GPRS performance estimation in GSM circuit switched services and GPRS shared resource systems *

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1 GPRS performance estimation in GSM circuit switche serices an GPRS share resource systems * Shaoji i an Sen-Gusta Häggman Helsinki Uniersity of Technology, Institute of Raio ommunications, ommunications Laboratory, P.O. Box 23, Otakaari 8, 25 FI-HUT, Finlan, Abstract GPRS is esigne for transmitting packet ata an suppose to take its raio resource from the pool of channels unuse by GSM oice serices. The number of channels allocate to GPRS is a ranom ariable epening on the oice traffic. In this paper, an metho is use for ealuating the GPRS performance of single-slot serice in the ariable raio resource. The metho coul be use for ealuating the GPRS performance when the aerage serice time of circuit switche serices is much longer than that of GPRS. The multi-slot serices cause higher blocking probability an longer elay to the network than the single-slot serice. Howeer, those effects can be reuce by implementing a GPRS resource allocation scheme with flexible multi-slot serices. I. ITRODUTIO The current metho of ata transmission in the pan-european Global System for Mobile ommunications (GSM) an the American Aance Mobile Phone Stanar (AMPS) cellular networks is circuit switching. This technique reseres the traffic channel for the entire communication time, an wastes the raio resource when ata traffic occurs in bursts with long silent interals. In the eelopment of GSM phase 2+, the European Telecommunications Stanar Institute (ETSI) has specifie a general packet raio serice (GPRS) oer the GSM to increase the utilization efficiency of the raio resource. The physical channels unuse by circuit switche serices are allocate ynamically to the GPRS accoring to the actual nees for packet transfers. Earlier stuies of GPRS performance foun in the literature [-2] focus on the protocol behaior with a fixe number of channels use for ata transmission. Howeer, the number of channels aailable to GPRS is a ranom ariable epening on the oice traffic an the oice channels occupancy, thus, the serice statistics is a moable bounary Marko process [3-4]. The analysis of GPRS performance is a complicate problem especially as multiple classes of quality of serice an multiple classes of users are supporte in GPRS. In this paper, the GPRS performance, e.g., the aerage queueing time an blocking probability, in the ariable resource is ealuate by an metho an simulations. The paper is organize as following: in section II, the principles of the raio resource allocation for GPRS calls are escribe; in section III, an metho for ealuating the performance of single-slot serice is introuce an the performance of GPRS is iscusse by the metho an simulations; the multislot serices are iscusse in etail; the conclusions are gien in section IV. II. PRIIPLES OF THE RESOURE ALLOATIO FOR GPRS GPRS is esigne to support from intermittent an burst ata transfers to occasional transmission of large olume of ata. The GPRS an GSM circuit switche serices share the same raio resource. Wheneer a channel is not use by circuit switche serices, it may be utilize by GPRS. The allocation of physical channels for GPRS can be base on the nees for actual packe transfers which is referre to as capacity on eman principle. When the packet ata channels (PDHs) share by all GPRS users are congeste ue to the GPRS traffic loa an more resource aailable in the cell, the network can allocate more physical channels as PDHs. The GPRS oes not require permanently allocate PDHs. The operator can ecie to eicate permanently or temporarily some physical channels for GPRS traffic. Howeer, the high spee circuit switche ata (HSSD) serice supports as well multiple slot serices an has higher priority to access the physical channels. As the introuction of HSSD serice into the GSM system, it might be ifficult to guarantee the quality of serice of GPRS if no channel is eicate to GPRS. The number of allocate PDHs in a cell can be increase or ecrease accoring to eman. In orer to implement this principle, a loa superision function, which monitors the loa of the PDHs an the number of allocate PDHs in a cell can be increase or ecrease, must be use in the system. Upon resource eman for circuit switche serices, some PDHs must be release as soon as soon as possible. The release can hae two alternaties: ) Immeiate Release: the GPRS user is force to stop its transmission until resource is aailable for GPRS again an the channel release by GPRS is allocate to circuit switche serices. 2) Delaye Release: the GPRS user can continue its transmission up to some frames or until the ening of packet transmission, before the channel is allocate to circuit switche serices. In the paper, the immeiate release is assume in orer to inestigate the relation between the aerage interruption time an interrupting probability an the GPRS traffic. If the aerage interruption time an interrupting probability are low, * The project is financially supporte by okia Research enter, Sonera, Technology Deelopment enter of Finlan an Helsinki Telephone ompany.

