Estimation of spectrum requirements for mobile networks with self-similar traffic, handover, and frequency reuse

Transcription

1 Moble Informaton Systems 6 (2010) DOI /MIS IOS Press Estmaton of spectrum requrements for moble networks wth self-smlar traffc, handover, and frequency reuse Won Seok Yang a, Eun Saem Yang b,, Hwa J. Km c and Dae K. Km d a Department of Busness Admnstraton, Hannam Unversty, Daejeon, Republc of Korea b Department of Computer Engneerng, Hallym Unversty, Chuncheon, KangwonDo, Republc of Korea c Department of Electroncs and Computer Engneerng, Kangwon Natonal Unversty, Chuncheon, KangwonDo, Republc of Korea d Department of Informaton Communcaton and Computer Networks, Hallym College, Chuncheon, KangwonDo, Republc of Korea Abstract. Ths paper consders self-smlarty n data traffc, handover, and frequency reuse to estmate the spectrum requrements of moble networks. An approxmate average cell capacty subject to a delay requrement and self-smlar traffc s presented. It s shown that handover traffc can be an addtonal load. Spectrum requrements are calculated based on carrer demand nstead of spectral effcency, as at least one carrer s necessary to transmt even 1 bt. The cell-splt operaton s consdered under frequency reuse of one. Estmaton methods are presented usng cell traffc n two cases. Frst, a procedure s presented that estmates cell traffc from prevous networks. Second, cell traffc s assumed to follow probablty dstrbutons. Numercal examples demonstrate the mpact of self-smlarty, handover, and the proporton of cell-splt occurrences on the spectrum requrements. Keywords: Spectrum requrement, self-smlarty, handover, frequency reuse, data traffc, QoS 1. Introducton Self-smlarty has been reported as a characterstc of data traffc. Examples nclude Ethernet, Web, FTP, telnet, and VBR traffc [9,18,25,30]. Self-smlar traffc s bursty [19]. The queue length s very senstve to the degree of self-smlarty [28]. On the other hand, moble traffc n GPRS (General Packet Rado Servce) was nvestgated by [14]. It has been reported that moble traffc shows self- smlarty. In addton, moblty may affect performance and plannng of wreless networks [1 3,13]. As a result, addtonal resources are requred compared to Posson traffc n moble networks. Prevous studes analyzed cell capacty usng M/M/c or M/G/1 queues that assume Posson traffc [10,16,17,21,26]. For example, the ITU-R model n [17] appled the Erlang C formula to analyze the servce channels per group for the packet communcatons servces. In [21,26], the requred system capacty for packet swtched Correspondng author. Tel.: ; Fax: ; E-mal: yanges@hallym.ac.kr X/10/$ IOS Press and the authors. All rghts reserved

