Modelling and Performance Analysis of Different Access Schemes in Two-tier Wireless Networks

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1 Modellng and Perforance Analyss of Dfferent Access Schees n Two-ter Wreless Networks Xaohu Ge, Jorge Martínez-Bauset, Vcente Casares-Gner, Bn Yang, Junlang Ye and Mn Chen Dept. Electroncs & Inforaton Engneerng, Huazhong Unversty of Scence & Technology, Wuhan, Chna Dept. de Councacones Unverstat Poltècnca de Valènca, Valenca, Span School of Coputer Scence & Technology, Huazhong Unversty of Scence & Technology, Wuhan, Chna Eal: xhge@al.hust.edu.cn, {jartnez,vcasares}@upvnet.upv.es, nchen2012@al.hust.edu.cn Abstract We develop a teletraffc odel to evaluate the perforance of two typcal access schees n two-ter wreless networks. Two of the an perforance paraeters are the blockng probablty and carred traffc. Nuercal results show that the fetocell prorty access schee perfors better than the acrocell prorty access schee as t acheves lower blockng probablty and carres ore traffc. Index Ters Wreless networks; access schee; Markov chan; blockng probablty I. INTRODUCTION To accoodate the rapd ncrease of wreless data traffc n ndoor envronents, two-ter wreless networks have been proposed to support hgh throughputs and ncrease the energy effcency of wreless councatons [1], [2]. The ncorporaton of fetocells to a cellular network s eergng as a potental soluton to acheve these two goals [3]. In ths scenaro, user ternals eet wth the dlea of choosng an adequate access schee [4], [5]. For exaple, frst ssue a setup requests to the fetocell and f blocked try wth the acrocell, or vce versa. We beleve that the developent of teletraffc odels to evaluate the perforance of the access schee n two-ter wreless networks s a proble that deserves further nvestgaton. Dfferent studes on the perforance of fetocell networks have appeared n the lterature [6] [9]. Zhang [6] focuses on the blockng probablty n fetocell networks, where a sall nuber of splt spectrus to support fetocells were recoended to ncrease the servce avalablty n the acrocell. K et al. [7] derved a per-ter outage probablty by ntroducng a splfed atheatcal odel whch closely approxates the fetocell nterference dstrbuton. Chandrasekhar and Andrews [8] analyzed the effect of channel uncertanty paraeters. The transt power level was deterned to provde the desred sgnal-to-nterference-plus-nose rato (SINR) for the ndoor cell edge fetocell users and the bea weght to axze the output SINR of acrocell and fetocell users. By evaluatng an nterestng networkwde spectral effcency etrc, an uplnk capacty analyss and nterference avodance strategy was developed for a twoter fetocell network. Hou and Laurenson [9] showed that the cellular and fetocell heterogeneous network archtecture s able to provde a hgh qualty of servce (QoS) and sgnfcantly reduce power consupton. Ge et al. [10] nvestgated the pact of nterference on access schees n wreless networks. Song et al. [11] analyzed the perforance of a hybrd wreless network wth cellular networks and wreless local area networks. However, ost of above studes were carred out deployng a specfc cell access schee n fetocell networks and no coparatve results were provded. Sangawong et al. [12] nvestgated three cell access schees n heterogeneous networks wth Long-Ter Evoluton (LTE)-Advanced downlnk: sgnal-to-nterference plus nose power rato (SINR)-based access schee, reference sgnal receved power (RSRP)-based access schee, and reference sgnal receved qualty (RSRQ)-based access schee. Sulaton results showed that the perforance of the RSRQbased access schee