Proceedngs of the 3th WSEAS Internatonal Conference on COMMUNICATIONS Traffc Modelng and Performance Evaluaton n GSM/ Networks Cornel Balnt, Georgeta Budura, Marza Eugen Poltehnca Unversty of Tmsoara Bd.. Parvan. No. 2 ROMANIA cornel.balnt@etc.upt.ro, georgeta.budura@etc.upt.ro Abstract: - The sharng of resources between dfferent users and dfferent servces s a key concept of rado resources dmensonng n GSM/ networks. In ths paper we present dmensonng rules based on traffc evaluaton and qualty of servce level for GSM/ users, focused on two rado resources allocaton strateges: (Complete Parttonng) and PP( Partal Parttonng).The qualty of servce s gve by the blockng probablty accordng to Erlang-B formula for voce users meanwhle for users the ndvdual throughput and the blockng probablty represent the performance parameters. The preempton probablty of voce over data users s also consdered. Key-Words: - GSM,, modelng, blockng probablty, Erlang-B law, Engset law, throughput Introducton The Internet popularty creates a large number of servces avalable onlne. These nclude, World- Wde-Web browsng, E-Mal,... The ntegraton of General Packet Rado Servce and Enhanced nto GSM system world wde rases many problems. For networks operators, equpment vendors and system ntegrators dmensonng rules have to be developed to plan and estmate the rado capacty that s needed for the predcted amount of data users when the rado resources are shared between crcut and packet swtched servces. GSM operators have been dmensonng ther networks for voce servce n terms of offered voce traffc and blockng probablty. The reference model for ths system s the Erlang-B formula []. Ths formula gves the proporton of calls that are blocked as a smple functon of system capacty and traffc ntensty. The network s desgned for supportng several types of data traffc such as Wap, Web, E-Mal, etc. Therefore traffc process characterzaton s very demandng. Usually the data traffc s very bursty and reles to the applcaton. A communcaton sesson may last for an extended perod of tme wth ntermttent packet transmssons. On the other hand the servce allows dynamc allocaton of bandwdth resources. Wreless channels are allocated to a moble termnal based on ts traffc demands whch results n a better resource utlzaton. Ths traffc behavor coupled wth flexble bandwdth allocaton n a network represent the startng pont for constructng an approprate model n order to evaluate the performance and to establsh dmensonng rules for the system. Another maor problem of GSM/ networks dmensonng s the choce of strategy to partton the avalable cell capacty between tradtonal GSM and new servces. The Rado Resources Manager (RRM) s n charge of optmzng the usage of rado resources, based on a specfc resource sharng algorthm. In ths paper we wll consder two statc resources sharng schemes: - In the frst one, called Complete Parttonng (), tme-slots (TS) are dvded nto two sets and each type of traffc s allowed to use only ts dedcated set. - The second scheme known as Partal Parttonng (PP), contans the followng channel sets: one set shared between voce and data traffc and two sets each one beng reserved for strct usage of ts dedcated traffc: voce or data. Ths scheme, offers many advantages: frst, reservng a set of tme-slots for each type of traffc allows guaranteeng, as n a mnmum QoS for each type of traffc. Second, PP scheme provde a better effcency than whch s not sutable for mzng rado utlzaton, especally n hghly varyng demand. ue to these advantages PP s wdely mplemented n a number of actually operatng GSM/ networks. Several papers have been publshed on traffc modelng and performance evaluaton n GSM/ networks. The maor works n ths feld ISSN: 79-57 47 ISBN: 978-96-474-98-7
