAx to the RAy , the LAi keeps an anchoring pointer which points to the location RAy in its.

(8) database. Generally speaking, the local anchor can be differentiated into static and dynamic ones. For the static LA, the LA doesn’t change its position until an incoming call arrives. For the dynamic LA, the LA changes its location dynamically. However, the dynamic LA performs much better than the static LA according to the previous research[4]. The reason why the static LA does not have good performance is that a user may have to register to his/her LA located at a far region. Thus the registration cost will increase potentially. In this paper, we will focus on studying the strategy how to dynamically adjust the position of the LA. Furthermore, this strategy is also similar to the caching strategy which reuses the user’s location information from the previous call to that user. For users who receive calls frequently, the cost of a call delivery procedure can be saved efficiently. However, the performance of the caching strategy depends upon the probability whether the cached information is valid or not. It should be noted that the cached information becomes invalid when users move out of the subtree rooted at the database t. The database t only stores location information of its child nodes. When a call request arrives the database t, the query message is propagated downward to find the called user. If the called user is not found under the database t, the cache miss happens. In order to avoid the cache miss, we view the location of the database t as the local anchor of called users, hence the called user can be found certainly at the database t. Besides, it is important to decide an appropriate position for the database t, which can make bypass pointers used efficiently. We adjust the position of the database t to the best position t according to the user’s mobility and calling patterns. The dynamic location tracking strategy for PCS includes two main operations, called Intelligent local anchor (ILA)Move and ILA Find..

(9) 2.1. Intelligent LA Move scheme When a user moves to a new RA, the ILAMove procedure is initialized. The user’s LA. will record the location of the RA where the user resides. We assume that there is a small memory in the mobile terminal that records which location database is the user’s current serving LA. Whenever the user moves across RA boundaries, the registration message is propagated to this LA. Before the LA changes its position from t to t , the user still registers to the LA at t. We denote the old RA of MT i as RAold and the new RA of MT i as RAnew . be the current LA of MT i and LAnew is the new LA of MT i. Let LAadjusted Let LAcurrent i i i be the adjusted LA. We describe the ILAMove as follows: Case 1: The LA serves a new user who has never performed the dynamic adjusting LA procedure, it collects his/her mobility patterns to decide the best position of the LA. Case 1.1: The MT i moves from RAold to RAnew . It does not move out of the subtree rooted at its serving LA, LAcurrent . i 1. The MT i deregisters at RAold and registers at RAnew . 2. The registration message is propagated to LAcurrent , and LAcurrent stores i i the move record in its event table for the MT i. to RAnew . 3. The acknowledgement message returns from LAcurrent i Case 1.2: The MT i moves from RAold to RAnew . It moves out of the subtree rooted (Figure 3). at is serving LA, LAcurrent i 1. The MT i deregisters at RAold and registers at RAnew . 2. The registration message is propagated to the least common ancestor (LCA) of these two RAs, and the LCA becomes the MT’s new LA, LAnew . i stores the move record for the MT i. LAnew i 3. The LA movement procedure is invoked. First, records of LAcurrent will i be copied to LAnew . Secord, the system will check whether LAcurrent exits i i reverse bypass pointers for the MT i. If it does exist, a LA movement will be crated at LAcurrent . pointer that points to the location of LAnew i i 4. The acknowledgement message returns from the LAnew to RAnew . i , has performed the dynamic adjusting LA procedure to Case 2: The LA at t, LAcurrent i change its position to t . Whenever the MT i crosses RA boundaries, it keeps (Figure 3). registering to the adjusted LA at t , LAadjusted i.

(10) new LAi. current LAi. old LAi. adjusted LAi. i. i. RAy RAz. RAy RAz (a)Case 1.2. (b)Case 2. Figure 3: The procedure of ILAMove. 1. The deregistration and registration messages are sent to RAold and RAnew respectively. 2. The registration message is propagated to LAadjusted of the MT i, and LAadjusted i i stores the move record for the MT i. to the RAnew , and 3. The acknowledgement message returns from the LAadjusted i the registration procedure is complete. Whenever we want to adjust the database t to t , we may encounter a problem that several forward bypass pointers need to be updated at the same time. The database update overhead will be increased potentially. Therefore, we setup a LA pointer which points to the new LA instead of updating these forward reverse bypass pointers at once..

