A Frequency-Based Find Algorithm in Mobile Wireless Computing Systems

Transcription

1 A Frequency-Based Find Algrithm in Mbile Wireless Cmputing Systems Seung-yun Kim and Waleed W Smari Department f Electrical Cmputer Engineering University f Daytn 300 Cllege Park Daytn, OH USA Abstract The rapid grwth in mbile and wireless cmputing technlgy cntinues t present new challenges Mbile users access infrmatin and services independent f their lcatin thrugh wireless and wired netwrks In a mbile cmputing envirnment, a lcatin management strategy is emplyed whenever users mve frm ne place t anther In rder t track a mbile user (als referred t as a Mbile Hst, MH), the system must stre infrmatin abut the hst s current lcatin and reprt its new lcatins t a hme base statin (referred t as a Mbile Base Statin, ) Several techniques have been prpsed in rder t manage ptimally the lcatin f mbile hsts In this paper, we intrduce the Frequency-Based Find Algrithm (FBFind) with lcal strages The basic bjective behind using the FBFind is t reduce the Signaling System N 7 (SS7) message traffic [10] and the database access traffic by maintaining a lcal strage, which is referred t as the Lcatin Infrmatin Library (LIL) We evaluate this algrithm and identify its ptimal cnditins as well as limitatins Lastly, we cmpare the algrithm with the caching algrithm prpsed by Jain et al [6] Keywrds: Frequency-based Find algrithm; Lcatin management; Mbile/wireless netwrk; Caching algrithm 1 Intrductin Mbile and wireless cmputing technlgy cntinue t witness steep grwth As many f its prblems are slved, new issues arise and sme existing nes persist One such challenge is the efficient and ptimal management f mbile units in such a system There are many ways f managing the users lcatin prblem We divide these int tw main basic techniques; lk up techniques, which fcus n reducing the cst f lking up a user and adjust the update prcess accrdingly, and update techniques, which fcus n reducing the cst f updating In a mbile and wireless cmputing envirnment, mbile hsts may relcate frm ne cell t anther In rder t keep track f mbile hsts, the system must recrd r knw the infrmatin abut mbile hsts current lcatin Elnahas and Adley [3] prpsed a scheme t define when an update and lkup ccur in a system Specifically, an update ccurs when a mbile hst sends a message t update its stred lcatin A lkup ccurs when it is required t lcate a user each time a call is placed t that user r a message is sent t him The lcatin updates and lkups are evaluated in terms f the number f messages sent, the size f messages, the distance the message needs t travel, the bandwidth cnsumed, the prcessing verhead and the delay incurred in answering lcatins queries A gd lcatin management scheme shuld attempt t ptimize these parameters while achieving the seamless mbility Seamless mbility [1] requires that when cnnectins are brken r established, the prcess f switching between cells shuld be dne transparently Pierre [12] discusses the mbility issue as ne f three majr challenges in mbile wireless cmputing envirnments Tracking mbile hsts and having efficient ruting are tw basic functins f a mbile cmputing system The system needs t be updated and prvided infrmatin abut the mbile hsts lcatin Usually, a lcatin area structure has several cells in it, and a mbile cmputing envirnment structure cnsists f several lcatin areas which may verlap, as shwn in Figure 1 In rder t reduce the lk up and update csts, there have been many prpsed techniques The mdified grup methd [15] yields sme imprvements ver the cnventinal methds in reducing csts Mrever, it ffers enhancements in the utilizatin f netwrk resurces fr mbile hsts that mve frequently Traditinally, an update ccurs when a mbile hst mves frm ne cell t anther Hwever, Weng s algrithm wuld require an update nly when a MH mves Lcatin Area Cell Lcatin Area Lcatin Area Lcatin Area Figure 1 A Mbile Cmputing Envirnment Structure While the abve attempts have cntributed t reducing the update csts, they d nt address detailed csts and ther updating issues The intent f this paper is t discuss the details f all cst functins and t present an

