A SELECTIVE POINTER FORWARDING STRATEGY FOR LOCATION TRACKING IN PERSONAL COMMUNICATION SYSTEMS

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1 A SELETIVE POINTE FOWADING STATEGY FO LOATION TAKING IN PESONAL OUNIATION SYSTES Seo G. hag ad hae Y. Lee Departmet of Idustrial Egieerig, KAIST 373-, Kusug-Dog, Taejo, Korea, ABSTAT Locatio maagemet is importat to effectively keep track of mobile termials with reduced sigal flows ad database queries. A system with sigle home locatio register ad poiter forwardig is assumed. A mobile termial is assumed to have memory to store the IDs of visitor locatio registers (VLs) each of which has the forwardig poiter to idetify its curret locatio. To obtai the registratio poit which miimizes the database access ad sigalig cost from the curret time to the time of power-off probabilistic dyamic programmig formulatio is preseted. A Selective Poiter Forwardig scheme is proposed which is based o oe-step dyamic programmig. The proposed locatio update scheme determies the least cost temporary VL which poit forwards the latest locatio of the mobile. The computatioal results show that the proposed scheme outperforms IS-4, pure Poiter Forwardig, ad Oe-step Poiter Forwardig at the expese of small storage ad a few computatios at the mobile termials. KEYWODS Locatio aagemet, IS-4, Poiter Forwardig, Dyamic Programmig. Itroductio The persoal commuicatio service (PS) is a system that aims to allow for commuicatio aywhere i the world. I a PS system, the locatio of a called mobile termial (T) must be determied before the coectio ca be established. Locatio trackig operatio i a PS etwork is expesive because may sigal flows ad database queries are eeded to achieve the task. Therefore, a locatio maagemet scheme

2 is ecessary to effectively keep track of the Ts ad to locate a called T whe a call is iitiated. ay locatio maagemet strategies use two classes of databases of user locatio iformatio: the home locatio register (HL), ad the visitor locatio register (VL). Uder two commoly used stadards of IS- 4 ad GS, the HL is required to store the locatio of a T. I additio to the strategy i IS-4 ad GS, several methods have bee proposed to improve the efficiecy of locatio maagemet strategy [4], [5]. They ca be classified ito two categories: Dyamic ad static locatio maagemet strategies. Three methods are prevalet as the dyamic locatio maagemet; time-based, movemet-based, ad distacebased methods. It is geerally demostrated that the dyamic locatio maagemet schemes produce better results tha the static locatio maagemet schemes. However, the dyamic locatio maagemet schemes caot be easily implemeted i the ear future because of the complexity of the procedures. Therefore, we cosider the static locatio maagemet schemes i this paper. The static schemes iclude Poiter Forwardig (), hierarchical HL, ad distributed HL schemes, i additio to the strategy i IS-4. strategy has bee proposed to avoid the expesive HL access each time a T moves to a ew A. The schemes proposed i [6] ad [7] are based o the observatio that it is possible to avoid the registratios at the HL by simply settig up a forwardig poiter from the previous VL. A call to a user will first query the user s HL to determie the first VL where the user was registered ad the follow a chai of forwardig poiters to the user s curret VL. However, the legth of a forwardig poiter chai may be legtheed i the traditioal poiter forwardig strategy. I [2], Oe-step Poiter Forwardig (O) with distributed HLs was proposed to overcome this potetial problem. The legth of ay forwardig poiter chai does ot exceed oe i the strategy. The idea of O ca be easily applied to the sigle HL case. Here, by assumig sigle HL for each subscriber we provide a more efficiet strategy which reduces locatio maagemet costs compared to the IS-4,, ad O with sigle HL. I the proposed scheme, a T stores the IDs of VLs which have iformatio about its locatio. Whe a T moves from oe A to aother, the T itself selectively determies how to make registratio operatio. While other schemes make registratio operatio idepedetly of call-to-mobility ratio, proposed scheme takes the call-to-mobility ratio ito accout to make optimal decisio. The proposed scheme decreases database access ad sigalig cost efficietly at the expese of a small storage ad a few umber of computatios at T. 2. A Selective Poiter Forwardig Scheme I this sectio, we first propose that a optimal locatio update ca be solved by dyamic programmig, which miimizes the registratio ad call delivery cost startig from the curret locatio update to the time of power-off. However, the computatioal burde to solve the dyamic programmig is ot appropriate to implemet i the real situatio. Thus, a predictio algorithm by oe-step dyamic programmig is proposed. The proposed Selective Poiter Forwardig (S) scheme selectively decides the registratio poit amog VLs the T has registered. learly, S is a advaced strategy compared to other schemes which make registratio to the poit previously determied. For example, registratio is always made to HL i IS-4 ad to the old VL i.