Proceedngs of the 3th WSEAS Internatonal Conference on COMMUNICATIONS are based on analytcal models usng queung theory and contnuous-tme Markov chans, and assumng an nfnte number of users n the cell [], [2] - [5]. In [7]-[9] analytcal models based on dscrete-tme Markov chans have been proposed and a sngle type of traffc (data traffc) s consdered. It s assumed to be generated by a fnte number of users and modeled by an Erlang-lke law. Other work s based on the modfed Engset model [6]. In our study we frst ntroduce some performance parameters for networks and then we propose a dmensonng method for estmatng the number of TS allocated for each traffc type. 2 System escrpton Our paper consders a sngle cell submtted to two dfferent types of traffc: GSM voce calls and data flows. In tradtonal crcut-swtched GSM networks, on each frequency carrer a 2 khz bandwdth s shared between 8 voce calls. Each voce call s gven a crcut, also called tme-slot (TS) because t s a Tme-vson multplexng scheme (TMA). Each voce call needs the assgnment of a sngle tme-slot for ts entre duraton. data traffc uses the same rado nterface as GSM voce calls hence rado resources avalable n the cell have to be shared among GSM and traffcs. As a remnder s a packet swtchng technology over crcut-swtchng based GSM system. In technology a moble staton can use several tme-slots smultaneously for one applcaton data flow to perform ts transmsson wth a hgher throughput. Each tme-slot can be shared among several users by assgnng dfferent Temporary Flow Identtes (TFI) to the mobles. Each TFI dentfes a physcal connecton called Temporary Block Flow (TBF). Up to 32 TFI s can be allocated per TMA frame due to the 5 bts allocated for TFI encodng at TRX level. ata flows are multplexed by a PCU- based schedulng algorthm. In addton to tme-slot parttonng, system allows tme-slot aggregaton: for a sngle moble user the system can allocate up to d- tme-slots smultaneously for downlnk and up to u- tme-slots smultaneously for uplnk, dependng on moble staton capablty class (d+u). The choce of the number of TBF s that a PCH can have n uplnk and downlnk depends on the operator s choce. For example, n Alcatel-Lucent technology up to 6 uplnk and downlnk TBF s are allocated per PCH. Our study s focused on the rado allocator whch dstrbutes the downlnk rado channels among voce calls and data flows. We make the followng assumptons regardng the system to be modeled: - TS : the number of tme-slots of the TMA parttoned nto a contguous set of TS tme-slots dedcated to voce calls, TS tme-slots shared between voce and data and TS tme-slots dedcated to ; tme-slots used by data TS + TS are on a sngle TMA whch has a total of 8 tme-slots. - d (resp. u ): s the number of tme-slots that can be used smultaneously for downlnk (resp. uplnk) traffc. All mobles have the same rado capablty, denoted d + u. - The RLC rado block sze and the data rate accordng to the codng are ndcated n TABLE. TABLE Codng CS- CS-2 CS-3 CS-4 Schemes RLC block rado 23 33 39 53 (bytes) ata rate: μ ( kbts / s ) 9.5 3.4 5.6 2.4 - oce calls have a preemptve prorty over data flows on the shared part of the TMA due to the fact that they generate the largest amount of revenue n most actual operatng systems. As a consequence, f all TS tme-slots dedcated to voce are occuped and all TS tme-slots are n use wth at least one of them allocated to data, then one tmeslot assgned to traffc n the shared part of the TMA wll be reallocated to voce on the arrval of a GSM request. 3 System Model 3. Cells wth Complete Parttonng Strategy Complete Parttonng strategy allows two separate sets of tme-slots dedcated to voce respectvely to data. As a consequence the GSM and systems can be analyzed separately. 3.. oce traffc model The classcal Markov chan model apples for voce. The steady-state voce probabltes gven by relaton () are generated by the brth-death structure of ths model shown n Fg.. ISSN: 79-57 48 ISBN: 978-96-474-98-7