2 algrithm which reduces the csts fr lcating a Mbile Hst in mbile and wireless netwrk envirnments by using lcal strage This paper is rganized as fllws In Sectin 2, we intrduce sme basic infrmatin n wireless netwrk architectures and a mdel t help understand the new algrithm Sectin 3 presents the FBFind algrithm with all calculatins and relatinships amng mdel parameters We evaluate the prpsed algrithm in Sectin 4 In Sectin 5, we cmpare the prpsed algrithm with anther lcatin management algrithm, namely, the caching algrithm and run sme experiments Finally, Sectin 6 includes sme final thughts and cncludes the paper 2 System Descriptin and Mdel Mst mbile wireless netwrks use a cellular architecture t achieve bandwidth efficiency [14] Over the past decade, several architectural mdels f mbile and wireless cmputing systems have been prpsed [5, 9]We use the mdel depicted in Figure 2 A general mbile cmputing system cnsists f mbile hsts (MHs) that interact with a static netwrk thrugh fixed hsts, knwn as mbile base statins (s) A mbile hst cmmunicates with ne mbile base statin at any given time is respnsible fr frwarding data between the mbile hst and the static netwrk As a result f mbility, a mbile hst may crss the bundary between tw cells while being active Thus, the task f frwarding data between the static netwrk and the mbile hst must be transferred t the new cell s mbile base statin [8] T assist in this prcess, s are augmented with a wireless interface, and functin as a gateway fr cmmunicatin between the wireless netwrk and the static netwrk The cnnectin between an MH and an is accmplished via wireless cmmunicatin, while the is wired t the fixed netwrk A mbile hst can cmmunicate with a mbile base statin within a limited regin arund it This regin is referred t as a mbile base statin s cell, as shwn in Figure 2 Cells can have different sizes The average size f a cell is abut 1 t 2 miles in diameter A mbile user within a cell receives calls via wireless access Each cell is primarily served by ne, and the serves ne cell In general, calls may deliver vice, data, text, r vide infrmatin The lcatin f a user is assciated with the registratin area (RA) in which the user is lcated The base statin lcates a user and delivers calls t and frm that user It is als cnnected t a Lcal Signaling Transfer Pint () via wired link Each has tw s since we are cnsidering binary tree architecture frm the level t the s Likewise, a pair f s are cnnected t a Reginal Signaling Transfer Pint () Hwever, several s may be cnnected tgether t a Public Switched Telephne Netwrk (PSTN), which acts as a rt f this hierarchical mdel Clearly, the system is mdeled using a hierarchical lcatin management methd [13] The cmplete system is illustrated in Figure 2 cell R C Figure 2 A Mbile Cmputing System Architecture 21 Mdel Parameters PSTN R B R B R B R B P P P L In the mdel laid ut abve, we define six different parameters Table 1 summarizes the definitin f these parameters Table 1 Parameter Descriptins : Cst f transmitting a lcatin request r respnse message between links and R B : Cst f transmitting a lcatin request r respnse message between links and R C : Cst f transmitting a lcatin request r respnse message between links and PSTN P L : Cst f ruting prcesses fr lcatin request message by P R : Cst f ruting prcesses fr lcatin request message by P P : Cst f ruting prcesses fr lcatin request message by PSTN We knw, R B, R C, P P, P R and P L are cst functins, and they are prprtinal t distance S, let us assume, R B, R C, P P, P R and P L are physical distances between parameters Fr simplicity, let us als assume that the distances between and, and between and are the same, ie, = R B = R, and P R = P L = P because we have binary tree up t This means that the cst f transmitting a lcatin request r respnse message between links, and the cst f ruting prcesses fr lcatin request message are the same up t the level With these assumptins, let us redraw Figure 2 as shwn in Figure 3(a) In this figure, we represent the tp view f the system architecture mdel If we say the distance between and, and and are the same, then we can have the diagram shwn in Figure 3(b) t find the relatinship between and PSTN R C P R