(11) 2.2. Intelligent LA Find scheme The ILAFind procedure is invoked when a calling MT sends a call request. The ILAFind. can be divided into four cases, each of them is described as follows. We denote the RAcaller as the caller’s RA, the RAcallee as the callee’s RA, and the LAcallee as the callee’s LA. Case 1: The caller and the callee are at the same RA. 1. The call request is sent to the RAcallee , and it is queried directly to find the callee. 2. In this case, no bypass pointers will be created. Case 2: No bypass pointer exists between the caller and the callee, and the RAcaller is under the coverage of the LAcallee . 1. The call request is sent to the LAcallee , and then the call request is forwarded to the RAcallee through the LAcallee . 2. The acknowledgement message returns from the RAcallee to the RAcaller through the LAcallee . 3. No Bypass pointers will be created for the callee in this case. Case 3: No bypass pointer exists between the caller and the callee, and the caller does not reside under the coverage of the LAcallee . 1. The call request is sent to the LAcallee , and then the call request is forwarded to the RAcallee through the LAcallee . Besides, the LAcallee stores the call record for the callee. 2. The acknowledgement message returns from the RAcallee to the RAcaller through the LAcallee . 3. A pair of bypass pointers is created between the RAcaller and the LAcallee . Case 4: A pair of bypass pointers exists between the caller and the callee, and the caller does not reside under the coverage of the LAcallee . Case 4.1: The position of the LAcallee has not been moved. 1. The forward bypass pointer is found at the RAcaller , then the call request is send to the LAcallee through this forward bypass pointer. 2. The LAcallee forwards the call to the RAcallee , and it stores the call record for the callee. If the LAcallee is just the RAcallee , then the LAcallee is queried directly to find the callee..

(12) LAj. LAj. t. s Find. j callee. RAx. j. i. Find. i. caller. callee. caller. RAy. RAx. RAy. (a)Case 3. (b)Case 4.1. Figure 4: The procedure of ILAFind. 3. The acknowledgement message returns from the RAcallee to the RAcaller through the reverse bypass pointer which is stored at the LAcallee . Case 4.2: The position of the LAcallee has been moved from t to t , and t is the leaf node. 1. The call request is send from the RAcaller to the old LAcallee t through this forward bypass pointer. 2. The old LAcallee is queried to find the callee. It also gets the location of the adjusted LAcalee t , and the reverse bypass pointer stored at t will be moved to t . 3. The acknowledgement message returns from the RAcallee to the RAcaller through the reverse bypass pointer stored at t . And the call record is stored at t . During the return path, the forward bypass pointer will be updated to cache t at the RAcaller . Case 4.3: The position of the LAcallee has been moved from t to t , and t is not the leaf node. 1. The call request is send from the RAcaller to the old LAcallee t through the forward bypass pointer. 2. The old LAcallee is queried to get the location of the adjusted LAcalee t ,.

(13) LAj. t’. LAj. t. t’. t. s Find. j callee. RAx. i caller. RAy (c)Case 4.2. s Find. j callee. i caller. RAx. RAy (d)Case 4.3. Figure 5: The procedure of ILAFind and the reverse bypass pointer which is stored at t will be moved to t . 3. When the call arrives t , LAcallee stores the call record and forwards the call to the RAcallee . 4. The acknowledgement message returns from the RAcallee to the RAcaller through the reverse bypass pointer stored at t . During the return path, the forward bypass pointer will be updated to cache t at the RAcaller .. 2.3. The Appropriate Position Deciding Scheme Each location database that serves as the LA has to record its serving user’s calling. and mobility patterns. Its primary function is to collect these information, and to compute the most appropriate location for the LA. By adjusting the position of the LA, it not only greatly reduces the registration cost, but also reduces the call delivery cost efficiently. We use a user event table to store a user’s mobility and calling patterns. They consists of registration events and call events. Whenever a user crosses RA boundaries or a caller makes a call through bypass pointers, these events will be saved in this event table. Table 1 shows an example of a user’s event table. In order to explain the appropriate position deciding scheme, we define some parameters as follows:.

(14) Revent :. The amount of the registration events. Cevent :. The amount of the call events. CLAi :. The set of M Ti ’s candidate LAs. cost(CLAi j ): RAi :. The set of RA where M Ti resides. RAi k :. The k-th RA where M Ti resides. d(s, CLAi j ):. cost(CLAi j ) =. The cost of the j-th candidate LA of M Ti. The distance from s to the candidate LAi j. ρs :. The registration rate of M Ti in s, and s ∈ RAi. γs :. The call rate of M Ti in s, and s ∈ RAi. Revent Revent +Cevent. ·2. Cevent + Revent ·2 +Cevent. . ρs · d(s, CLAi j ). s∈RAi. . γs · [d(s, CLAi j ) + d(s , CLAi j )]. s∈RAi. where s = LCA(RAi , CLAi j ) Figure 6: The appropriate position analysis function.