Proceedngs of the 3th WSEAS Internatonal Conference on COMMUNICATIONS t p ()! t = t, t [, TS] TS! () of actve users n progress and represents a fnte state space. λ λ Fg. The brth-death model appled to voce traffc process λ = represents the voce traffc. μ Obvously the Erlang-B [] formula gves the call blockng probablty necessary to dmenson the cell n order to guarantee a mnmum QoS for voce traffc. B, TS TS = TS!! (2) 3..2 ata Traffc Model ata traffc s modeled assumng that there s a fxed number N of data mobles n the cell. Each moble s dong an ON/OFF traffc wth an nfnte number of pages: ON perods correspond to the download of an element lke a WAP, a WEB page, an emal, a fle, etc. Its sze s characterzed by a dscrete random varable X on, wth an average value E[ σ ]. OFF perods correspond to the readng tme of the last downloaded element, whch s modeled as a random varable T off wth an average value of τ seconds. The mum number of users n actve transfer s gven by: n ( TS ) = mn( N,32, mts ) (3) t t t + tμ ( t + ) μ m- s the mum number of users that can use a sngle tme-slot. The system model s based on the Engset model [6] and ncludes partcular specfcatons as ndcated n Fg.2. Ths stochastc process descrbes the number Fg.2 The Engset model appled to data traffc process As can be seen from Fg. 2 the transton rate from state to +, λ, s gven by: λ = ( N ) λ = ( N ), τ for =,, n (4) We can express the transton rate of death process as: μ μ = mn( d, TS) μ = mn( d, TS), E[ σ] (5) for =,, n As ndcated n Fg.2, the state of the Markov chan corresponds to the number of the data mobles that are smultaneously n actve transfer (n ON state). The mum bandwdth capacty they can use sts. Because of the mum downloadng capacty d of each moble, two stuatons can be dstngushed: () If d < TS, the avalable bandwdth s not fully utlzed by data mobles. As a consequence the transton rate from state to state, gven by the accomplshed transfer of one moble, s μ d E [ σ ] ; (2) If d TS the allocator has to share the TS tme-slots among the data mobles and the transton rate from state to state s μ TS E[ σ ] ; Let p ( ) be the steady-state probablty that users are n actve transfer. Accordng to the Engset model t s gven by the closed form here below: p ( ) = p () CN TS μ mn( d, ) E[ σ] τ (6) ISSN: 79-57 49 ISBN: 978-96-474-98-7
Proceedngs of the 3th WSEAS Internatonal Conference on COMMUNICATIONS We can express the steady-state probablty n terms of data traffc, defned by relaton (7): E[ σ] = τ μ CN p ( ) = p () TS mn( d, ) (7) (8) As can be seen the steady-state dstrbuton depends E[ σ] only trough the rato on data traffc τ parameters E[ σ ] and τ. Based on ths dstrbuton we have calculated the average performances of the system. As performance measures the average downlnk throughput per user ( X u ), the average downlnk total throughput ( X ) and the blockng probabltes ( B ) for data are consdered. All these parameters are functon of the load, the avalable cell capacty TS; TS, the user capablty d and the total number N of users. The average total throughput was determned usng the expresson bellow: X = p ( ) r( ) (9) = where r() represents the effectve bandwdth receved by each user: TS r( ) mn( d, ), for,, n = μ = () From formula (9) we derve the average throughput per user: X p( )mn( d, TS ) X = u/ = = μ E[ ] = p( ) () The data blockng probablty can be expressed based on Engset model as follows: CN B = p() n (2) mn( dts, / ) and represents the probablty that TS tme-slots are beng used by n users among the other ( N ) users. 