2 282 W.S. Yang et al. / Estmaton of spectrum requrements for moble networks wth self-smlar traffc, handover servces was calculated usng M/G/1 non-preemptve prorty queung models. Therefore, prevous studes may have underestmated the spectrum requrements when appled to self-smlar data traffc. A handover provdes a contnuous connecton whle a moble staton moves from one cell to another. A moble staton may communcate wth multple base statons (BSs) durng a handover, for example durng a soft handover. In ths case, handover traffc can be an addtonal load on moble systems. The porton of handover traffc to total traffc s approxmately 12% consderng only soft handovers n cdma2000 1x networks [24]. In moble envronments, each cell has a dfferent spectrum requrement snce traffc s unevenly dstrbuted n a regon. The spectrum requrement requred to serve a regon s not the average but the maxmum demand of cells. Ths s the basc concept of prevous methods. It s theoretcally feasble but lacks the practcal aspects of frequency reuse. Recent moble technologes, ncludng cdma2000 1x, WCDMA, and moble WMAX, support frequency reuse of one. All cells can operate on the same frequency channel, whch allows splttng a cell nto multple cells to share the coverage and traffc of the orgnal cell. As a result, we can reduce the spectrum requrements by usng a cell-splt. Not consderng frequency reuse may result n the overestmaton of the spectrum requrements. On the other hand, even though users at the cell edge may suffer degradaton n connecton qualty due to heavy cochannel nterference n the cell-splt, the possblty of a cell-splt wth a frequency reuse of one s theoretcally clear [7,11,12]. In addton, cell-splts are wdespread n CDMA systems, whch support a frequency reuse of one. For example, a moble operator n Korea operated around 4,000 cdma2000 1x base statons n 2003, and that number ncreased to around 6,000 n The operator s network covered the whole country, even as far back 2000, mplyng that around 2000 cells are splt. Prevous research has pad no attenton to self-smlarty, handover, and frequency reuse, although these factors affect spectrum requrements sgnfcantly. However, a recent study dd consder these three factors [5]. The method used n [5], however was smple and ntutve. It consdered self-smlarty but merely used a parameter to reflect self-smlarty wthout analyzng t mathematcally. The scheme of the cell-splt was not specfc. In addton, the study dd not consder when the data of the cell traffc s nsuffcent. Ths paper presents a robust method that estmates the spectrum requrements of moble networks consderng self-smlarty, handover, and a frequency reuse of one. Frst, we analyze an approxmate average cell capacty per carrer subject to self-smlar traffc consderng delay for the QoS requrement, smlar to [20,23]. A queue length wth the Fractonal Brownan Moton (FBM) process s utlzed to obtan the mean delay. The FBM process, a generalzaton of the Brownan moton process, s frequently used n the analyss of self-smlar traffc [28]. Second, we show that handover traffc can be an addtonal load n some handover technologes. Thrd, we present a specfc procedure for estmatng the spectrum requrements based on a cell-splt wth a frequency reuse of one. We consder two cases accordng to the degree of cell traffc nformaton. Frst, we deal wth an estmaton method assumng the cell traffc s known or can be estmated from the traffc nformaton of prevous networks. Second, we extend ths method to a case when the cell traffc s dstrbuted unformly, exponentally, and normally. Unlke prevous research, the carrer bandwdth s used nstead of spectral effcency as moble networks requre at least one carrer, even when they transmt 1 bt. The rest of ths paper s organzed as follows. In Secton 2, the model s descrbed. In Secton 3, the average cell capacty s presented. In Secton 4, handover s nvestgated. In Sectons 5 and 6, specfc estmaton methods are presented. Secton 7 shows numercal examples. Secton 8 concludes ths study.

3 W.S. Yang et al. / Estmaton of spectrum requrements for moble networks wth self-smlar traffc, handover Model descrpton It s assumed that there are K types of packets accordng to ther length. Let x k and p k denote the length of a type k packet and the probablty that a packet s type k, respectvely. Let C F denote the full capacty per carrer, for example the average throughput. Let λ k, s k, and ρ k denote the arrval rate, transmsson tme, and utlzaton of type k packets, k = 1,,K, respectvely. Let d k denote the average delay of type k packets. Let C F and C Q denote the capacty physcally provded by a system and the capacty that supports the QoS requrement, respectvely. In ths paper, the QoS requrement s delay. That s, C Q represents the maxmum traffc that a system can accommodate under the condton n whch the average delay s less than a target delay. Let ˆλ k be the maxmum traffc of the type k packet that fulflls the delay requrement. Then, ˆλ k can be calculated numercally. C Q s derved from ˆλ k and p k. The parameter H represents the Hurst parameter or the self-smlarty parameter. Let us defne the handover rato as the porton of handover traffc to the total traffc and denote t by h. It s assumed that h s fxed n all cells. We do not consder the mpact of handover mechansms on QoS n wreless networks [6,8]. It s assumed that a moble system supports a frequency reuse of one. Accordngly, t s possble to dvde a cell nto multple cells and share the coverage and traffc. Ths operaton s called cell-splt. Let M be the carrer requrement that stands for the number of carrers requred n a regon. Let B and S denote the carrer bandwdth and the spectrum requrement n a regon, respectvely. The spectrum requrement s gven by S = BM. Let N U and T U denote the number of subscrbers n a regon and traffc per user, termed user traffc, respectvely. Let N C be the number of cells n a regon. Let us defne u k as the cell traffc densty whch represents the traffc porton of the k th cell to the total traffc n a regon, for k = 1,,N C. Note that u k are not only values but are also dstrbuted unformly, exponentally, and normally. Let G(m) be the cumulatve dstrbuton defned as the proporton of cells n a regon that requres m or less than m carrers. G(m) s obtaned from u k, N U, T U, C Q and h. The carrer requrement M s determned as the maxmum number of carrers where G(m) s less than 1 α. That s, M = max {m : G(m) < 1 α}. It s assumed that the cells requrng more carrers than M are splt. As a result, the spectrum requrements are reduced by a cell-splt. 3. Capacty analyss wth self-smlarty and delay requrement A recent study [4] reported that common packet lengths were present n actual traffc flows, although the packet lengths could vary from 7 to 65,542 bytes. Therefore, the packet length s approxmated to have a dscrete dstrbuton. Usng the relatonshp between transmsson speed and capacty results n s k = x k C F, ρ k = λ k s k = λ kx k C F. Accordng to [28], an FBM process s used frequently n the analyss of self-smlar traffc. The mean queue length, denoted by q, wth an FBM process and constant servce tmes s gven by q = ρ 1/2(1 H) (1 ρ) H/(1 H), (1)