(15) The best LA position deciding algorithm Input: A set of RA where M Ti resides. Output: The most appropriate position for M Ti ’s LA. Step 1: Select the location databases as the candidate LAs for evaluating which one is better. The candidate LAs contain the databases which locate between RAi and the LCA of RAi . Step 2: Gather statistics of the registration rate and the call rate for each RA of RAi . Step 3: For each candidate LA, compute its link costs of registration and call, respectively. Step 4: Execute the appropriate position analysis function. If all candidate LAs finish computing, then go to Step 5, else go to Step 3. Step 5: Return the position of the candidate LA with the minimum cost, t , to be M Ti ’s new serving LA. Adjust M Ti ’s LA to this new LA t .. We use the best LA position deciding algorithm to compute the appropriate position t for a user’s LA according to his/her mobility and calling patterns. The registration rate and the call rate of each RA are known through a user’s event table. They will be useful to decide the best position for a user’s LA. First, we select several location databases as the candidate LAs. These candidate LAs contain the databases which locate between the RAs where the user resides and the LCA of these RAs. After these candidate LAs have been choosed, we compute the cost of each candidate LA. The cost can be divided into registration and call costs. The cost of the candidate LA is computed by the appropriate position analysis function (Figure 6). When the costs of all candidate LAs have been computed, the most appropriate LA is with the minimum cost. Thus we will adjust the user’s LA to the best position..

(16) RA id. Reg. events. Call events. RA555. 1. 2. RA556. 2. 1. RA557. 2. 3. RA558. 4. 2. RA559. 11. 19. RA560. 12. 9. RA560. 4. 0. Table 1: An example of the user event table RA id. Reg. rate. Call rate. RA555. 0.0278. 0.0556. RA556. 0.0556. 0.0278. RA557. 0.0556. 0.0833. RA558. 0.1111. 0.0556. RA559. 0.3056. 0.5278. RA560. 0.3333. 0.25. RA561. 0.1111. 0. Table 2: The registration rate and the call rate of the event table We give an example to explain our appropriate position deciding scheme. Table 1 shows a user’s event table of his/her current LA61 , and it records call and registration events of each RA respectively under this subtree (Figure 7). We can know the registration rate and the call rate of the event table (Table 2). Each database which locates between these registration areas where the user resides and the LCA of these registration areas will be computed for deciding the most appropriate LA for the user. In this example, DB61 , DB184 , DB185 , DB185 , and DB555 ∼ DB561 will be computed respectively, and we have to compute registration and call costs for each DB. For example, DB555 is computed as follows: DB555 : Reg. cost = 2 ∗ 4 ∗ 0.9722 = 7.778 Call cost = 2 ∗ 2 ∗ 0.0556 + 2 ∗ 6 ∗ 0.9444 = 11.556 Total cost = 7.778 + 11.556 = 19.333.

(17) 61. 184. 553. 554 555. 556. 185. 186. 557. 558 559 560. 561. Figure 7: An example of the position deciding scheme. Weighted cost = 0.5 ∗ 7.778 + 0.5 ∗ 11.556 = 9.667. The total cost means that we sum up the registration and call costs directly, and the weighted cost means that we assign different weight values to registration and call costs according to the user’s registration and call events. In this example, we can choose DB186 as the most appropriate LA for the user according to the computing result(Table 3)..

(18) Database id. Reg. cost. Call cost. Total cost. Weighted cost. DB61. 4. 4. 8. 4. DB184. 5.889. 7.778. 13.667. 6.883. DB185. 5.111. 7.333. 12.444. 6.222. DB186. 3. 4.889. 7.889. 3.944. DB555. 7.778. 11.556. 19.333. 9.667. DB556. 6.889. 11.222. 18.111. 9.056. DB557. 6.889. 11. 17.889. 8.944. DB558. 6.667. 11.111. 17.778. 8.889. DB559. 3.778. 6.778. 10.556. 5.278. DB560. 3.667. 7.889. 11.556. 5.778. DB561. 4.556. 8.889. 13.444. 6.722. Table 3: The result of computing the best position Generally speaking, we can decide the most appropriate LA according to the total cost of each DB (Table 3). However, we should consider the relation between registration and call events. In some cases, the most appropriate LA will not be decided clearly if it is only decided according to the total cost. Figure 8 is a special example, and we are not sure which one is the most appropriate LA. We describe this situation as follows.. 1. 2. 4. RA id RA5 RA6. 3. 5. 6. Reg. events Call events 60 9 40 1. 7. Figure 8: An example of the position decideing scheme. In this case, we cannot decide the best position of the LA according to the total cost. We are not sure whether DB5 is better than DB1 and DB2 , because their total costs are the same (see Table 4). However, we can observe that the number of registration events is.

