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1 ISSN -985, CODEN RUXUEW Journal of Software, Vol., No.6, June, pp doi:.374/sp.j Tel/Fax: by Institute of Software, the Chinese Academy of Sciences. All rights reserved.,, + (, 34) Research on Location Management Based on Irregular Cellular Network Topology Model ZHAO Xiao-Min, LANG Mei-Ya, CHEN Qing-Zhang + (College of Information Engineering, Zhejiang University of Technology, Hangzhou 34, China) + Corresponding author: qzchen@zjut.edu.cn Zhao XM, Lang MY, Chen QZ. Research on location management based on irregular cellular network topology model. Journal of Software,,(6): Abstract: Most strategies of location management are based on the hypothesis that the cellular network is regular in size, shape and distribution. This paper proposes a location management strategy based on irregular cellular network topology, including macro-cell, micro-cell and pico-cell. The terminal will compute the physical distance between the current cell and the last reported cell by regrouping neighbor cells and comparing the CCs (cell coordinates) which are broadcasted by each base station. In the paper a dynamic location update algorithm based on distance and direction angle is presented. Finally, the formula for the total cost of location management between two paging arrivals is deduced by a semi-markov decision process. The numerical analysis shows that the total costs of location updating and paging of individuation sector location management scheme is superior to that of circle location cell when the mobile user moves frequently. Key words: location management; cell regrouping; cell coordinate; physical distance :, ( ), CC(cell coordinates),.,.,,. : ; ; ; : TP393 : A,, (personal communication services, Supported by the Special Program for the Science and Technology Plan of Zhejiang Province of China under Grant No.7C364 ( ); the Natural Science Foundation of Zhejiang Province of China under Grant No.Y63 ( ) Received 8-5-; Revised 8-7-8; Accepted 8--8; Published online 9-6-6

2 354 Journal of Software Vol., No.6, June PCS), PCS,, (cell).,. (mobile terminal, MT), PCS []., (location area, LA),,. :., ;.,,.., LA, LA,LA, GSM IS-4.,LA,,.,, LA. 3. [], T,, T,. [3], 3.,,. [4,5] (cell identification code, CIC). [6,7],,,. [8],.. [9 ],,. [], (reporting cells).,,,., PCS,,.,.,, (cell coordinates, CC) [3] (physical distance)(m km),,.,..,,,..,,,,.,,., 3 : ;

3 : 355 ;.,, ( ). A(x a,y a ) (x,y ) Cell Cell Cell Cell 3 Cell Cell 6 Cell 5 Cell 7 Cell 3 Cell 9 Cell Cell 4 Cell 8 B(x b,y b ) (x,y ) Cell Micro-Cell Pico-Cell Macro-Cell Fig. Irregular cellular network topology model. (cell coordinates, CC) CIC ( ) [4,5].,, LA.,., LA,. CIC LA,,,CIC MSC BCD, ( ), LA., CC [3].,, i xm( km) ym( km), i CC(x i,y i )., LA, CC(x,y ), D. BTS CC CIC., CC. CC CC(x i,y i ), j, LA., j LA d = ( x x ) + ( y y )., j j j,., CC, BTS,, BCCH.,., d, = ( x x ) + ( y y )., A,, B CC,

4 356 Journal of Software Vol., No.6, June dab, = ( xb xa) + ( yb ya)., d A,B d,i d, d= d A,B d,i,, d., d,i d 5 d, d. d. d. d,i, d,, [3]. [4], 9% 5. :,..3,,,,. LA,,., CC CC,.,. m~m, ( ) ( ),, CC CC., CC(x,y ), CC(x,y )., CC(x,y ),,, BCCH, CC.,,,?, ,., : (),., , 4.,,, CC. (), 3., ~ 3 5., 3, 7 3, 5, CC,,,, LA. (3),,.,.,.,., LA, R(