2 the Delaye Release protocol can be consiere to simplify the system. III. GPRS PERFORMAE EVALUATIO A. System moel For a system with m physics channels, m channels are share by oice an GPRS serices an m channels are eicate to GPRS (Fig. ). In the pool of m channels, when channels are not use by oice serices, those channels are use for GPRS transmission. The oice serices own preemptie priority oer GPRS, i.e., wheneer channels use by the GPRS serice are neee by oice serices, the GPRS transmission in those channels is stoppe until some channels are aailable for GPRS. The users interrupte serice hae higher priority for resource allocation than those in queue. 2 m m Voice m Data m Fig.. Illustration of raio resource structure allocate to GSM oice serices an GPRS. The number of m channels are share with oice an GPRS serices an m channels are eicate to GPRS. Assume that oice users arrial is a Poisson process with a rate of λ an the call serice time is exponentially istribute with a mean of /µ. All GPRS users share the physical channels unuse by the oice serices. The arrial of GPRS ata users are assume to be a Poisson process with rate λ an the serice time is exponentially istribute with a mean of /µ. The maximum number of ata users accepte into the system (in serice an queue) is. GPRS calls are sere accoring to the first in first out (FIFO) principle. The arriing GPRS user is allowe to transmit ata if a sufficient number of free channels is aailable; otherwise it is queue or blocke. B. An Approximation Metho for Performance Ealuation The oice serices are inepenent of GPRS. Because GPRS is mainly esigne to transmit intermittent an burst ata, the serice time of GPRS is rather smaller than that of oice serices. As an, the ecomposition technique [4] can be use to analyze the GPRS performance. The essential of this technique is to use the oice serices probability istribution to escribe the interaction of oice serices to GPRS. Thus, the GPRS performance in the ynamically ariable resource is obtaine by combining this istribution with the performance in a fixe resource. For the oice serices, the probability of n users in serice is λ n rn = r ( ), n =, 2,..., m () µ n! where r m n = λ ( ) µ n! The channels unuse by the oice serices may be use for the ata serices. The probability of x channels aailable for the ata serices is equal to that of m -x channels use by oice serices an is obtaine as by (): λ m x gx ( ) = r ( ), x =, 2,..., m (2) µ ( m x)! For the transmission of single slot GPRS in a fixe number of channels, the aerage queueing time can be obtaine from the M/M// queueing system, where is the maximum number of users in the system (in serice an in queue). The steay-state probability p n is: n ρ p n< n!, pn = (3) n ρ p n n,! where n is the number of users in the system, ρ = λ /µ an n n ρ ρ p = [ + + n ] n!! ρ + = [ ρ n ρ ( ( ) ) + ] n!!( ρ / ) A new arrial is accepte into the system only if the number of GPRS users in the system is below the maximum accepte number. Otherwise, the new arrial is blocke. The blocking probability is ρ P ( ) = p (4)! The aerage number of user in the system is obtaine as n n ρ nρ W ( ) = np n = p ( + n ) ( n )!! + n ρ = p{ + ( n )!! ρ + ρ + 2 ρ + ρ + 2 ( + )( ) ( ) ( + )( ) + ( ) } (5) ρ 2 ( ) ombining (2) with (4) an (5), the aerage blocking probability, throughput an aerage queueing time of single slot GPRS in a ynamically arie resource are obtaine as following expressions respectiely: m P = g( x) P ( x+ m ) x= (6) TH = λ ( P) (7) m T = gxwm ( ) ( + x) (8) λ ( P) µ x= For multiple class (slot) serices, it is ery ifficult to analyze the state istribution probability of queueing system een in a fix number of transmission channels because of the large size of the state space. Here, we use simulation to ealuate the performance.