for downlnk cell-central and cell-edge users perfors better than the other two access schees, n ters of axzng the cell-edge user throughput. Fooladvanda proposed a sple cell access schee,.e., Pcocell Frst (PcoF) that perfors uch better than two exstng cell access schee,.e., receved sgnal power access schee and range extenson (RE) access schee [13]. All above studes of cell prorty schees were based on sulaton odels. We beleve that analytcal odels fro the traffc perspectve to analyze the perforance of cell prorty schees n two-ter wreless networks have nor receved suffcent attenton n the lterature. In ths paper, we develop a coparatve perforance evaluaton study of two cell access schees for a two-ter wreless network fro a traffc perspectve. We refer to these two odels as: acrocell prorty access schee and fetocell prorty access schee. Perforance paraeters, such as blockng probablty, carred traffc and the traffc congeston perceved by the fetocell base statons are derved. Also, we valdate the analytcal odels by sulaton. The results obtaned provde gudelnes for the selecton of the cell access schee n two-ter wreless networks. The rest paper s organzed as follows. Secton II descrbes the syste odel of a two-ter wreless network. In Secton III and IV, two contnuous-te Markov chan (CTMC) odels are proposed to evaluate the perforance of the two access schees that we study. In Secton V we defne expresson for the perforance paraeter of nterest: the blockng probablty, carred traffc and traffc congeston. The results of a coparatve nuercal evaluaton study are

2 C (1, C ) ( C 1, C) ( C, C) C 2 ( C 1) C C C p (1, C 1) ( C 1, C 1) ( C, C 1) 2 ( C 1) ( C 1) ( C 1) C ( C 1) p (0, ) (0, C 1) C ( C 1) p 2 (0,1) (1,1) ( C 1,1) ( C,1) 2 ( C 1) C p (0,0) (1,0) ( C 1,0) ( C,0) 2 ( C 1) C Fg. 2. State transton dagra of acrocell prorty access schee n a syste wth a one fetocell. Fg. 1. BS fbs MS Syste odel of two-ter wreless network. shown n Secton VI. Fnally, Secton VII concludes the paper. II. SYSTEM MODEL A splfed scenaro of a two-ter wreless network s shown n Fg. 1, whch ncludes a sngle acrocell and several fetocells. Three types of functonal unts are consdered n Fg. 1,.e., the acrocell base staton (BS), fetocell base statons (fbss) and oble statons (MSs). The BS has C channels and an hexagonal shape coverage area wth surface S. There are N fetocells unforly dstrbuted n the acrocell coverage area, and we assue that ther coverage areas do not overlap wth each other. We denote by S the surface of the coverage area of the fbs, and by C the nuber of channels assocated to t, 1 N. For atheatcal tractablty, we follow the coon assupton that calls arrve to the syste followng a Posson process of rate λ. We also assue that call duratons are exponentally dstrbuted wth rate µ. Accepted calls occupy one channel. Our odel does not consder oblty. However t can be easly ncorporated at the expense of ncreasng ts coplexty. Fnally, we assue that a MS s able to access both the BS and any fbs that falls wthn ts councaton range (the locaton of the MS s wthn ts coverage area). III. MODELLING OF MACROCELL PRIORITY ACCESS SCHEME We odel the acrocell prorty access schee as an overflow syste [14]. We consder a syste wth one acrocell and a sngle fetocell. Let the BS channels be the prary group of servers and the fbs channels the secondary group of servers. A new call arrval s frst offered to the BS. If a free channel s avalable, the call s carred by the BS. Otherwse, t s offered to a fbs, provded that the MS s n the coverage area of a fbs. If no free channels are avalable at the fbs, then the call s