(19) Database id. Reg. cost. Call cost. Total cost. Weighted cost. DB1. 4. 4. 8. 4. DB2. 3.6. 4.4. 8. 3.673. DB3. 4.4. 7.6. 12. 4.691. DB5. 3.2. 4.8. 8. 3.345. DB6. 4.8. 11.2. 16. 5.382. Table 4: The result of computing the best position more than the number of call events. Hence, the weight value of registration cost should be more expensive than that of call cost. Because the registration cost of DB5 is smaller than those of DB1 and DB2 , we can still easily decide that DB5 is the most appropriate LA than the others. In other words, it can greatly reduce registration cost to select DB5 as the LA; because DB5 is close to the region where the user frequently registers. This result leads to the conclusion that we should decide the most suitable position for the LA by the weighted cost. So far, we have seen how to decide the most appropriate position of the LA for a user through our computing scheme. The LA periodically collects the user’s mobility and calling patterns to decide whether the LA should be adjusted its position. We execute the appropriate position deciding scheme off-line, and it won’t increase the system load dramatically. We assume each location database has the computing function for adjusting LA dynamically. Besides, the LA does not necessary proceed computing everyday, it depends on the user’s behavior. If the user’s behavior changes frequently, the system trends to collect and to compute everyday. If the user rarely changes his/her behavior, then the system will collect this user’s information of a week and compute the most suitable LA for him/her. Therefore, the user’s LA dynamically changes according to his/her behavior..

(20) 3. Cost Analysis In this section, we derive the cost function of the basic, eager caching, and dynamic. location tracking strategies to analyze the registration and call delivery costs. We assume that s and t are location databases with forward and reverse bypass pointers for callee j. Let RAx and RAy be the RAs where caller i and callee j reside respectively, and RAz is the RA which callee j moves to. We assume the level of the leaf node is zero. Suppose b1 be the levels from s to LCA(RAx , RAy ) and b2 be the levels from t to LCA(RAx , RAy ). And q is the levels from RAy to RAz . The levels from RAx (or RAy ) to LCA(RAx , RAy ) is r. The user’s LA will be dynamically adjusted its position from t to t according to our appropriate position deciding scheme. Assume that the levels from t to LCA(RAx , RAy ) is . The total cost of a location management strategy depends on Move cost and Find cost. Our cost analysis considers communication and database access as the basic measurement of costs. In order to estimate the total cost clearly, we define the cost parameters as follows:. Table 5: Define the cost parameters n1. Average number of move operations.. n2. Average number of find operations.. T (t) γ. The coverage area of database t. Average probability of moving out the subtree rooted at database t between two consecutive calls.. α(i) β(t, i). The probability of i moves between two consecutive calls. The probability of the user moves out of database t given there are i moves between two calls.. 3.1. R. The cost of reading a database.. U. The cost of updating a database.. C. The cost of traversing a signal link.. Analytical Model We select m-way search tree as the architecture of hierarchical location database for our. analytical model [11]. First, we discuss the probability of the user moving out of the subtree.

(21) rooted at database t between two consecutive calls. Between two calls arrive, we assume the user moves i times. Therefore, we can describe the probability as follows: γ= =. i . P[ a user moves out t and there are i moves between two calls ] γ(t, i) = α(i)β(t, i). i. i. α(i) denotes the probability of a user who moves i times between two consecutive calls. The probability β(t, i) denotes a user moving out of the subtree rooted at database t. Let h be the level of database t, and the RAs under database t are numbered from 1 to mh . Hence, β(t, i) =. mh . P[ the user starts in j ]β (t, i, j). j=1. β (t, i, j) denotes the probability of the user moving out of database t in i steps given that he/she starts in RA j. Assume that the probability of the user’s moving to the right is u, and the probability of the user’s moving to the left is v. Thus we can get the following equations. β (t, i, j) = β (t, i − 1, j + 1)u + β (t, i − 1, j − 1)v for 2 ≤ j ≤ mh − 1 , 1 < i β (t, i, 1) = β (t, i − 1, 2)u. , for 1 < i. β (t, i, mh ) = β (t, i − 1, mh − 1)v. ,for 1 < i. The boundary conditions are described as follows: β (t, 1, 1) = v ,. β (t, 1, mh ) = u. β (t, 1, j) = 0 , for. 2 ≤ j ≤ mh − 1. Finally, we get the value, γ, and we use it to evaluate the costs of different strategies later.. 3.2. Basic Strategy First, we analyze the costs of the basic strategy. As we know, there are two main opera-. tions in the basic strategy: BasicMove and BasicFind. They are involved in the registration and call delivery procedures respectively. • The cost of BasicMove When an MT moves form RAy to RAz , the registration and deregistration messages propagate from RAy to RAz through LCA(RAy , RAz ). The databases un-.