4 284 W.S. Yang et al. / Estmaton of spectrum requrements for moble networks wth self-smlar traffc, handover where ρ denotes the utlzaton. The closer the Hurst parameter H s to 1, the greater the degree of self-smlarty. In the case of the absence of self-smlarty, H s 0.5. Applyng Lttle s Law [15] to Eq. (1) results n d k = ρ 1/2(1 H) k λ k (1 ρ k ) H/(1 H), where ρ k represents the utlzaton wth the type k packets. Let ˆλ k be the maxmum traffc under the condton n whch the average delay n Eq. (2) s less than the target delay. Here, ˆλ k can be obtaned numercally from Eq. (2). Ths gves the average capacty per carrer wth a delay requrement as follows: C Q = K p kˆλk x k. k=1 (2) (3) 4. Handover traffc Moble networks support handover to provde moblty to users. Assumng that a moble staton communcates wth multple BSs when t moves from one cell to another, the orgnal BS and the neghbor BSs partcpatng n the handover use rado resources to support the handover. In ths case, the traffc generated durng a handover, called handover traffc, s clearly an addtonal load on a moble system. cdma2000 1x supports hard handovers, soft handovers, and softer handovers. Among these types of handovers, a moble staton communcates wth multple BSs durng soft handovers and multple sectors durng softer handovers [7]. The operaton of handovers n WCDMA s smlar to that n cdma2000 1x [29]. In WMAX, a moble staton communcates wth all BSs n an actve set durng Macro Dversty Handover (MDHO) [11]. As a result, handover traffc should be consdered for soft and softer handovers n CDMA and WCDMA, and MDHO n WMAX. The values of N U and T U can be forecasted by a market research survey. The handover rato can be obtaned from the operatonal data n moble networks. Let T R denote the total traffc load of a network n a regon. User traffc does not contan handover traffc, yeldng T R (1 h) = N U T U. (4) 5. Estmaton of the spectrum requrements wth cell traffc Let T k denote the traffc loaded on the k th cell, termed the cell traffc. T k s assumed to be unknown whle u k s known. Usng Eq. (4) results n T k = u k T R = u kn U T U (1 h) for k = 1,,N C. (5) Let us defne f k as the number of carrers requred n the k th cell. For convenence, f k has a real value. Dvdng T k n Eq. (5) by C Q n Eq. (3) yelds f k = T k C Q = u kn U T U C Q (1 h) for k = 1,,N C. (6)