defntely blocked by the two-ter wreless network. We denote by p = S /S the probablty that a MS s n the coverage area of the fbs. Let (x, x ) be the syste state vector, where x, 0 x C, s the nuber of ongong calls at the prary group (occuped BS channels), and x, 0 x C, the nuber of ongong calls at the secondary group (occuped channels at the fbs ). We note that the syste state vector defnes an rreducble ergodc CTMC and Fg. 2 llustrates ts transton dagra. The dfferent transtons shown n Fg. 2 are: 1) (x, x ) (x + 1, x ), a new call arrves and t s accepted by the BS. 2) (x, x ) (x 1, x ), a BS call ternates. 3) (C, x ) (x, x + 1), a new call arrves and t s accepted by the fbs, as all BS channels are busy. 4) (x, x ) (x, x 1), a fbs call ternates. Let π (x, x ) be the steady state probablty of fndng x ongong calls at the BS and x ongong calls at the fbs. The statonary dstrbuton s obtaned by solvng the global balance equatons (1). IV. MODELLING OF FEMTOCELL PRIORITY ACCESS SCHEME We odel the fetocell prorty access schee as an overflow syste. We consder a syste wth one acrocell and a sngle fetocell. Let the fbs channels be the prary group of servers and the BS channels the secondary group of servers. A new call arrval s frst offered to the fbs, provded that the MS s n the coverage area of ths fbs. If a free channel s avalable at the fbs, the call s carred by ths fbs. If all fbs channels are busy or the MS does not fall wthn the coverage area of any fbs, then the new call s offered to the BS. If no free channels are avalable at the BS, then the call s defntely blocked by the two-ter wreless network. We denote by pλ the arrval rate of calls to the fbs. As n prevous Secton, let (x, x ) be the syste state vector, where x, 0 x C, s the nuber of ongong

3 π (x, x ) (λ + x µ + x µ) = π (x 1, x ) λ + π (x + 1, x ) (x + 1) µ + π (x, x + 1) (x + 1) µ f 0 < x < C, 0 < x < C, π (0, C ) (λ + C µ) = π (1, C ) µ, π (0, 0) λ = π (0, 1) µ + π (1, 0) µ, π (C, C ) (C µ + C µ) = π (C, C 1) pλ + π (C 1, C ) λ, π (C, 0) (pλ + C µ) = π (C, 1) µ + π (C 1, 0) λ, π (x, C ) (λ + x µ + C µ) = π (x 1, C ) λ + π (x + 1, C ) (x + 1) µ, f 0 < x < C, π (x, 0) (λ + x µ) = π (x, 1) µ + π (x 1, 0) λ + π (x + 1, 0) (x + 1) µ, f 0 < x < C, π (0, x ) (λ + x µ) = π (1, x ) x µ + π (0, x + 1) (x + 1) µ, f 0 < x < C π (C, x ) (C µ + x µ + pλ) = π (C, x + 1) (x + 1) µ + π (C 1, x ) λ + π (C, x 1) pλ f 0 < x < C. (1) (1 p) ( C 0) ( C 1) ( C, C 1) ( C, C) (1,0) C ( C 10) (1 p) (1 p) (1 p) ( C 1) p C ( C 1) 2 C 2 (1 p) 2 (1 p) 2 p p p p p p p p (1 p) ( C 11) (1 p) (1 p) (1,1) 2 p 2 ( C 1) (1 p) p ( C 1, C 1) (1, C 1) C ( C 1) 2 ( C 1) C (1 p) p p p (0,0) (01) (0, C 1) (0, ) ( C 1) ( C 1) (1 p) C p p C C ( C 1, C) ( C 1) C 2 (1, C ) Fg. 3. State transton dagra of fetocell prorty access schee n a syste wth a one fetocell. calls at the secondary group (occuped BS channels), and x, 0 x C, the nuber of ongong calls at the prary group (occuped channels of the fbs ). We note that the syste state vector defnes an rreducble ergodc CTMC and Fg. 3 llustrates ts transton dagra. The dfferent transtons shown n Fg. 3 are: 1) (x, x ) (x, x + 1), a new call arrves and t s accepted by the fbs. 2) (x, x ) (x, x 1), a fbs call ternates. 