3.2 Cells wth Partal Parttonng Strategy In ths case, the avalable tme slots (TS) of the TMA are parttoned nto TS tme-slots dedcated to voce, TS tme-slots dedcated to data and TS tme slots shared between voce and data wth a total preemptve prorty of voce over data on the shared part as mentoned before n Secton 2. TS = TS + TS + TS (3) 3.2. oce traffc model The voce traffc process s modeled as mentoned before by relaton (). As voce has a preemptve prorty over data, the blockng probablty for voce can be obtaned by Erlang-B formula (because data traffc s transparent to voce), wth a number of resources equal to TS + TS: B ( TS + TS) ( TS = + TS )!, PP TS + TS! (4) 3.2.2 oce traffc model The model appled to ths system has to deal wth two traffc processes: voce and data, sharng the same ar nterface and usng the same physcal channels. In our prevous work [] we have mplemented the b-dmensonal model proposed n [8] and have deduced the blockng probabltes formulas accordng to the PP strategy. In ths paper we appled the modfed Engset model proposed n [6] to analyze the performances and to establsh dmensonng rules. The basc dea n constructng the model reles on 2 assumptons: the voce calls are ndependent of connectons and the voce and data traffc evolves at dfferent tme scales. The tme requred to transfer data s about several seconds and should be shorter than the mean call duraton whch s about several mnutes. As a consequence between two varatons of the number of voce calls, the number of data transfers reaches ts statonary regme. For voce calls the steady-state probabltes are gven by relaton () wth the mum number of avalable resources equal to: TS TS. Among the TS tme slots, those not used by the voce calls may be used for data traffc wth a probablty ISSN: 79-57 5 ISBN: 978-96-474-98-7
Proceedngs of the 3th WSEAS Internatonal Conference on COMMUNICATIONS equal to the probablty that TS TS s are used by GSM users: p( TS TS s). The data traffc model s constructed wth respect to the Engset model and the partculartes mposed by the resources sharng capablty as presented above. The total number of avalable resources s gven by: * = mn( N, 32, mts ) (5) * We denoted by TS the avalable cell capacty for data traffc. The average performance parameters are determned as follows: - the average throughput per user can be expressed as [6]: TS TS XuPP / = p( s) Xu / (mn( TS TS, TS s)) (6) dfferent offered voce traffc values:.62, = 2.94 and = 2. The frst two values correspond to the dfferent occupances of the tme-slots that can be used by voce: 3 and 7, consderng n that case a 2% for the lost voce traffc accordng to Erlang-B formula. The thrd traffc value corresponds to 7 voce TS occupancy but wth a blockng probablty closed to 9%. In Fg. 3 we have plotted the total average throughputs X and X PP, the average throughputs per user X u, and X upp, as well as the blockng probabltes B and B PP. = - for the total average throughput we propose the formula: TS TS X = p ( s) X (mn( TS TS, TS s)) (7) PP - the data blockng probablty s deduced smlarly as n [6]: TS TS B = p () s B (mn( TS TS, TS s)) (8) PP - fnally we propose a formula for estmatng the preempton probablty due to voce calls prorty over data users: TS TS BPPP, = p() s B(mn( TS TS, TS s)) (9) TS 4 Experments and results The models have been mplemented by smple programs wrtten n Matlab and varous scenaros were expermented. For the data traffc we have adopted the followng parameters: E[ σ ] = 5KB, E[ τ ] = 2s, moble class: 4+ and CS2 codng scheme ( μ = 3, 4 kbts / s ). In the frst scenaro we have consdered a cell wth strategy, equpped wth a sngle TRX that provdes: TS = 8, TS = 7, and TS =. In the second scenaro we have consdered a cell wth PP strategy, equpped wth a sngle TRX that provdes: TS = 8, TS = 3, and TS =. We have consdered three loadng stuatons, accordng to Fg.3 Performance parameters The PP scheme takes advantages regardng the throughput and the blockng probablty comparng wth scheme. The typcal network dmensonng problem s to compute how many tme-slots to allocate for data traffc. Current used dmensonng rules need to estmate the number of actve users per cell []. Our dmensonng method avods ths estmaton usng dmensonng crtera based on the throughput per actve user combned wth blockng probabltes n an nteractve algorthm. Blockng probabltes n commercally networks must be small enough n order to avod nterrupton caused by TBF reecton. As we can see n Fg 3 for a reasonable number of users n the cell the mnmum accepted throughput s reached, that means that the lmtng factor for dmensonng s the throughput rather then the blockng probablty. To llustrate the proposed rule, n Fg.4 we have ISSN: 79-57 5 ISBN: 978-96-474-98-7