3 A. A Optimal Locatio Update by Dyamic Programmig For a optimal locatio update by dyamic programmig, we itroduce a temporary locatio register (TL) of the T. A TL is a VL which stores a forwardig poiter for a specific T. Suppose that a T has K TLs. If K = 0, the HL records the curret VL. Otherwise, The HL records the first TL. The kth TL ( k < K) has a poiter which poits to the (k+)th TL. The forwardig poiter of Kth TL poits the curret VL. Whe a T moves from oe A to aother, the TL is determied which is to be iformed of the mobile s ew locatio i the proposed scheme. It selects oe of the followig three cases to miimize the locatio maagemet costs. ase : Iform the HL of the mobile s ew locatio. ase 2: Iform the old VL of the mobile s ew locatio. ase 3: Iform the TL k of the mobile s ew A. I ase 3, the poiter of kth TL is set to poit the curret VL. Icludig ase ad 2, K+2 cases eed to be compared ad the oe which miimizes the expected registratio ad call delivery costs for the future N itervals is selected. Here we assume a T makes N locatio updates util the power-off ad a iterval deotes time betwee two cosecutive locatio updates. If ase is selected as the miimum, the the registratio strategy correspods to the IS-4. If ase 2 is selected, it correspods to the method. Wheever a locatio update occurs the best oe amog the K+2 cases is selected i the proposed scheme. To geeralize the otatio, let TL 0 ad TL K+ deote the HL ad the old VL, respectively. The the scheme is to determie the TL to which the ew VL seds the locatio iformatio of the T. For the optimizatio of the expected cost for the N cosecutive itervals, we itroduce the cocept of probabilistic dyamic programmig. Assume that ( TL,..., TL K ) is the set of TLs recorded at the T at the begiig of th ( N) locatio update. The the set of cadidate registratio poits r at that time becomes ( TL 0,..., TL K, TL K + ), where TL 0 ad TL K + deote the HL ad the old VL, respectively. Now, the iput variables at the time of th locatio update are represeted by ( r, v ), where r ad v deote the set of cadidate registratio poits ad the ew VL at that time, respectively. Let the decisio variables k ( N ) be the decisio of registratio poit which is oe of the set r. Let f (r, v ) be the miimum expected cost from th locatio update to the time of power-off. Note i the f (r, v ) that r is determied by the previous decisio ad the ew VL v is probabilistically distributed which depeds o the move directio. Thus, probabilistic dyamic programmig eeds to be solved to obtai the optimal decisio. Now, our goal is to obtai f ( r, v ) which miimizes the expected cost for the N time itervals. The optimal registratio poits k, k2, L, k N ca be obtaied by solvig a set of recursive equatios give i () ad (2). I the equatios, two cost fuctios,, v ) ad, v ) are used., v ) deotes registratio cost from the ew VL v to the registratio poit k. Ad, v ) deotes call delivery cost traversig TL 0, TL,..., TL k, ad the ew VL v whe registratio is made to TL k. Especially, HL, v ) is the call delivery cost of the succeedig calls, where HL already ( has the iformatio about the curret locatio of the T from the delivery of the first call. I additio, two radom variables, N ad V +, are icluded i the equatios. N is the umber of call arrivals for a

4 iterval ad is assumed to be idetically ad idepedetly distributed. V + is the VL of the A ito which the T is to move at the ed of th iterval, ad is depedet o T. It is assumed that the system is composed of As. v ad the mobility patter of the ad f (r, v ) = mi [, v ) + P( N = 0) k r P( V v f r, ) + = ) + ( + v + P ( N = i) {, v ) + ( i ) ( HL, v ) + P( V + = v) f + ( r+, v) }], i= for =, L, N, () f N (rn, vn ) = mi rn k N [ N, vn ) + P ( N = i) { N, vn ) + ( i ) ( HL, vn ) }]. (2) i= The total cost at the time of th locatio update is the sum of registratio ad call delivery cost for the iterval ad expected costs f + ( r+, v) for the ext N cosecutive itervals to follow. Obviously, whe N = 0, call delivery cost for the iterval is zero. I geeral,, v ) is the highest whe registratio is made to TL 0 or HL, ad the lowest whe registratio is made to TL K + or old VL. Whe N = 0, sice the set of TLs recorded at the T at the ed of the iterval is TL,...,TL ) ( k, r + becomes ( TL 0,...,TL k, v) if V + is v. Whe N > 0, ote that the call delivery costs for the first call i the iterval ad the followig calls are differet. This is because whe a call arrival occurs, the curret VL returs a TLDN to HL ad the followig calls are delivered directly from HL to the curret VL. oreover, if a call arrival occurs, the set of TLs recorded at the T is updated to (TL 0 ) to keep valid iformatio about the modified situatio. Therefore, whe N > 0, r + becomes ( TL 0, v ) if V + is v. From the above formulatio it is clear that the optimal strategy at a particular locatio depeds o the probability distributio of the future trajectory of a T. However, the probability distributio of the mobility patter of a T may ot be well predicted. I additio, the computatioal burde to solve the dyamic programmig grows explosively with the umber of locatio updates. I the followig subsectio, we propose a selective poiter forwardig scheme that is based o the dyamic programmig discussed i this subsectio. B. Selective Poiter Forwardig At the time of iitial locatio update we have K +2 cadidate TLs for locatio registratio poit. Amog them, optimal registratio poit k is determied based o the expected cost. The cost fuctio is give by the followig equatio. f ( r, v ) = mi [, v ) + P( N = 0) P( V2 = v) f 2 ( r 2, v) k r + P ( N = i) {, v) + ( i ) ( HL, v ) + P( V2 = v) f 2 ( r 2, v) }]. (3) = i I the above equatio whe N > 0, sice the record of HL ad the set of TLs recorded at the T are