3) (x, x ) (x + 1, x ), a new call arrves and t s accepted by the BS, as all fbs channels are busy or the MS does not fall wthn the coverage area of the fbs. 4) (x, x ) (x 1, x ), a BS call ternates. Note n Fg. 3 that when there are free channels at fbs the BS call arrval rate s (1 p) λ. However, when all channels at fbs are occuped, the BS call arrval rate s λ. Let π (x, x ) be the steady state probablty of fndng x ongong calls at the BS and x ongong calls at the fbs. The statonary dstrbuton s obtaned by solvng the global balance equatons (2). V. PERFORMANCE PARAMETERS Consderng a syste wth one BS acrocell and N fbss, we denote by π (x, x 1,..., x N ) the jont statonary probablty of fndng x (x ) ongong calls n the BS (fbs ). For splcty, we assue that all fbs have the sae nuber of channels and the coverage areas of all fetocells have the sae surface,.e., C =, S = S f,, p = S f /S and Np 1. Then, the blockng probablty s gven by BP = (1 Np) π (C,,..., ) + pπ (C,,,..., ) + pπ (C,,,..., ) pπ (C,,..., ) = (1 Np) π (C,,..., ) + Npπ (C,,,..., ). (3) Clearly, a new call s blocked when the correspondng MS s not covered by any of the N fbss and the BS has all channels occuped, or when t s covered by a fbs but all channels of the fbs and BS are occuped. Note that for syetry and regardless of the access schee adopted, the fracton of te wth all BS channels busy and all fbs channels busy s equal to the fracton of te wth all BS channels busy and all fbs j channels busy, 1, j N,.e., π (C,,..., C,..., ) = π (C,,..., C j,..., ). For the acrocell prorty access schee, the ters n (3) requred to deterne the BP can be easly obtan fro the two densonal syste defned n Secton III. As an exaple, the statonary probabltes n (3) for a syste wth N = 2 can be deterned as follows. π (C,, ) = π (C,, j) = π (C ), (4) =0 j=0 π (C,, ) = π (C,, ) = π 1 (C, ), (5) =0 π (C,, ) = π (C,, ) = π 2 (C, ). (6) =0

4 π(x, x ) (λ + x µ + x µ) = π(x, x 1) pλ + π(x, x + 1) (x + 1)µ + π(x + 1, x ) (x + 1)µ +π(x 1, x ) (1 p)λ, f 0 < x < C, 0 < x < C, π(c, 0) (pλ + C µ) = π(c, 1) µ + π(c 1, 0) (1 p)λ, π(0, 0)λ = π(1, 0) µ + π(0, 1) µ, π(c, C ) (C µ + C µ) = π(c 1, C ) λ + π(c, C 1) pλ, π(0, C ) (λ + C µ) = π(1, C ) µ + π(0, C 1) pλ, π(c, x ) (pλ + x µ + C µ) = π(c, x 1) pλ + π(c, x + 1) (x + 1)µ, f 0 < x < C, π(0, x ) (λ + x µ) = π(1, x ) µ + π(0, x 1) pλ + π(0, x + 1) (x + 1)µ, f 0 < x < C, π(x, C ) (λ + x µ) = π(x, 1) x µ + π(x + 1, 0) (x + 1)µ + π(x 1, 0) (1 p)λ, f 0 < x < C, π(x, C ) (C µ + x µ + λ) = π(x + 1, C ) (x + 1)µ + π(x, C 1) pλ + π(x 1, C ) λ, f 0 < x < C. (2) Note that π (C ) s the blockng probablty n a Erlang-B syste wth C channels. Also, the probablty π 1 (C, ) was already obtaned n Secton III. For the acrocell prorty access schee, the total traffc carred by the two-ter syste wth one BS and N fbss s gven by [15] A C = C x =0 x π (x ) + N = A C + NA Cf, C x =0 x 1 =0 x 1 π 1 (x, x 1 ) (7) Blockng Probablty Sulated M-F Nuercal M-F Sulated F-M Nuercal F-M where A C s the traffc carred by the acrocell, A Cf s the traffc carred by any fetocell, and the dstrbuton π 1 (x, x 1 ) can be obtaned wth the odel of Secton III. Fnally, the traffc lost by the acrocell A L and any fetocell A L, and the traffc congeston perceved by any fetocell T C M F f are gven by A L = A O π (C ), A O = λ/µ, T C M F f A Lf = A Of A Cf = pa L A Cf = pa O π (C ) = A Lf A Of, C x =0 x 1 =0 x 1 π 1 (x, x 1 ), respectvely, where A O s the total traffc offered to the twoter network, A Of s the traffc offered to any fetocell. For the fetocell prorty schee, we assue that the probabltes π (C,,..., C,..., ) requred to deterne the blockng probablty (3) can be approxated as n (4), (5) and (6), but now π (x, x ) are obtaned by the odel defned n Secton IV. Then, the perforance paraeters of nterest are gven by the sae expressons provded for the acrocell prorty schee except the traffc congeston, whch s gven by pa O C T C F M f = x =0 x 1 =0 x 1 π 1 (x, x 1 ) pa O Fg Nuber of channels n a fetocell Blockng