3 PSTN PSTN (a) (b) Figure 3 Distances between and, and, and and PSTN The triangle illustrates the relatinships between the s and a PSTN and an If we let the distances between an and an, and an and an equals t 1 unit, als fr simplicity, then the distance frm an RSTN t an RSTN will always be 4 units Nw, let us cnsider the angles The angle α can be expressed as α =, where t is the ttal number f t s The angle β can be fund frm the triangle since α + β + β = 180 = + 2β Slving fr β, we t get β = 90 2t T find the distance d between an RSTN and a PSTN, sin( ) sin(90 ) we emply the sine law: t = 2t 4 d 180 4cs( ) Slving fr d, we btain d = t sin( ) t If we have t s, we may express the cst parameters R c and P p as fllws R C = [4cs (180 /t) / sin ( /t)]r = d R (1) P P = [4cs (180 /t) / sin ( /t)]p = d P (2) where R is the cst f transmitting a lcatin request r respnse message between links, frm t r frm t, and P is the cst f ruting prcesses fr lcatin request message by r r PSTN, as was assumed befre Hence, all parameters are nw defined 22 User Characterizatin Using Lcal Call-t- Mbility Rati (LCMR) Classes f users are characterized by their call-tmbility rati (CMR) [7] The call-t-mbility rati f a user is the average number f calls t a user per unit time, divided by the average number f times the user changes registratin areas per unit time We als define a lcal CMR (LCMR), which is the average number f calls t a user frm a given riginating signal transfer pint per unit time The LCMR can be used t relate the hit rati t α d d β β 4 users calling and mbility patterns directly T d s, we need t make sme assumptins abut the distributins f the user s calls and mves Let the call arrivals frm an t a user be a Pissn prcess with arrival rate λ, and the time that the user resides in an RA be 1/µ Then, LCMR can be expressed as: LCMR = λ / µ Since we are dealing with nn-negative randm variables, it is cnvenient t assciate with a prbability density functin, f(s), its Laplace transfrm, f * (s) Let the residual time f a user at a registratin area be a randm variable with a general density functin f m Then, its * Laplace transfrm is given by st f m(s) = f t= 0 m(t)e dt Let t be the time interval between tw cnsecutive calls frm the t the user, and t 1 be the time interval between the first call and the time when the user mves t a new RA Frm the randm bserver prperty f the arrival call stream [4], if call arrivals are Pissn distributed and F(t) is an expnential distributin, the hit rati f a user calling can be given by p = λe -λt t= 0 =t f t dt dt t ( 1 ) 1, 1 where in expnentially distributed with parameter µ That µt is, 1 µx f(t1 ) = µe, and F(x) = 1 e,x 0 Frm these relatinships, we can express the hit rati as fllws [7] p = λe -λt t= 0 µt t = µe 1dt t 1dt = λ/(λ+µ) (3) 1 Nte that fr different values f LCMR, there will be different values f hit rati 3 The FBFind Algrithm Next, we prpse a mdified algrithm that is based n the Per-User Lcatin Caching algrithm f Jain et al [6] In ur algrithm, we specify all the previusly intrduced parameters and add sme mre t accunt fr further details The basic idea behind using FBFind algrithm is t reduce the SS7 message traffic and database access traffic by maintaining a lcal strage[10] The lcal strage is called Lcatin Infrmatin Library (LIL), and each maintains a LIL A LIL is a table lkup that maintains entries f recently visited lcatins infrmatin The FBFind methd uses LIL entries