(22) der LCA(RAy ,RAz ) are queried and updated during the registration and deregistration operations. The communication signal traverses from RAy to RAz through LCA(RAy , RAz ), and it returns from RAz to RAy . Assume that M Cbasic is the cost of a BasicM OV E operation, then M Cbasic = 2(2q + 1)R + (2q + 1)U + 4qC. • The cost of BasicFind When caller i at RAx calls callee j at RAy , the query message is propagated from RAx to RAy through LCA(RAx , RAy ). The acknowledgement message returns form RAy to RAx . Let F Cbasic be the cost of a BasicF ind operation, then F Cbasic = 2(2r + 1)R + 4rC Thus the total cost for callee j in the basic strategy is defined as follows: T Cbasic = n1 · M Cbasic + n2 · F Cbasic.

(23) 3.3. Eager Caching Strategy The two main operations in the eager caching strategy are called EagerMove and. CacheFind. They are involved in the registration and call delivery procedures respectively. • The cost of EagerMove EagerMove is similar to BasicMove, but it pays an additional cost to delete invalid bypass pointers. We assume that there is a pair of bypass pointers constructed at the ancestors of RAx and RAy for callee j. When an MT moves from RAy to RAz , it leaves the area of the coverage of database t. The forward bypass pointer of database s becomes invalid, and it will be deleted by EagerMove. In order to delete invalid bypass pointers, EagerMove deletes records in database s and t. The communication signal for deleting invalid bypass pointers propagates from RAy to RAx through LCA(RAx , RAy ). Thus the additional cost for deleting a pair of bypass pointers for callee j is 2U + 2(b1 + b2 )C. We should notice that the more forward bypass pointers cache the location of database t, the more costs need to pay to delete invalid bypass pointers when a callee leaves database t. Assume that the maximum height of the tree is H. Let M be the average cost of a BasicMove operation. M (t, i) denotes the cost of i EagerMove operations between two consecutive calls given a bypass pointer directed at database t. M Ccache denotes the average cost of a EagerMove operation, hence we can obtain it as follows:. M =. H q=1. H−q. m M (q) m H−1. M (t, i) = [(M + 2U + 2(b1 + b2 )C)γ(t, i)]i + [M (1 − γ(t, i))]i M Ccache =. ∞ . M (t, i)α(i). i=0. • The cost of CacheFind The difference between CacheFind and BasicFind is that CacheFind locates a callee by using bypass pointers. If no bypass pointers exist between the caller and the called party. A pair of bypass pointers will be constructed when the first time the caller calls the callee. To setup bypass pointers, CacheFind updates records in database s and t. The cost for constructing a pair of bypass pointer is 2U . If there is a pair of bypass pointers between caller i and callee j, the cost of reading databases from s to t can be saved. The saving cost of reading databases through bypass pointers is.

(24) 2(b1 + b2 − 1)R. When the communication shortcut is available between database s and t, the cost of communication between s and t can also be saved. The saving cost of communication is 2(b1 + b2 )C. In this paper, we assume that communication shortcuts are unavailable in the underlying signaling network. Let F Ccache be the average cost of a CacheFind operation, and it can be described as follows: F Ccache = (F Cbasic + 2U )γ + (F Cbasic − 2(b1 + b2 − 1)R)(1 − γ) Finally, the total cost for callee j in the eager caching strategy is defined as follows: T Ccache = n1 · M Ccache + n2 · F Ccache.