probablty n a syste wth one fetocell. VI. NUMERICAL EVALUATION In ths Secton we copare the perforance of the two access schees studed n two-ter wreless networks. To ths end, we defne a network wth the followng confguraton: C = 40, C = 4, λ = 5, µ = 0.05, S /S = 20, and 1 N 20. The results of the analytcal odels are valdated by sulaton. Fgure 4 shows the evoluton of the blockng probablty wth the nuber of channels of the fbs n a splfed scenaro wth one BS and a sngle fbs. As expected, the blockng probablty decreases wth the nuber of channels of the fbs. An nterestng observaton s that the decrease s ore acute for the fetocell prorty schee (F-M) than for the acrocell prorty schee (M-F). Note also that analytcal and sulaton results atch qute well. Fgure 5 shows the evoluton of the blockng probablty wth an ncreasng nuber of fetocells. Also as expected, the blockng probablty decreases as the nuber of fetocells ncreases. An nterestng observaton s that for a syste wth only one fetocell the blockng probabltes of both access schees are very close. However, as the nuber of fetocells ncrease, the blockng probablty of the F-M schee decreases

5 Blockng Probablty Sulated M-F Nuercal M-F Sulated F-M Nuercal F-M Traffc Congeston Sulated M-F Nuercal M-F Sulated F-M Nuercal F-M Fg. 5. Carred Traffc Fg Nuber of fetocells Blockng probablty n a syste wth ultple fetocells. Sulated M-F Nuercal M-F Sulated F-M Nuercal F-M Nuber of fetocells Total carred traffc n a syste wth ultple fetocells. ore rapdly than the blockng probablty of the M-F schee. Fgure 6 shows the evoluton of the total traffc carred by the two-ter syste wth an ncreasng nuber of fetocells. Agan as expected, the total carred traffc ncreases as the nuber of fetocells ncreases. An nterestng observaton s that the traffc carred by the syste wth the F-M schee ncreases ore rapdly than the traffc carred by the syste wth the M-F schee wth the nuber of fbss. Clearly, ths trend s n snthony wth the one shown n Fg. 5. Also, note that analytcal results closely follow the sae trend than the sulaton results. Fgure 7 shows the evoluton of the traffc congeston rate perceved by a fbs wth the nuber of channels of the fbs, n a splfed scenaro wth one BS and a sngle fbs. Clearly, the fracton of traffc that s lost decreases as the nuber of channels of the fbs ncreases. Note that, for a gven nuber of channels of the fbs, the traffc congeston s lower for the F-M access schee than for the M-F schee. Fnally, note that the traffc congeston perceved by a fbs for when deployng Nuber of channels Fg. 7. Traffc congeston perceved by a fbs n a syste wth a sngle fetocell. each of the two access schees converge to very close values when the nuber of channels of the fbs s 10 or larger. Based on above nuercal results, we can conclude that the fetocell prorty access schee outperfors the acrocell prorty access schee n ters of the syste blockng probablty acheved, the total syste carred traffc and the traffc congeston. VII. CONCLUSIONS In ths paper, we have odeled two cell access schees n a two-ter wreless network. One s the acrocell prorty schee, where a new call arrval s frst offered to the acrocell base staton. If blocked by t and the MS s the coverage area of a fbs, then the call s offered to ths fbs. The other s the fetocell prorty schee, where a new call arrval s frst offered to a fbs f the MS s n the coverage area of the fbs. If blocked by the fbs or the MS s not covered by any fbs, then the new call s offered to the BS. We odeled both schees by two CTMCs and defned three perforance paraeter: the blockng probablty of new calls offered to the