5 W.S. Yang et al. / Estmaton of spectrum requrements for moble networks wth self-smlar traffc, handover 285 Then, G(m) s derved from Eq. (6). Addng BSs ncreases nterference, whch deterorates the call qualty and the deployment cost of BSs. These factors are dependent on the moble envronments and busness structures. Thus, operators can determne the acceptable range for the porton of the cell-splt n a regon. Fnally, t s necessary to obtan T k or u k to calculate f k n Eq. (6). In exstng networks, T k s easly collected. Whle deployng and plannng a new network, however, T k must be forecasted. In contrast to N U and T U n Eq. (4), t s mpossble to forecast the traffc of each ndvdual cell by a survey, as ths requres numerous samples to collect the traffc nformaton of each cell. The cell traffc densty u k of a new network, however, can be estmated from the traffc nformaton of a prevous network that covered the same area. A moble operator may deploy a new network whle t operates dfferent networks. For example, CDMA or GSM operators may deploy WCDMA. The cell traffc densty of the latter may be smlar to that of the former, as the moblty of users does not change rapdly. Consequently, although they have dfferent amounts of traffc, they may have a smlar traffc densty. It s assumed that a prevous network has J cells n a regon. Let us dvde the regon nto I grds. Let g and b j denote the locaton of grd and cell j, respectvely. Let L(g,b j ) denote the dstance from grd and cell j. It s assumed that grd s ncluded n cell k f L(g,b k ) s the smallest among all of the cells. When = 1,,I and j = 1,,J, g (j) = 1 f L(g,b j ) s mnmzed at j. (7) Otherwse, g (j) = 0. In ths case, g (j) n Eq. (7) ndcates that grd s ncluded n cell j f g (j) = 1. Let Π j denote the number of grds ncluded n cell j. Usng Eq. (7) yelds Π j = I =1 g (j). Let Ω j and ω denote the traffc n cell j and the estmated traffc n grd, respectvely. It s assumed that the grds ncluded n cell j have an equal amount of traffc. Ths yelds ω = Ω j /Π j for and j such that g (j) = 1. The cells n a new network can be placed dfferently from ther prevous postons n the prevous network f they use a dfferent frequency. Let c k denote the locaton of the cell k n the new network. Smlar to Eq. (7), let ĝ (k) = 1 f L(g,c k ) s mnmzed at k for = 1,,I and k = 1,,N C. Let ˆΩ k denote the summaton of the traffc n cells ncluded n cell k. Ths yelds ˆΩ k = I N C ĝ (k) ω for k = 1,,N C. =1 k=1 The cell traffc densty u k s then estmated as follows: / µ k = ˆΩ NC k ˆΩ k for k = 1,,N C. (8) k=1

6 286 W.S. Yang et al. / Estmaton of spectrum requrements for moble networks wth self-smlar traffc, handover 6. Estmaton of the spectrum requrements wth cell traffc dstrbuton A new operator wthout prevous networks does not have the data of cell traffc. In ths case, a method s presented here that estmates the spectrum requrements assumng a certan cell traffc dstrbuton. An exponental and a normal dstrbuton are consdered. In addton, a case n whch the traffc of each cell s equal s consdered. Let Y k denote an ndependent and dentcal random varable for the cell traffc n the k th cell for k = 1,,N C. The expected total traffc n a regon s E ( Nc ) Y k = N c E[Y ], k=1 whch s equal to T R n Eq. (4). Ths yelds E[Y ] = N UT U N C (1 h). (9) Assumng that Y s exponentally dstrbuted wth parameter θ, E[Y ] = 1/θ. Let ˆθ denote an estmator of θ. Applyng the method of moments n [27] yelds ˆθ = 1 E[Y ] = (1 h)n C N U T U. Let F defne a random varable for the requred number of carrers n a cell. Ths corresponds to f k n Eq. (6) wth real values. It s clear that F = Y /C Q. Ths gves G(m) = P(F < m) = P(Y < mc Q ) = 1 e ˆθmC Q. (11) Let S exp denote the spectrum requrements under the assumpton of an exponental cell traffc dstrbuton. Usng Eq. (11) gves [ S exp = ln(α)n ] UT U B, (12) N C C Q (1 h) where the notaton [x] denotes the maxmum nteger that s less than the real value x. Next, t s assumed that the traffc n each cell s equal. Hence, T k = E[Y ]. Substtutng E[Y ] n Eq. (9) wth T k n Eq. (6) gves f k = N U T U N C C Q (1 h) for k = 1,,N C. (13) Let S equal denote the spectrum requrements when the cell traffc s equal. Let us defne M = [f k ]. From Eq. (7), t s straghtforward that G(M) = 0 and G(M + 1) = 1. Ths yelds [ ] N U T U S equal = B. (14) N C C Q (1 h) Note that the spectrum requrement s equal to Eq. (14) when α = e 1. Ths mples that a case wth equal cell traffc s equvalent to splttng the e 1 porton of cells wth exponentally dstrbuted cell traffc. (10)