5 : 357 ), LA (paging area, PA). LA,LA, LA,.,, PA, LA., LA, LA.,,,,,.,,,,.,,,.,.,., α R LA, LA,., θ,β. Two previous reported cell Cell Last reported cell θ Cell i α R Cell j β Current cell Fig. Individuation sector cellular LA LA LA : (), LA,, R( ). CC(x,y ), LA. (),, CC. (3) CC CC(x,y ) :, () ;, (4). (4) CC, LA :, () ;, (5). LA. (5), : R α

6 358 Journal of Software Vol., No.6, June θ, θ CC, LA. (6) LA, ().. LA.. CC LA, d;. CC LA, β; 3. d R, d>r, 5; d R, 4; 4. β θ α/, β θ >α/, 5 ;, 6 ; 5. LA, ; 6. LA,. LA,, LA,. 3 3.,..,,,, t t+., [5].,, LA.,,.,.,,,,. 3.,, : t n : n T: X n : n Y n : n U(X n,y n ): n, X n Y n φ(t): P(X φ(t) ): C µ : C p : λ: λ f(v): g(β): A c : η:

7 : 359 E[ ]: 3,t =, T.t,t,t,, X n, LA d, LA β v CC, LA,. Y n n,y n =,Y n =,. X,Y X,Y X,Y X φ(t),y φ(t) Time t = t t τ τ t φ(t) T Fig.3 Timing diagram 3,, U(X n,y n ) P(X φ(t) ).U(X n,y n ) n X n Y n,,y n,, U( Xn,) = Cµ, Yn = () U( Xn,) =, Yn =,C µ. 3,φ(T) T,P(X φ(t) ), LA. LA, LA. A c, LA., LA,., f(v) g(β) LA π π, v, f() v, β, g( β ). =, v < =, π f() v g( β ) V = d v, ω = d β π v, η β π f() v g( β ) η = π α dd β = ω α vβ R v V R. η α R v β. C T, : Φ ( T ) EC [ T] = EC [ U] + EC [ P] = E U( Xn, Yn) + P( XΦ ( T) ) () n= λ, () ( ) [ ] Φ T (, ) ( ) e t d λ ECT = E U X n Yn + P XΦ ( T) λ t (3) n= k T, Φ(T)=k (3):

8 36 Journal of Software Vol., No.6, June tk+ ()d t = ()dt t,, k tn k= n () : t k k+ λt EC [ T] = E U( Xn, Yn) P( Xk) λe dt t + k k= n= E U X Y t P X t t k+ λt tk+ λt = ( n, n) λe d + ( k) λe d t k tk n= k= n k= E U X Y t P X t. t k+ λt tk+ λt = ( n, n) λe d + ( k) λe d t k tk n= k= n k = EC E U X Y t P X λt λtk λtk+ [ T] = ( n, n) λe d + ( k)(e e ) tn n= k= λt λtk λtk+ = E U( Xn, Yn) λe d t + P( Xk)(e e ) tn n= k= λtn λtk λtk+ = E U( Xn, Yn)e + P( Xk)(e e ) n= k= λtn λtn λ tn = E U( Xn, Yn)e + P( Xn)(e e + ) n= n= λtn λtk λt λt λt3 λtk U( Xn, Yn)e = Cµ e = Cµ lim(e + e + e e ) k n= k= (5),t k. η, η=t k t k, t =, (5) λη λη k λη λt e [ (e ) ] e C n µ U( Xn, Yn)e = Cµ lim = Cµ = (6) k λη λη λη e e e n= C p,, A c, α R LA,, A c C α R λtn λtn+ p λtn λtn+ PX ( n)(e e ) = (e e ) n= Ac n= C αr p λt λt λt λt λtn λtn+ = lim(e e + e e e e ) A n c Cpα R = lim e A n c Cpα R = A c λτ ( + τ+ τ τn+ ),τ,τ,. (6) (7) (4), Cµ CpαR Cµ CpαR EC [ T ] = E + E λη = + λωvα R e Ac e Ac (8), C T α A c R, R (distance threshold, DT). (4) (7) (8)