syste, the total carred traffc by the two-ter syste and the traffc congeston perceved by a fbs. The nuercal results showed that the fetocell prorty access schee outperfors the acrocell prorty access schee for the perforance paraeters of nterest. Our results provde gudelnes for the desgn of two-ter wreless networks. ACKNOWLEDGMENTS X. Ge, B. Yang and J. Ye would lke to acknowledge the support fro the Natonal Natural Scence Foundaton of Chna (NSFC) (Grant No.: and ), Natonal 863 Hgh Technology Progra of Chna (Grant No.: 2009AA01Z239) and the Mnstry of Scence and Technology (MOST), Chna, Internatonal Scence and Technology Collaboraton Progra (Grant No.:0903), Hube Provncal Scence and Technology Departent (Grant No.: 2011BFA004), RCUK for the UK -Chna Scence Brdges Project: R&D on

6 (B) 4G Wreless Moble Councatons, the Korea Chna Scence and Technology Jont Research Center by the Natonal Research Foundaton (NRF) under Grant No of the Mnstry of Educaton, Scence and Technology (MEST), the Korean governent.. X. Ge, J. Martnez-Bauset and V. Casares-Gner acknowledge the support fro the EU FP7- PEOPLE-IRSES progra, project acrony S2EuNet (Grant no.: ). V. Casares-Gner contrbuton was supported by the Spansh Governent through project TIN C REFERENCES [1] I. Huar, X. Ge, L. Xang, et. al., Rethnkng Energy-Effcency Models of Cellular Networks wth Eboded Energy, IEEE Network Magazne, vol. 25, no.3, pp.40 49, Mar [2] C. Wang, T.Q.S. Quek, M. Kountours, Throughput optzaton, spectru allocaton, and access control n two-ter fetocell networks, IEEE J. Select. Areas Coun., vol. 30, no. 3, pp , Apr [3] Z. Lu, Y. Sun, X. Wen, T. Su, D. Lng, An energy-effcent power control algorth n fetocell networks, n Proc. Internatonal Conference on Coputer Scence & Educaton 2012, pp , July [4] M. Chen, S. Gonzalez, A. Vaslakos, H. Cao and V. C. M. Leung, Body Area Networks: A Survey, ACM/Sprnger Moble Networks and Applcatons, Vol. 16, No. 2, pp , Aprl [5] M. Chen, MM-QoS for BAN: Mult-Level MAC-Layer QoS Desgn n Body Area Networks, IEEE Globeco 2013, Atlanta, Georga, USA, Dec. 9-13, [6] Y. Zhang, Resource sharng of copletely closed access n fetocell networks, n Proc. IEEE WCNC 2010, pp. 1 5, Apr [7] Y. K, S. Lee and D. Hong, Perforance analyss of two-ter fetocell networks wth outage constrants, IEEE Trans. Wreless Coun., vol. 9, no. 9, pp , Sept [8] V. Chandrasekhar, J. G. Andrews, Uplnk capacty and nterference avodance for two-ter fetocell networks, IEEE Trans. Wreless Coun., vol. 8, no. 7, pp , July [9] Y. Hou and D. I. Laurenson, Energy effcency of hgh QoS heterogeneous wreless councaton network, n Proc. IEEE VTC 2010-Fall, pp. 1 5, Sept [10] X. Ge, K. Huang, C.-X. Wang, et. al., Capacty analyss of a ult-cell ult-antenna cooperatve cellular network wth co-channel nterference, IEEE Trans. Wreless Coun., vol. 10, no. 10, pp , Oct [11] W. Song, H. Jang and W. Zhuang, Perforance analyss of the WLANfrst schee n cellular/wlan nterworkng, IEEE Trans. Wreless Coun., vol. 6, no. 5, pp , May [12] J. Sangawong, Y. Sato, N. Mk, et. al., Investgaton on cell selecton ethods assocated wth nter-cell nterference coordnaton n heterogeneous networks for LTE-advanced downlnk, n Proc. European Wreless 2011, pp. 1 6, Apr [13] D. Fooladvanda, C. Rosenberg, Jont resource allocaton and user assocaton for heterogeneous wreless cellular networks, IEEE Trans. Wreless Coun., vol. 12, no. 1, pp , Jan [14] H. Akaru, A. Kagechka and H. Takahash, Mean and varance of overflow traffc for te dependent nputs, IEEE Trans. Coun., vol. 34, no. 3, pp , Mar [15] R.B. Cooper, Queueng Theory, New York: North-Holland, 1981.