3 . umerical an Simulation Results For single slot serice, the results from the an simulation are presente, but for multiple slot serice, only results from simulation are gien. In the numerical calculations an simulations, 4 carriers, i.e., 4 8=32 channels in a cell are assume, from which channel is resere for GPRS ata an 3 channels are share by circuit switche serices an GPRS. In the simulations, when a new circuit switche call arries, if no free channel is aailable an the number of circuit calls in serice is below 3, one of GPRS calls is stoppe its transmission in orer to allocate one channel to the new circuit call. When resources are aailable, the interrupte GPRS calls hae higher priority to be allocate resource than the queueing calls. The aerage interruption time an probability of interruption are simulate. The aerage serice time of circuit switche serices is exponentially istribute with a mean of 8 s. This traffic loa of circuit serices is Erlang corresponing to 2% blocking probability for 3 channels. The maximum number of GPRS users allowe into network is 4. coing scheme is mainly use for signaling traffic an 2, 3 an 4 coing schemes are use for user ata traffic. The 2 scheme corresponing with a transmission rate of 3.4 kb/s is assume to be use. The GPRS message size is exponentially istribute with means of kb, kb, 3.4 kb respectiely, corresponing to the mean serice time (/µ) of 2s, 5s an s with single slot transmission. The results of single slot serice are calculate from (6) an (8). Fig. 2, 3 an 4 show the mean queueing time an blocking probability of single-slot serice istribute to the traffic loa for the aerage serice time (/µ) of 2s, 5s an s respectiely. In this paper the aerage interruption time is inclue into the mean queueing time. omparing the results with simulation results, we fin the metho coul be use for ealuating the GPRS performance when the aerage serice time of circuit switche serices is much longer than that of GPRS, e.g., µ /µ >. As the aerage serice time of GPRS increases, the error becomes larger. The reason of error might be that the metho oer-estimates the blocking probability (Fig. 4). The simulations show that the interruption probability of GPRS calls epens on the aerage message size (serice time) more strongly than on the traffic loa. In the simulations of multislot serices, the traffics in Table are use. Two schemes are use for resource allocation to GPRS calls. - scheme-: On the arrial of a multislot (two or three slots) call from the queue, if the aailable channels are not enough for the call s requirement, it still stays in queue until its resource requirement is fulfille. - scheme-2: On the arrial of a multislot (two or three slots) call from the queue, if the aailable channels are not enough for the call s requirement, the aailable channels are allocate to the call. TABLE: GPRS traffics Traffic- All arrial traffics are require single-slot serice. Traffic-2 In the arrial traffics, 7%, 2%, % of them are require single-slot, two-slots an three-slots serices respectiely, i.e., λ=λ /.7=λ 2 /.2=λ 3 /.. Traffic-3 In the arrial traffics, 5%, 3%, 2% of them are require single-slot, two-slots an three-slots serices respectiely, i.e., λ=λ /.5=λ 2 /.3=λ 3 / simulation Traffic loa(erlang) Fig2. The mean queueing time of single-slot serice for the aerage serice time (/µ) of 2 s simulation (/µ=5 s) simulation (/µ= s) Traffic loa(erlang) Fig3. The mean queueing time of single-slot serice for the aerage serice time (/µ) of 5 s an s respectiely simulation(/µ=2 s) simulation (/µ=5 s) simulation(/µ= s) Traffic loa(erlang) Fig. 4 The blocking probability of single-slot serice for the aerage serice time (/µ) of 2 s, 5 s an s respectiely.

4 Fig. 5 an 6 show the mean queueing time of the three types of serices with the resource allocation scheme- istribute with the call arrial rate for the aerage message size of kb an kb respectiely. The soli lines are use for the traffic-3 an the ashe lines for traffic-2. In the same traffic type, the mean queueing time of the three types of serices oes not hae much big ifference, but it is much higher than that of single-slot serice. Fig. 7- show the mean queueing time (aerage for all sere calls) an blocking probability with resource allocation scheme- an scheme-2 istribute with the call arrial rate for the aerage message size of kb an kb respectiely. The performance of scheme-2 is better than that of scheme- an is similar to that of the single-slot-serice system. To inestigate the multislot serice, a parameter of the multislot sere rate is efine as: sere rate = number of calls sere for three slots (or two slots) number of calls require for three slots (or two slots) 3 slots (2%) 2 slots (3%) slot (5%) 3 slots (%) 2 slots (2%) slot (7%) Fig. 5 The mean queueing time of the three types of serices with the resource allocation scheme- for the aerage message size of kb. The soli lines are use for the traffic-3 