that are stred in the t determine the lcatin f a user Each LIL has at least n number f entry lists, which are frequency based infrmatin f MHs in the When a call is made t an MH, the algrithm checks whether the called is in the same RA r nt If the called is in the same RA, there is n need t perfrm any update since the respective already has knwledge f bth the callee and the caller When the callee and the caller are nt in the same RA, the algrithm is called int actin t take the fllwing steps 1 When an MH is called and it is nt in the same RA, and there is an entry fr this MH in the LIL, then the FBFind Algrithm must be emplyed G t Step 3 in this case

4 2 If there is n LIL entry fr that MH, then g t Step 6 where the Basic Find algrithm is executed 3 Select the LIL entry, V L, with the highest request frequency in the list The current MSB f the caller queries the lcatin f the called V L 4 If the caller MSB gets the ruting infrmatin f the called frm V L, FBFind results in a hit, and the cnnectin between the caller and called is established 5 If the caller MSB des nt get the ruting infrmatin frm V L, FBFind results in a miss 6 Otherwise, the Basic Find Algrithm[6] is emplyed t find the called MH As was stated befre, each has a strage, referred t as Lcatin Infrmatin Library (LIL) A LIL stres the mbility patterns infrmatin f the MHs which visit that This infrmatin is retrieved during a call delivery In a distributed infrmatin library architecture with multiple LILs, it is beneficial t avid unnecessary perfrmance bttlenecks because we d nt need t g t the HLR f the caller and get the infrmatin abut it As illustrated in Figure 4, the hme lcatin register (HLR) f MH A is A and the HLR f MH B is B and s n Likewise, LIL A has the lcatin and ruting infrmatin f MH A, LIL B has thse infrmatin f MH B, LIL C has thse infrmatin f MH C, and s n Clearly, LIL A and LIL B shuld nt be in 1 because A and B are under 1, and they have the infrmatin n bth MH A and MH B respectively A t t-1 Wired Netwrk 1 LIL C 2 LIL D C D B cell LIL N 3 LIL A LIL B LIL E Figure 4 System Mdel 4 Evaluatin f the FBFind Algrithm We evaluate the FBFind algrithm intrduced in the previus sectin in terms f fur parameters that will identify varius cst functins assciated with the algrithm implementatin We can relate the fur parameters t the algrithms tw parts: Basic Find algrithm which is assciated with the cst f the Basic Find (C B ), and FBFind algrithm which is assciated with three csts: FBFind with miss (C M ), FBFind with hit (C H ) and FBFind ttal cst (C F ) Figure 5 depicts the steps and relatinships between these fur parameters LIL N E F LIL C LIL B LIL D LIL N Basic Find Algrithm Cst f the Basic Find C B Ttal Frequency Based Find Algrithm Ttal Cst Of FBFind C F =(1-p) C M + pc H FBFind Algrithm Cst f FBFind With Miss: C M = C H + C B Cst f FBFind With Hit: Figure 5 The Fur Cst Parameters Assciated with FBFind and The Relatinships 41 Cst f the Basic Find Algrithm, C B We recall that the Basic Find algrithm is based n the IS-41 Basic HLR/VLR Scheme [2, 11] Als Basic Find algrithm is intrduced by Jain et al [6] In here, we extended and detailed their algrithm ne step further As such, the HLR maintains lcatin infrmatin fr the user When a user travels t a new RA, his HLR is updated and an entry in the VLR is made When a call is placed t lcate this user, the caller s first checks the lcal VLR fr the callee s prfile The steps and the pseudcde t find the cst f Basic Find (C B ) are as fllws 1 The call t the MH j is directed t 2 Assuming that the callee is nt lcated within the same RA, the 2 queries the HLR f MH j, 7, fr ruting infrmatin 2 The HLR f MH j, 7, cntains a pinter t the VLR, 15 in whse assciated RA the caller party is currently situated 3 The VLR in turn queries the f MH i t check if the callee is available 4 The 7 returns a rutable address t the VLR f MH j, 2, if callee is available 5 The VLR shuld send