(25) 3.4. Dynamic Location Tracking Strategy In the dynamic location tracking strategy, a pair of bypass pointers is created between. the caller and the called party. The forward bypass pointer for the callee caches the location of the callee’s LA, and the reverse bypass pointer which caches the location of the caller’s RA is created at the callee’s LA. The two main operations in this strategy are called ILAMove and ILAFind. They are involved in the registration and call delivery procedures respectively. • The cost of ILAMove Whenever callee j crosses RA boundaries, he/she reports the current location to his/her LA (database t). The LA keeps callee j ’s location information; thus the bypass pointers for callee j are still valid. When callee j moves from RAy to RAz , the registration message is propagated from RAz until it reaches LCA(RAy , RAz ). The acknowledgement message is returned from LCA(RAy , RAz ). Hence, the communication cost of ILAM ove is 2qC, and it saves. 1 2. communication cost than BasicMove. or EagerMove. ILAM ove just updates 3 databases, RAy , RAz , and LCA(RAy , RAz ). The cost of updating databases is 3U, which saves (2q −2)U than BasicMove or EagerMove. Futhermore, there is a LA address mapping table stored at each RA. So, we get the location of the LA by querying this table of the RA. Besides, the cost of querying databases becomes 4R, which saves (4q − 2)R than BasicMove or CacheMove. Let P M (q) be the cost of a ILAMove operation without leaving database t. P M (q) = M Cbasic − (4q − 2)R − (2q − 2)U − 2qC) = 4R + 3U + 2qC If callee j leaves the subtree rooted at database t, then the LA movement procedure is invoked by ILAMove. And the new serving LA of callee j is LCA(RAy , RAz ). Besides, callee j ’s profile is moved from the old LA to LCA(RAy , RAz ), and a LA movement pointer kept at the old LA points to the new serving LA. The bypass pointers for callee j are still stored at this old LA. In this situation, ILAMove pays an additional cost for changing the location of the LA, but saves the cost for updating bypass pointers at once. This additional cost for changing the LA is 2R + 2C + U . Assume that the maximum height of the tree is H. Let P M be the average cost of a ILAMove operation without leaving its LA. M (t, i) denotes the cost of i ILAMove operations between two consecutive calls given a bypass pointer directed at database t. Then, we can obtain the average cost of a ILAMove operation denoted M CILA ..

(26) PM =. H q=1. H−q. m P M (q) m H−1. M (t, i) = [(P M + (2R + 2C + U ))γ(t, i)]i + [P M (1 − γ(t, i))]i M CILA =. ∞ . M (t, i)α(i). i=0. • The cost of ILAF ind If callee j does not leave database t, there is no need to update the location information of the forward bypass pointer stored at database s. When caller i at RAx makes a call to caller j at RAy through bypass pointers, the cost of reading databases between s and t can be saved. The saving cost of reading databases between s and t is 2(b1 + b2 − 1)R. Besides, the cost of reading databases from t to RAy can also be saved through the anchoring pointer. Hence, the saving cost of reading databases between t and RAy is 2(r − b2 − 1)R. If caller i calls callee j and callee j has left databse t, it implies that the bypass pointers for callee j cache the location of his/her old LA. In this circumstance, the cache information needs to be updated. When the call request arrives database t, the call request needs to be forwarded to his/her current serving LA through the LA movement pointer stored at the old LA. By querying this old LA, the reverse bypass pointer for callee j can be acquired. This reverse bypass pointer should be moved to callee j’s current serving LA. Hence, the bypass pointers for callee j will be updated at his/her current LA and database s through the return path of the acknowledgement message. Let F CILA be the average cost of a ILAF ind operation. F CILA = (F Cbasic + (3U + C) − (b1 + b2 − 1)R − (b1 + b2 − 2)R − 2(r − b2 − 2)R)γ + (F Cbasic − 2(b1 + b2 − 1)R − 2(b1 + r − 2)R)(1 − γ). Before deciding the most appropriate position for callee j’s LA, the total cost for callee j in the dynamic location tracking strategy is defined as follows: T CDLT = n1 · M CILA + n2 · F CILA. Finally, we formula the cost of callee j after deciding the most appropriate location for his/her LA. Assume that callee j’s LA has been adjusted from t to t . Before.