Proceedngs of the 3th WSEAS Internatonal Conference on COMMUNICATIONS plotted as a detal of Fg.3 the throughput per user and the blockng probablty as functon of number of actve users n the cell, for two dfferent total tme-slots values. The same prevous PP scenaro was used for dmensonng algorthm llustraton, except that the ntal value of TS number was set to 7 (3 dedcated for voce, dedcated for data and 3 shared between voce and data). Fg.4 mensonng algorthm llustraton The A pont gves the number of actve users that can obtan a desred throughput value. Accordng to ths number the C pont ndcates the reached blockng probablty. If that probablty s greater that an mposed value, an ncrement of the number of tme slots gves the new users number (pont B) and the correspondng smaller blockng probablty (pont ). The algorthm wll be repeated untl the desred value for blockng probablty s reached. 5 Concluson In our paper we have ntroduced a dmensonng algorthm for GSM/ networks wth PP strategy. The proposed algorthm s based on performance parameters as the average downlnk throughput per user ( X u ), the average downlnk total throughput ( X ) and the blockng probabltes ( B ). All these parameters are functon of the cell load (voce and data), the avalable cell capacty, the user capablty d and the total number of users. As qualty crtera we have consdered the blockng probablty, accordng to Erlang-B law, for voce and the average downlnk throughput per user for data. References: [] L. Klenrock, Queung Systems: ol. I Theory, New-York Wley, 976 [2] S. Pedraza, J. Romero, J. Munoz, (E) Hardware mensonng Rules wth Mnmum Qualty Crtera, Proc. of IEEE TC Sprng, pp. 39-395, May 22 [3] C. Lndemann, A. Thummler, Performance Analyss of the General Packet Rado Servce, Computer Network, 4, pp. -7, Jan., 23 [4] S. N, S. Haggman, Performance Estmaton n GSM Crcut-Swtched Servces and Shared Resources Systems, WCNC, ol.3, pp.47-42, 999 [5] M. Mahdav, R. Edwards, P. Ivey, Performance Evaluaton of ata Subsystem n GSM/ Usng Complete Sharng, Proc. of London Communcatons Symposum, Unv. College of London, 2 [6] H. ahmoun,. B. Morn, S. aton, Performance Modellng of GSM/ Cells wth fferent Rado Resource Allocaton Strateges, IEEE Wreless Communcatons and Networkng Conference, March 25, olume 3, pp: 37-322 [7] B. Baynat, K. Boussetta, P. Esenmann, N. Ben Rached, screte-tme Markov Model for EGE/ Rado Engneerng wth Fntelength Sessons, Int. Symp. On Performance Evaluaton of Computer and Telecommuncaton Systems (SPECTS 24), San Jose, Calforna, USA, July, 24 [8] B. Baynat, K. Boussetta, P. Esenmann, N. Ben Rached, Towards an Erlang-lke Law for the Performance Evaluaton of /EGE Networks wth Fnte-Length Sessons, Proc. of 3 rd IFIP-TC6 Networkng Conference, May 24, pp. 288-293 [9] B. Baynat, P. Esenmann, Towards an Erlanglke law for /EGE network engneerng, Proceedngs IEEE ICC, June 24 []G. Budura, C. Balnt, E. Marza, Blockng Probabltes n GSM/(E) Cells wth fferent Rado Resources Allocaton Strateges, Scentfc Bulletn of Poltehnca Unversty of Tmsoara, Electronc and Telecommuncaton seres, Tom 53(67), Fasc.2, 28, pp. 85-92 []P. Stuckmann, O. Paul, mensonng GSM/ Networks for Crcut- and Packet- Swtched Servces, Proceedngs of the th Symposum on Wreless Personal Communcatons, Aalborg, enmark, 2, pp. 69-74 ISSN: 79-57 52 ISBN: 978-96-474-98-7