5 updated after the first call delivery, the succeedig call delivery cost ad cadidate registratio poit for the very ext iterval are idepedet of the decisio of the curret iterval. Also, to approximate the above objective fuctio let us assume that the set of cadidate registratio poits r 2 is idetical uder ay decisio k. The, the three items P( N = 0) P( V = v f r, ), ( i ) HL, v ), ad 2 ) 2 ( 2 v ( P( N > 0) P( V = v f r, ) are idetical uder ay iitial decisio. Thus, the followig 2 ) 2 ( 2 v approximatio results. I the equatio, the subscript deotig the iterval is omitted. f (r, v) = mi [, v) + P ( N > 0), v) ]. (4) k r 3. Performace Aalysis This sectio examies the performace of S ad compares it with IS-4,, ad O. Let call-tomobility ratio () be λ / µ, where λ is the call-arrival rate, ad µ is the locatio update rate from curret A. We assume that call-arrivals follow poisso distributio ad the residece times of a T have expoetial distributio. We also assume that the two distributios are idepedet of each other. I additio, estimates of etwork cost are made as follows to simplify the compariso. ) The database access cost of the HL is ormalized to. 2) The database access cost of the VL is α. Sice HL is a sigalig bottleeck, α is expected. 3) The sigalig cost is β distace. The assumptio that sigalig cost is proportioal to the distace is reasoable. Ad β represets sigalig cost of a uit distace (Euclidea distace betwee ceters of two adjacet As) give that the database access cost of the HL is ormalized to. A. The Aalytical odel Sice the call delivery cost from the call origiator to the HL ad radio lik cost betwee the curret VL ad the T are the same i three schemes to compare they ca be excluded i this aalytical model. We thus cosider the call delivery cost from the HL to the curret VL ad the registratio cost from the curret VL. Let d (A - B) deote the Euclidea distace from A to B ad c deote the umber of callarrivals durig the iterval. a. IS-4 Durig the registratio operatio, oe access to HL occurs. egistratio ad call delivery costs i IS-4 are respectively IS 4 = + β d ( VL ew - HL), IS 4 ad = β d (HL - VL ew ), where, VL ew deotes the ew VL. Therefore, the total cost betwee two cosecutive registratios becomes (5)

6 b. Poiter Forwardig IS 4 = IS 4 IS 4 + c. (6) Assume that the legth of forwardig poiter chai is P ad the chai cosists of VL, VL 2,, VL P after registratio operatio. VL P deotes the VL of the old A from which the T departs. The the registratio cost is = α + β d ( VL ew - VL P ). (7) The first call delivery cost i is F = α P + β d (HL VL ) + β d (VL - VL 2 ) + + (8) + β d (VL P - VL ew ). After the first call arrives, the HL updates its poiter to the curret VL. Thus the call delivery cost of the succeedig calls is S = β d (HL - VL ew ). (9) Therefore, the total cost betwee two cosecutive registratios becomes =, if c = 0 (0) = + F + (c ) S, if c. c. Oe-step Poiter Forwardig The legth of forwardig poiter chai is always oe i the O. Let VL pre deote the Previous VL. The the registratio cost is O = α + β d ( VL ew - VL pre ). () The first call delivery cost i O is O F = α + β d (HL VL O ) + β d (VL pre - VL ew ). (2) After the first call arrival, the HL updates its poiter to the curret VL. Thus the call delivery cost of the succeedig calls is O S = β d (HL - VL ew ). (3) Therefore, the total cost betwee two cosecutive registratios becomes O = O, if c = 0 (4) O O O = + F + (c ) S, if c. d. Selective Poiter Forwardig This sectio cosists of two parts. The first part is to determie the TL k satisfyig Equatio (4), which is iformed of the latest locatio update. The secod part is to obtai the registratio ad call delivery cost i the iterval whe registratio is made to the TL k i the proposed scheme. First to determie the registratio poit Equatio (4) is solved. To compute P[N > 0] i Equatio (4), let X ad Y respectively deote the first occurrece time of call-arrival ad locatio update from the begiig of each iterval. The, X ad Y are both expoetially distributed radom variables with respective meas / λ ad / µ. Thus, we have P[N>0] = P[X<Y] = µy P[ X < Y Y = y] µ e dy y λx µy e dx µ e 0 0 = λ dy = 0 λ = λ + µ +. (5) Assume that the legth of forwardig poiter chai is K ad the chai cosists of TL, TL 2,, TL K before registratio operatio. If TL k is iformed of the ew VL, the the registratio cost i