(27) next time the LA invokes a dynamic adjusting procedure, the postion of this LA won’t be changed, even callee j leaves database t . Let γ denote the probability that the user leaves T (t ) between two consecutive calls. M (t , i) denotes the cost of i ILAM ove operations between two consecutive calls given a bypass pointer directed at database t . which denotes the average cost of a ILAM ove operation We can clearly obtain M CILA. when callee j’s LA has been dynamically adjusted from t to t : PM =. H q=1. H−q. m P M (q) m H−1. M (t , i) = [(P M + 4C)γ (t , i)]i + [P M (1 − γ (t , i))]i = M CILA. ∞ . M (t , i)α(i). i=0. Furthermore, Let F CILA be the average of a ILAF ind operation when callee j’s LA. has been dynamically adjusted from t to t , which is described as follows: F CILA = (F Cbasic + 4C − 2(b1 + − 1)R − 2(r − − 1)R)γ . + (F Cbasic − 2(b1 + − 1)R − 2(r − − 1)R)(1 − γ ) Therefore, after deciding the most appropriate position for callee j’s LA, the total cost for callee j in the dynamic location tracking strategy is defined as follows: = n1 · M CILA + n2 · F CILA T CDLT.

(28) 4 4.1. Simulation Results Simulation Environment In our simulation, m-way search tree is selected as the architecture of hierarchical lo-. cation databases. Each node of the tree implies that the location database stores users’ profiles. A database at a higher level stores users’ profiles when users locate at the levels below it. Location databases are interconnected by the signal links of the network. Besides, Leaf nodes are location databases of the RAs. The user can store the records for his/her friends in the friend table of the mobile terminal. When the system starts, each user gets an event per hour, move or find. If he/she gets a find event, it implies that someone makes a call to him/her. 85% of a user’s calls comes from his/her friends and 15% of those comes from other users in the system. When he gets a move event, he chooses a direction, left or right, and then moves to the neighbor RA. We define system parameters listed in Table 6 for our simulation environment. We use different levels of the tree structure, different cost value, and different measure days to compare the performance between different strategies: the basic, eager caching, and dynamic location tracking (DLT) strategies. Table 6: System parameters values Parameter. Value. L. 6, 7. Maximum height of the tree structure. M. 4, 3. The degree of the tree structure. DB. Comment. 1365, 1099 The number of location databases. MT. 100,000. The number of mobile terminals. FT. 5. CMR. 1 ∼ 20. D. 3, 5. U. 2, 0.4, 2. The cost of updating a database. R. 1, 0.2, 1. The cost of reading a database. C. 1, 1, 0.2. The cost of traversing a signal link. The number of a user’s friends Call-to-Mobility Ratio Measure days.

(29) 4.2. Experiment Results We use different parameters such as tree level, cost value, and measure day to observe. the effect of the simulation. Besides, for the dynamic location tracking strategy, we assume that the system performs computing the appropriate LA for users every three and five days. First, we use different levels of the tree structure to compare their performance (See Figure 9 and Figure10), our strategy performs better than the basic and eager caching strategies. In this case, we can see that the eager caching performs worst when the CMR is smaller than 6. When the CMR is small, it implies that users may move to neighbor RAs frequently. When the user moves, the eager caching has to pay an extra cost to delete invalid bypass pointers. When the CMR is large, it implies that the user receives call frequently rather than moves. The eager caching has better performance than the basic because of using the bypass pointers to save the call setup time. Our strategy has the same performance in different tree structure. When the CMR is small, our strategy is better than the eager caching and basic, because it saves the cost of location registration. Our strategy uses the local anchor to keep the user’s location information. 24000. Basic Eager-Caching DLT. 22000. Total cost[1:10000]. 20000 18000 16000 14000 12000 10000 8000 6000 2. 4. 6. 8. 10 CMR. 12. 14. 16. 18. 20. Figure 9: L=6, M=4, MT=100,000, D=3, FT=5, U=2, R=1, C=0.2.

(30) 26000. Basic Eager-Caching DLT. 24000 22000. Total cost[1:10000]. 20000 18000 16000 14000 12000 10000 8000 2. 4. 6. 8. 10 CMR. 12. 14. 16. 18. 20. Figure 10: L=7, M=3, MT=100,000, D=3, FT=5, U=2, R=1, C=0.2. When the CMR is large, our strategy still performs well because of the fact that the DLT also uses bypass pointers to efficiently reduce the cost of the call delivery operation. Furthermore, the DLT uses the appropriate position deciding scheme to evaluate whether the position of the user’s LA should be adjusted. When the CMR is small, the LA will adjust its position to be close to the region where the user frequently moves. Thus the cost of location registration can be greatly saved . Besides, the position which the LA is adjusted to is also the region where the user receive calls frequently. When the CMR is large, the find events are much more than move events. The LA at a higher level of the tree is better than that at a lower level of the tree. Hence, the location of the LA is the same as before, it implies that the location of the LA won’t be changed. Figure 10 and Figure 11 shows that the appropriate LA deciding scheme is invoked in three and five days respectively, and users rarely change their behavior. We can see if a user rarely changes his/her behavior, and then his/her LA will keep static according to our appropriate position deciding scheme. The system can extend the period for invoking the dynamic adjust procedure. In Figure 10, Figure 12, and Figure 13, we use different cost value to compare the performance. When the communication cost is more expensive than the cost of accessing databases, the eager caching does not perform well because of paying an addiction cost to delete invalid bypass pointers when the user leaves database t. If several.