9 : 36. C T DT., C µ =,C p =,ω=3/π,v=,λ=.. 4 R,., A c =.65,.5Km., R, R.5km~3km( 3~6.5km ),., α. α, LA LA. LA,,,, ; α π, LA LA,, LA, LA,,. Total cost of location management between two paging arrivals C T α=π/ α=π/3 α=π/ α=π R (km) Distance threshold Fig.4 Relationship between C T and DT under different α 4 α,c T DT 5 6 A c,,r c, α=π/3., A c, r c,, ; A c, r c,,. Total cost of location management between two paging arrivals C T A c =.3km A c =.65km A c =.66km A c =5.85km Distance threshold R (km) Total cost of location management between two paging arrivals C T 5 R=.5km R=.km R=.5km Radius of equal-area hexagon r c (km) Fig.5 Relationship between C T and DT under different A c 5 A c,c T DT Fig.6 Relationship between C T and r c under different DT 6 DT,C T r c

10 36 Journal of Software Vol., No.6, June 3.3.,,,,.,, [3] ( C total Cµ CpπR = k +, λrω A c k ),,λ, /λ, C T C total. 7,,. 4 Total cost of location management between two paging arrivals C C total λ=. λ= C T C T 5 5 R (km) Distance threshold Fig.7 Relationship between C T and DT under different λ 7 λ,c T DT (mobile computing).,,,.,,,. C total References: [] Akyildiz LF, Ho JSM, Lin YB. Movement-Based location update and selective paging for PCS networks. IEEE/ACM Trans. on Networking, 996,4(4): [] Naor Z, Levy H. Minimizing the wireless cost of tracking mobile users: An adaptive threshold scheme. In: Proc. of the INFOCOM 98. San Francisco: IEEE Computer Society Press, papers/6b_.pdf [3] Bar-Noy A, Kessler I, Sidi M. Mobile users: To update or not to update? Wireless Networks, 995,(): [4] Zhang JY. A cell ID assignment scheme and its applications. In: Proc. of the Int l Workshop on Parallel Processing. Washington: IEEE Computer Society Press, [5] Naor Z, Levy H, Zwick U. Cell identification codes for tracking mobile users. Wireless Networks,,8(): [6] Liang B, Haas ZJ. Predictive distance-based mobility management for PCS networks. In: Proc. of the INFOCOM 99. San Francisco: IEEE Computer Society Press,

11 : 363 [7] Liang B, Haas ZJ. Predictive distance-based mobility management for multidimensional PCS networks. IEEE/ACM Trans. on Networking, 3,(5): [8] Bhattachary A, Das SK. LeZi-Update: An information-theoretic approach to track mobile users in PCS networks. In: Proc. of the 5th Annual ACM/IEEE Int l Conf. on Mobile Computing and Networking. New York: ACM Press, carleton.ca/~adhocnow/networks/das99.pdf [9] Hwang HW, Chang MF, Tseng CC. A direction-based location update scheme with a line-paging strategy for PCS network. IEEE Communications Letters,,4(5):49 5. [] Zheng J, Regentova E. An enhanced direction-based location update scheme for PCS networks. In: Proc. of the Vehicular Technology Conf. Piscataway: IEEE Press, [] Ou DX, Dong DC, Liu WZ. Location management model based on movement directions for PCS network. Journal of Tongji University, 3,3(): (in Chinese with English abstract). [] Hac A, Zhou X. Location strategies for personal communication networks: A novel tracking strategy. IEEE Journal on Selected Areas in Communications, 997,5(8): [3] Ng CK, Chan HW. Enhanced distance-based location management of mobile communication systems using a cell coordinates approach. IEEE Trans. on Mobile Computing, 5,4():4 55. [4] Wong VWS, Leung VCM. An adaptive distance-based location update algorithm for next-generation PCS network. IEEE Journal on Selected Areas in Communications,,9(): [5] Zheng J, Zhang Y, Wang L, Chen J. Adaptive location update area design for wireless cellular networks under D Markov walk model. Elsevier Computer Communications, 7,3:6 69. : [],,.PCS.,3,3(): (976 ),,,, (955 ),,,,CCF,,,,,.,. (98 ),,,,.

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