rutable address t the HLR f MH i 6 The HLR f MH i frwards the address t the f the caller Steps and the system mdel used is shwn in Figure 6 In this figure, we use the SS7 mdel [10] t shw hw t find the cst f the Basic Find algrithm [6] The signaling netwrk cst incurred in lcating a user in the event f a call is the sum f the cst f querying the HLR and the cst f querying the VLR Let Q H be the cst f a query t the HLR t btain the current VLR lcatin; Q V be the cst f a query t the VLR t btain the ruting address; Q A be the cst f a query t the HLR and receiving a respnse, and Q B be the cst f querying the pinted t VLR and receiving a respnse The calculatin f the Basic Find csts f the wrst case is as fllws C H

5 C B = Q A +Q B = 2( + R B + R C + P P + R C + P R + R B + P L + ) + Q H + 2( + R B + R C + P P + R C + P R + R B + P L + ) + Q V Under the assumptins that = R B = R, and P R = P L = P, the expressin abve can be written as, C B = 16R + 8R C + 4P P + 8P + Q H + Q V (4) 42 Cst f the Ttal FBFind Algrithm, C F The cst f the ttal Frequency-Based Find algrithm (C F ) can be defined as the sum f the cst f the FBFind with hit (C H ) times hit rati (p) and the cst f the FBFind 1 2 PSTN R C R C R P C p Figure 6 Basic Find Algrithm Steps: Callee MH j is calling a caller MH i with miss (C M ) times the miss rati (1 p) We define the hit rati as the relative frequency f getting the crrect user s lcatin when it is cnsulted in the LIL entries In Sectin 23, we defined the hit rati as p = λ/(λ+µ), while LCMR = λ/µ Then we have, C F = pc H + (1-p)C M (5) Let us define the Cst f the FBFind with Hit Let Q L and Q R be the cst f querying (query and respnse) a lcal and a remte respectively; and q be the prbability f getting the MH s infrmatin n a lcal s LIL Als, as befre we define Q H as the cst f a query t the HLR t btain the current VLR lcatin, and Q V as the cst f a query t the VLR t btain the ruting address Then, C H = q(q L + Q V )+ (1 q)(q R + Q V ), where, Q L = 2 =2R since it is necessary t g the and cme back, and Q R =2(R B + R C + P P + R C + P R + R B + P L + ) = 6R + 4R C + 2P P + 4P Substituting these values, we btain: C H = 6R + 4R C + 2P P + 4P + Q V q(4r + 4R C + 2P P + 4P)(6) The cst f the FBFind with miss (C M ) algrithm can be determined by adding the cst f the FBFind with hit plus the cst f the Basic Find algrithm because miss ccurs there is n entry fr that specific MH after all LIL entries are checked P R P R P R R B R B R B R B R B R B R B P L P L P L cell MH j! $ 7 15 HLR j # " MH i C M = C H + C B (7) Finally, we substitute C H, and C M int equatin (5), then: C F = pc H + C M pc M = C H + C B pc B (8) C F = 22R + 12R C + 6P P + 12P + 2Q V + Q H q(4r+ 4R C + 2P P + 4P) p[16r + 8R C + 4P P + 8P + Q H + Q V ] (9) 43 Evaluatin f the Ttal FBFind Algrithm Let us simplify little mre fr each f cst equatin We have tw equatins (1) and (2), R C = dr and P P = dp respectively We can assume that t, the ttal number f, be any numbers Let t be 6 s that we can have integer value f d, this case d equals t 4 Then we have R C = 4R and P P = 4P Nw we substitute these results int equatin (4), the cst f the Basic Find Algrithm, and equatin (9), the cst f the ttal FBFind algrithm then we have fllwing tw new equatins C B = 48R + 24P + Q H + Q V (10) C F = R(70 20q 48p) + P(36 12q 24p) + Q V (2 p)+ Q H (1 p) (11) Nte that in equatin (11), Q V and Q H depend nly n the value f LCMR If we have lwer LCMR value, that will crrespnd t higher Q V, and Q H Nw, let s take a lk at the hit rati, p We have the equatin fr hit rati in Sectin 23, and they are: p = λ/(λ+µ), and LCMR =λ/µ S λ = µlcmr then, µlcmr LCMR p = = (12) µlcmr + µ LCMR + 1 Frm this equatin, we can have the relatinship between LCMR and ther parameters We substitute equatin (12) int equatin (11), and rearrange the result equatin as the simple frm: C F = ar + bp + c, where a = 70 20q 48p, b = 36 12q 24p, c = Q V (2 p)+ Q H (1 p) (13) We can have different values f lcal call-t-mbility rati, LCMR, and q, the prbability f getting the MH s infrmatin n the lcal s LIL Table 2 shws the results f different values f LCMR and q With these results, we can say few things abut ur algrithm When we have the same LCMR, we have lwer cst with higher q When we have the same q, we have lwer cst f FBFind with higher LCMR Table 2 Cefficients f C F when d = 4 LCMR p q a b c Q V + 05 Q H Q V + 02 Q H Q V + 01 Q H Q V + 05 Q H Q V + 02 Q H Q V + 01 Q H Q V + 05 Q H Q V + 02 Q H Q V + 01 Q H