7 W.S. Yang et al. / Estmaton of spectrum requrements for moble networks wth self-smlar traffc, handover 287 Table 1 C Q and carrer requrements compared wth H = 0.5 H C Q Carrer requrements compared to H = Table 2 f k, an example k f k Table 3 G(m), an example m G(m) 0% 0% 20% 30% 70% 100% Fnally, a heurstc method s presented that estmates the spectrum requrements when the cell traffc s normally dstrbuted. Let ˆµ and ˆσ 2 denote the estmators of the mean and varance, respectvely. Usng the method of moments [27], ˆµ s equvalent to E[Y ] n Eq. (9). The random varable Y s postve as t represents traffc. However, t can have a negatve value because t follows a normal dstrbuton. Let β = P(Y < 0). β can be nterpreted as a statstc pertanng to the valdty of Y. Thus, ˆσ 2 s obtaned under a gven value of β. Let S nor and M nor denote the spectrum requrements and the carrer requrement wth a normal cell traffc dstrbuton. Summarzng the above results yelds S nor = M nor B, (15) where M nor s obtaned by M nor = max {m : P(Y < mc Q ) < 1 α}, and Y s normally dstrbuted wth ˆµ n Eq. (12) and ˆσ 2, whch satsfes P(Y < 0) = β. 7. Numercal example Modfyng the frequency of the common packet szes as n [22] yelds a dscrete dstrbuton for packet length, as follows: There are fve types of packet lengths, 40, 52, 576, 1420, and 1500 bytes, wth probabltes of 0.42, 0.06, 0.24, 0.06, and 0.22, respectvely. It s assumed that the delay requrement s 0.1 and C F = 8.8 Mbps. Table 1 shows that the case wth H = 0.95 requres double the carres of the case wth H = 0.5. Ths mples that more carrers are needed wth hgher self-smlarty. Next, let us assume that there are 10 cells and f k n Eq. (6) has the followng values. Then, we have G(m) n Eq. (7) as follows. When α = 0.1, the carrer requrement becomes 5. In Table 2, three cells requrng sx carrers are splt. Fnally, we show numercal examples wth a cell traffc dstrbuton. Suppose that B = 10 MHz, h = 12%, N C = 30, N U = 50000, T U = 23 Kbps, and β = 0.1%. An operator can obtan the real values of the above parameters. The delay requrement depends on the QoS polcy. The moble networks that an operator deploys determnes C F and B. The handover scheme that an operator mplements determnes