(31) bypass pointers cache this location t, the cost of deleting invalid bypass pointers will increase dramatically. Our strategy doesn’t delete bypass pointers when the user leaves database t. The bypass pointers are updated through the acknowledgement messages of the call delivery procedure. Finally, we compare the difference between the DLT before invoking the appropriate position deciding scheme (DLTbef ore ) and the DLT after invoking the appropriate position deciding scheme (DLTaf ter ) in Figure 14. When the CMR is small, the performance of DLTaf ter is better than DLTbef ore . We see that the move events do influence the result of deciding which location is suitable for the user’s LA. As the CMR increases, DLTbef ore and DLTaf ter will be the same because of the fact that call events are more than move events. When the user’s call events are more than move events, the LA won’t be adjusted to a lower level of the tree..

(32) 40000. Basic Eager-Caching DLT. Total cost[1:10000]. 35000. 30000. 25000. 20000. 15000. 10000 2. 4. 6. 8. 10 CMR. 12. 14. 16. 18. 20. Figure 11: L=7, M=3, MT=100,000, D=5, FT=5, U=2, R=1, C=0.2 40000. Basic Eager-Caching DLT. Total cost[1:10000]. 35000. 30000. 25000. 20000. 15000. 10000 2. 4. 6. 8. 10 CMR. 12. 14. 16. 18. 20. Figure 12: L=7, M=3, MT=100,000, D=3, FT=5, U=2, R=1, C=1.

(33) Basic Eager-Caching DLT. 24000 22000. Total cost[1:10000]. 20000 18000 16000 14000 12000 10000 8000 2. 4. 6. 8. 10 CMR. 12. 14. 16. 18. 20. Figure 13: L=7, M=3, MT=100,000, D=3, FT=5, U=0.4, R=0.2, C=1. DLTafter/DLTbefore 1.4. Cost Ratio. 1.2. 1. 0.8. 0.6. 0.4 2. 4. 6. 8. 10 CMR. 12. 14. 16. 18. 20. Figure 14: L=7, M=3, MT=100,000, D=3, FT=5, U=0.4, R=0.2, C=1.

(34) 5. Conclusion The main contribution of the paper is to propose the dynamic location tracking strategy,. which dynamically adjusts the position of the local anchor according to the user’s behavior. Our strategy is based on the caching strategy, but modifies the registration and call delivery procedures to get a great benefit in reducing communication and database access costs. For registration procedures, we uses the LA to track a user’s current location, and it can greatly reduce the registration cost. For call delivery procedures, we make the forward bypass pointers cache each user’s LA, which can avoid cache miss when the user leaves t. Besides, the appropriate position deciding scheme is invoked in our strategy to decide which position is better for a user’s LA according to his/her mobility and calling patterns. Then we adjust his/her LA to the best position. We can get a great benefit in location registration through this dynamic adjusting LA procedure. Besides, while the position of the LA has been changed from t to t , several forward bypass pointers which cache the previous position t may need to be updated at the same time. In our strategy, these bypass pointers will be updated through the acknowledgement messages of the call delivery procedure. In other words, the bypass pointer will be updated through the acknowledgement message only when it is used by a user to perform the call delivery procedure. Thus we do not need to update several bypass pointers at once. With a small CMR, the frequency of successive move operations is high. Our strategy greatly reduces registration cost by using a LA to keep a user’s current location. With a large CMR, the frequency of successive find operations is high. Our strategy still greatly reduces call delivery cost by using bypass pointers to locate mobile users. In our strategy, each location database which serves as a LA must store a user’s information and provide the computing function for adjusting LA dynamically. Besides, each user’s LA will not locate at the same level; thus all users’ profiles are efficiently distributed in the tree structure. We compare the performance of different strategies in the simulation. The results clearly indicate that our strategy has better performance than the basic and caching strategies..

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