6 5 FBFind and Caching Algrithms: A Cmparative Study In this sectin, we cmpare tw algrithms: ur FBFind Algrithm and Jain s Caching Algrithm [6] The caching algrithm has scheme fr very similar defining the cst f Basic Find and the ttal cst The main difference between these tw algrithms is the cst fr hitting We use the same assumptins fr the tw algrithms under cmparisn as thse used in FBFind algrithm in previus sectins The assumptins are: = R B = R, P R = P L = P, R C = dr, P = dp, Q L = 4R + 2P, and Q R = 4 R + 2dR + dp + 2P, where, d = 4cs(180/t)/sin(/t) = 4 Let s take a lk at these parameters fr the caching algrithm next 51 Calculatins f Parameters in the Caching Algrithm The cst f the Basic Find in caching algrithm is the same as FBFind ne equatin (10), and that is, C B = 48R + 24P + Q H + Q V (14) The cst f the caching algrithm with hit is different frm that fr FBFind with hit since there is n lcal strage fr the caching algrithm In this case, the cst functin can be written as C Hc = q(q Lc + Q V )+ (1 q)(q Rc + Q V ), where, Q Lc = 4 + 2P L and Q Rc =2(R B + R C + P P + R C + P R + R B + P L + ) = 6R + 4R C + 2P P + 4P Substituting these values in the C Hc equatin abve, we btain C Hc = 22R + 12P + Q V q(18r + 10P) (15) Then the ttal cst f caching algrithm C C is, C C = C Hc + C B pc B Substituting the values f C Hc and C B in equatin (14) and (15), we have C C = R(70 18q 48p) + P(36 10q 24p) + Q V (2 p) + Q H (1 p)(16) This equatin can be rewritten using the same frm as equatin (13) C C = er + fp + g (17) with, e = 70 18q 48p, f = 36 10q 24p, and g = Q V (2 p)+ Q H (1 p) As we can see in equatin (17), the value f g fr bth FBFind and cache algrithms are the same, ie, c = g The cefficients f the C C are summarized in Table 3 fr different values f LCMR, p, and q 52 Algrithms Cmparisns Equatins (11) and (16) were derived fr a fixed value f d since this d affects bth algrithms similarly This means that if we change the value f d fr bth algrithms and cmpare them, we will have the similar result fr bth Hwever, if we cmpare FBFind algrithm with ther algrithms ther than caching, we may nt want t Table 3 Cefficients f C C when d = 4 LCMR p q e f g Q V + 05 Q H Q V + 02 Q H Q V + 01 Q H Q V + 05 Q H Q V + 02 Q H Q V + 01 Q H Q V + 05 Q H Q V + 02 Q H Q V + 01 Q H fix this parameter By examining Tables 2 and 3, we ntice that cefficients f the equatins, ie, a, b, c, e, f, and g, are clsely related t the parameter q, the prbability f getting the MH s infrmatin n lcal s LIL If we have higher q values, we have mre cst saving fr FBFind algrithm under the same LCMR Figure 7 shws the cmparisn between FBFind algrithm and caching algrithm When q equals t 01, the gap between these tw algrithms is 02 But when q is 09, the gap increases t 18 This tells us that the FBFind algrithm wrks better with higher q Nw let s lk at the efficiency fr different values f LCMRs We define the efficiency f cst saving (E) ver the caching algrithm as fllws: (Caching_Cst) (FBFind_Cst) E(%) = 100 (Caching_Cst) Figure 8 shws the efficiency with three different values f LCMRs When LCMR is 1, FBFind has abut 05% better saving at q is 01 But when we have q f 09 the savings jump t 6% better efficiency than caching In the case f LCMR is 10, FBFind has 08% better efficiency at q = 01 but at q = 09, we have abut 18% f better efficiency The verall behavir indicates that the FBFind algrithm wrks best with higher LCMR and higher q Ttal Cst f Algrithm Caching FBFind Prbability f Getting MH's Inf (q) Figure 7 Cst Functins with Respect t Values f q