8 288 W.S. Yang et al. / Estmaton of spectrum requrements for moble networks wth self-smlar traffc, handover Fg. 1. Spectrum requrements over H when α = 10%. Fg. 2. Spectrum requrements over H when α = 20%. h. A moble operator s busness plan contans N U, T U, and N C to desgn moble networks and analyze the cost and revenue. Fgure 1 shows that the spectrum requrements over Hurst parameter H. As mentoned n Secton 1, self-smlar traffc s bursty. Traffc wth hgher values of H requres more capacty than Posson traffc. A moble system requres more capacty to accommodate traffc wth hgher self-smlarty. Accordngly, the spectrum requrements ncrease over H n Fg. 1. Ths trend holds even though the cell traffc dstrbuton changes. On the other hand, the spectrum requrements wth H = 0.9 are twce what they were wth H = 0.5. Spectrum requrements are essental parameters when a government desgns and allocates the spectrum, the natonal resource. Consequently, gnorng self-smlarty may cause estmaton errors and result n an neffectve and neffcent spectrum polcy. Next, the spectrum requrements drop as α ncreases from 10% to 20% n Fgs 1 and 2, respectvely. The results are apparent snce more cells are splt wth a hgher value of α. Ths observaton has mportant mplcatons n the economc operaton of spectrums for moble operators. Addng carrers to obtan a spectrum ncreases the cost. Smlarly, addng base statons ncurs nvestment and operatonal costs. Then, operators can analyze the optmal spectrum operaton, comparng the costs between addng new carrers and addng new base statons, whch mples a cell-splt. Fgures 3 and 4 show that an addtonal spectrum s needed at a hgher handover rato. The results are clear snce handover traffc s an addtonal load on moble systems. As a result, self-smlarty, handover, and frequency reuse affect the spectrum requrements consderably.

9 W.S. Yang et al. / Estmaton of spectrum requrements for moble networks wth self-smlar traffc, handover 289 Fg. 3. Spectrum requrements over H wth exponental cell traffc dstrbuton. 8. Concluson Fg. 4. Spectrum requrements over H wth normal cell traffc dstrbuton. Ths study consdered three factors that should be nvolved n estmatng spectrum requrements: selfsmlarty n data traffc, handover, and frequency reuse. An approxmate average cell capacty subject to self-smlar traffc was presented. It was shown that handover traffc was an addtonal load n some handover scenaros. The cell-splt operaton under the frequency reuse of one was consdered. An estmaton method of the spectrum requrements was presented that utlzes the cell traffc nformaton of a prevous network. In addton, the estmaton method handled cell traffc dstrbuton. Numercal examples demonstrated that the spectrum requrements were senstve to self-smlarty, handover traffc, and the proporton of cell-splt operatons. Our study demonstrated that consderng these factors s essental to guaranteeng the accuracy of spectrum demand estmatons. Acknowledgements Ths paper has been supported by the 2010 Hannam Unversty Research Fund. Ths research was supported by the MKE(The Mnstry of Knowledge Economy), Korea, under the ITRC(Informaton Technology Research Center) support program supervsed by the NIPA(Natonal IT Industry Promoton Agency) (NIPA-2010-(C )).

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11 W.S. Yang et al. / Estmaton of spectrum requrements for moble networks wth self-smlar traffc, handover 291 Won Seok Yang receved hs master s degree and Ph.D. from KAIST(Korea Advanced Insttute of Scence and Technology), Daejeon, Korea. Currently, he s a professor of Department of Busness Admnstraton at Hannam Unversty. Hs research nterests nclude stochastc modelng, queueng theory, producton management, telecommuncaton networks and polcy, nformaton securty. Eun Saem Yang receved her master s degree and Ph.D. from Kangwon Natonal Unversty, Chuncheon, Korea. She s currently workng as a professor of Department of Computer Engneerng at Hallym Unversty. Her research nterests nclude moble and wreless systems, nterworkng of heterogeneous wred and wreless networks and moblty management. Hwa J. Km was born n Seoul n He receved the M.S. and Ph.D. degree at KAIST(Korea Advanced Insttute of Scence and Technology) all n Electroncs Engneerng. He s currently workng as a professor at Kangwon Natonal Unversty, Korea snce Hs work s related to the area of communcaton protocol and network programmng. Dae K. Km receved hs master s degree and Ph.D. from Kangwon Natonal Unversty, Chuncheon, Korea. Currently, He s a professor of Department of Informaton Communcaton and Computer Networks at Hallym College. Hs research nterests nclude communcaton systems and network archtecture.

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