7 β Fig.. egistratio cost per locatio update whe ( α, ) = (0.5, 0.5). Fig. 2. all delivery cost per call arrival whe ( α, ) = (0.5, 0.5). β Equatio (4) becomes, VL ew ) = α + β d ( VL ew - TL k ). (6) The cost of first call delivery at the ew A is, VL ew ) = α k + β d (HL - TL ) (7) + β d (TL - TL 2 ) + + β d ( TL k -TL k ) + β d ( TL k - VL ew ). From Equatios (5), (6), ad (7) the expected cost of (4) is computed. Let TL k deote the TL determied i Equatio (4). Give that the registratio poit is determied, we calculate the cost of S for the iterval to compare it with IS-4,, ad O. Whe registratio is made to the TL k, the cost of registratio ad first call delivery is calculated i the same way as above. That is, S =, VL ew ) ad F S =, VL ew ). (8) After the first call arrives, the HL updates its poiter to the curret VL. Thus the call delivery cost of the succeedig calls is S S = β d (HL - VL ew ). (9) Therefore, the total cost betwee two cosecutive registratios becomes S = S, if c = 0 (20) S S S = + F + (c ) S, if c. I the ext sectio, we compare the S with IS-4,, ad O strategy. B. Simulatio esults I the experimet te thousad cosecutive locatio updates are performed for each value of differet ragig from zero to three. The area is divided ito 25 As. The average registratio cost per locatio update ad call delivery cost per call arrival of IS-4,, O, ad S are compared as i Fig As was expected, the highest registratio ad lowest call delivery costs are obtaied by the IS-4. The scheme shows the opposite result. Note that IS-4 ad show costat registratio cost uder ay because the umber of call arrivals is ot cosidered i the two methods. Sice the registratio poit i the O is depedet o the umber of call arrivals durig the previous iterval, registratio cost varies with the eve though O does ot take ito accout the. The registratio cost of O is much higher tha that of the uder relatively low. This is because whe is low, the O behaves like the IS-4. A tradeoff betwee registratio ad call delivery is achieved by the proposed S. The total cost durig a

8 iterval is obtaied by summig the total call delivery cost ad the registratio cost. We defie the relative cost as the ratio of the total cost durig te thousad iterval of each scheme to that of the proposed scheme. Fig. 3 compares the relative costs of IS-4,, O, ad S. The proposed S outperforms three other schemes. The HL access cost is Fig. 3. elative registratio ad call delivery cost whe ( α, β ) = (0.5, 0.5). ormalized to oe. Aother tedecy worth otig i the figures is that the cost differeces by the four strategies become smaller as the icreases. This is maily due to the fact that call delivery costs are idetical i the four schemes after the first call arrival. EFEENES. Sue, K.-L. ad Tseg,.-. (997). Oe-step poiter forwardig strategy for locatio trackig i distributed HL eviromet. IEEE J. Select. Areas ommu., 5, Li, Y.-B. ad Tsai, W.-N. (998). Locatio trackig with distributed HL s ad poiter forwardig. IEEE Tras. Veh. Techol., 47, Li, Y.-B. (997). educig locatio update cost i a PS etwork. IEEE/A Tras. Network. 5, Akyildiz, I. F., Ho, J. S.., ad Li, Y.-B. (996). ovemet-based locatio update ad selective pagig for PS etworks. IEEE/A Tras. Network., 4, Abutaleb, A. ad Li, V. O. K. (997). Locatio update optimizatio i persoal commuicatio systems. A-J Wireless Networks, Jai,., Li, Y.-B., Lo,.N., ad oha, S. (994). A cachig strategy to reduce etwork impacts of PS. IEEE J. Select. Areas. ommu., 2, Jai,. ad Li, Y.-B. (995). A auxiliary user locatio strategy employig forwardig poiters to reduce etwork impacts of PS. A-J Wireless Networks, 97-20