7 Cst saving (%) Cnclusins Efficiency f FBFind ver Caching LCMR=1 LCMR=5 LCMR= Prbability f getting the MH s infrmatin n lcal s LIL (q) Figure 8 Efficiency Cmparisns T further the research in the area f lcatin and mbility management, the Frequency-Based Find (FBFind) algrithm is intrduced in this paper This algrithm saves sme csts by using lcal strage called Lcatin Infrmatin Library (LIL) The scheme requires each t maintain a LIL A LIL is a table lkup that maintains entries f recently visited lcatin infrmatin, thereby saving n unnecessary ruting and querying csts In additin, the paper intrduces a new mdeling technique which wrks with the FBFind algrithm This technique uses hierarchical binary tree, up t the level, t mdel the system architecture Based n the simulatin results btained, we shw that the perfrmance f FBFind algrithm depends heavily n tw cnditins: lcal call t mbility rati and the prbability f getting the mbile hst s infrmatin n lcal s infrmatin library We bserved that the FBFind algrithm can save n the cst f searching fr infrmatin by 6% t 18% ver different values f LCMR between 1 t 10 We als cmpared the FBFind algrithm with the well knwn Caching algrithm Hwever, if we cmpare FBFind algrithm with ther algrithms than caching, we may nt want t fix this parameter since we cannt guarantee that this parameter will affect bth algrithms in similar way As can be seen frm ur results, if we have lw LCMR and a MH travels many cells within shrt perid f time, the FBFind algrithm will nt give gd results As an extensin f the existing wrk, architectures with different numbers f s, s and s, and tplgies as well as mdels will be studied References [1] Bharghavan, V, Challenges and Slutins t Adaptive Cmputing and Seamless Mbility ver Hetergeneus Wireless Netwrks, Wireless Persnal Cmmunicatins, Vl 4, pp 217 pp 236, 1997 [2] EIA/TIA, Cellular radi-telecmmunicatins Intersystem Operatins, Technical Reprt IS-41 Revisin B, EIA/TIA, 1991 [3] Elnahas, A, and N Adly, Lcatin Management Techniques fr Mbile Systems, Infrmatin Sciences, Vl 130, pp 1 22, 2000 [4] Feller, W, An Intrductin t Prbability Thery and Its Applicatins, Wiley, New Yrk, 1996 [5] Gdman, TJ, Trends in cellular and crdless cmmunicatins, IEEE Cmmunicatins Magazine Vl 29, N 6, pp 31 40, 1991 [6] Jain, R Y B Lin, C L, and S Mhan, A Caching Strategy t Reduce Netwrk Impacts f PCS, IEEE Jurnal n Selected Areas in Cmmunicatins, Vl 12, N 8, pp , 1994 [7] Jain, R, and YB Lin, An Auxiliary User Lcatin Strategy Emplying Frwarding Pinters t Reduce Netwrk Impacts f PCS, Prceedings Internatinal Cnference n Cmmunicatins, pp 1 26, 1995 [8] Krisha, P, N H Vaidya, and D K Pradhan, Static and Adaptive lcatin Management in mbile Wireless Netwrks, Cmputer Cmmunicatins, Vl 19, pp , 1996 [9] La Prta, T F, M Veeraraghavan, P A Treventi, and R Ramjee, Distributed Call Prcessing fr Persnal Cmmunicatins Services, IEEE Cmmunicatins Magazine, Vl 33, N 6, pp 66 75, 1995 [10] Mdarressi, A R, and Skg, Signaling System N 7: A Tutrial, IEEE Cmmunicatins Magazine, pp 19 35, July 1990 [11] Mhan, S, and R Jain, Tw User Lcatin Strategies fr Persnal Cmmunicatins Services, IEEE Persnal Cmmunicatins, Vl 1, pp 42 50, First Quarter 1994 [12] Pierre, S, Mbile Cmputing and Ubiquitus Netwrking: Cncepts, Technlgies and Challenges, Telematics and Infrmatics, Vl 18, pp , 2001 [13] Suh, B S, J S Chi, J K Kim, Design and Perfrmance Analysis f Hierarchical Lcatin Management strategies fr Wireless Mbile Cmmunicatin Systems, Cmputer Cmmunicatins, Vl 23, pp , 2000 [14] Tabbane, S, Lcatin Management Methds fr Third-Generatin Mbile Systems, IEEE Cmmunicatins Magazine, Vl 35, N 8, pp 72 78, 1997 [15] Weng, C M, and P W Huang, Mdified Grup Methd fr Mbility Management, Cmputer Cmmunicatins, Vl 23, pp , 2000