an the ashe lines for traffic slots (2%) 2 slots (3%) slot (5%) 3 slots (%) 2 slots (2%) slot (7%) Fig. 6 The mean queueing time of the three types of serices with the resource allocation scheme- for the aerage message size of kb. The soli lines are use for the traffic-3 an the ashe lines for traffic traffic-3(strategy-) traffic-2(strategy-) traffic-(single slot) Fig. 7 The mean queueing time (aerage for all sere calls) with resource allocation scheme- an scheme-2 for the aerage message size of kb traffic-3(strategy-) traffic-2(strategy-) traffic-(single slot) Fig. 8 The aerage blocking probability with resource allocation scheme- an scheme-2 for the aerage message size of kb. Fig. shows the sere rate of multislot serices with resource allocation scheme-2 istribute with call arrial rate for the aerage message size of kb an kb respectiely. The soli lines are use for an aerage message size of kb an ashe lines for an aerage message size of kb. For the traffic with the same aerage message size, the sere rate for the same type of multislot serice is almost same een though those traffics hae ifferent percentage of multislot serice traffics. The sere rate ecreases as the increment of call arrials an the aerage traffic size. Therefore, the resource allocation scheme-2 not only can reuce the blocking probability an elay cause by multislot serices, but also can aapt to the GPRS traffic to proie the optimal performance to the network The simulations of the multislot serices also show that the interruption probability of GPRS calls epens on the aerage message size more strongly than on the traffic loa. Those simulations show that the higher blocking probability an longer elay cause by multislot serices coul be reuce by using a flexible multislot serice scheme. The protocol of a flexible multislot serice scheme is:

5 on the arrial of a multislot call, - if the aailable resource is enough to proie its require serice, the call is allowe to transmit its require rate; - if the aailable resource is not enough to proie its require serice, the network negotiates with the call to reuce its transmitte rate to the alue which the network can proie; - if the call agrees to transmit with the rate which the network can proie, the network further inquires the call if it wants to restore its require transmission rate when the network can proie; - if the call oes not agree to reuce its transmission rate, put it into the queue until the network can proie its require transmission rate. IV. OLUSIOS In this paper, an metho is use for ealuating the GPRS performance of single-slot serice in the ariable raio resource. By the comparison of numerical results an simulate results, it shows that the metho coul be use for ealuating GPRS performance when the aerage serice time of circuit switche serices is much longer than that of GPRS, e.g., µ /µ >. The simulations show that the interruption probability of GPRS calls ue to releasing its channel to the eman of circuit switche serices epens on the aerage message size more strongly than on the traffic loa. The multi-slot serices cause higher blocking probability an longer elay to the network than the single-slot serice. Howeer, accoring to the simulation those effects can be reuce by implementing a GPRS resource allocation scheme with flexible multi-slot serices. In this scheme, when the aailable network resource cannot proie a call with its require transmission rate, the network negotiates with the user an agrees on a transmission rate which the network can proie. REFEREES [] G. Bianchi, A.apone, L. Fratta, L. Musumeci, Packet Data Serice oer GSM etworks with Dynamic Stealing of Voice hannels, in proceeings of IEEE Globecom 95, 3-7 o. 995, Singapore, pp [2] D. Turina, P. Beming, E. Schster, A. Anersson, A Proposal for Multi-slot MA Layer Operation for Packet Data hannel in GSM, in proceeings of IUP'96. Sep 29-Oct 2 996, ambrige, USA, pp [3] J.E. Wieselthier an A. Ephremies, Fixe- an Moable Bounary hannel-access Schemes for Integrate Voice/Data etwork, IEEE Trans.on ommuni. Vol. 43, o., January 995, pp [4] S. Ghani an m. Schwartz, A Decomposition Approximation for the Analysis of Voice/Data Integration, IEEE Trans.on ommuni. Vol. 42, o. 7, July 994, pp traffic-3(strategy-) traffic-2(strategy-) traffic-(single slot) Fig. 9 The mean queueing time (aerage for all sere calls) with resource allocation scheme- an scheme-2 for the aerage message size of kb traffic-3(strategy-) traffic-2(strategy-) traffic-(single slot) Fig. The aerage blocking probability with resource allocation scheme- an scheme-2 for the aerage message size of kb. Sere rate traffic-2(2 slots) traffic-3(3 slots) Fig. The sere rate of muitlslots serices with resource allocation scheme-2 for the aerage message size of kb an kb respectiely. The soli lines are use for the aerage message size of kb an ashe lines for the aerage message size of kb.

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