Single channel occupied voice and multi-channel occupied HSCSD over GSM

Computer Communications 25 2002) 522±533 www.elseier.com/locate/comcom Single cannel occupied oice and multi-cannel occupied HSCSD oer GSM Jaangir H. Sarker*, Seppo J. Halme Communications Laboratory, Helsinki Uniersity of Tecnology, PO Box 2300, FIN-02015 HUT, Finland Receied 13 July2001; accepted 13 July2001 Abstract Random access and traf c cannel parts are utilized, respectiely, for call establisment and information transmission in te uplink direction, comprising mobile to base station of te Global System for Mobile Communication GSM) networks. Voice V) and Hig Speed Circuit Switced Data HSCSD) calls use two parallel random access parts and a common traf c cannel part were a V call occupies a single traf c cannel and a HSCSD call occupies a multiple number of traf c cannels. A call is eiter rejected or blocked if it is unsuccessful eiter in te random access part or in te traf c cannel part. Te optimum number of random access slots is directlyproportional to te aerage access arrial rate. According to te speci cation, four types of retransmission cut-off policies can be executed in te random access part werein only one type can proide almost zero call rejection probability, pertaining to a limited amount of traf c arrial rate per random access slot. A complete analysis for te traf c cannel utilization and call blocking probability for V and HSCSD calls wit an exact number of random access slots in collaboration wit four different types of retransmission cut-off scemes is introduced. Te oerall call success probabilityis deised resorting to call rejection and call blocking probabilities. Results demonstrate tat te oerall call success probability can be independent of random access part up to a certain call arrial rate if a special type of retransmission cut-off is utilized. q 2002 Elseier Science B.V. All rigts resered. Keywords: Call blocked; Call rejection; GSM; HSCSD; Random access; Traf c cannel 1. Introduction Te core network of te Uniersal Mobile Communication Systems UMTS) is peraps based on Global System for Mobile GSM) [1]. Te data communications, especially Internet Protocol IP) based data transmissions increased a lot in te last decade. Expectations sow increasing demand for a wide range of serices from oice, inoling low to ig bit rate data and adanced data serices for te cellular communication system. At te beginning of tis century, mobile subscribers enjoyarious kinds of data serices togeter wit regular oice serice. Worldwide actiities presere te continuance in implementing te tird generation mobile radio system International Mobile Telecommunications byte year 2000 IMT-2000), in te International Telecommunication Union ITU), or Uniersal Mobile Telecommunication System UMTS), in Europe. Te implemented tird generation system will proide serice to anyone, anytime, anywere in all radio enironments. * Corresponding autor. Tel.: 1358-9-451-2347, 2367; fax: 1358-9- 431-2345. E-mail address: jaangir.sarker@ut. J.H. Sarker). Te WCDMA based tird generation system will proide te serices: oice and low rate data 144 kb/s) in eicular, medium rate data 384 kb/s) for outdoor and indoor, and up to 2 Mb/s for indoor enironment [2]. Billions of subscribers use te tree most successful second generation TDMA based cellular systems: GSM; TDMA 136); and PDC, were speec is te main teleserice. Mobile communication network operators enisage te demand for new mobile subscribers, and teyexpand te networks continuously. Some operators may not be able to get license to tird generation spectrum to support te new serices, suc as ig-speed data. Some operators do not wis to consider a jump to te tird generation system due to its large inestment in te current second generation tecnology. Terefore, tey look for possible solutions to aciee serices comparable to te tird generation in te existing second generation systems [3]. Te European Telecommunications Standards Institute ETSI) as been de ned two new tecnologies called General Packet Radio Serices GPRS) and Hig Speed Circuit-Switced Data HSCSD), and currentlyare operated for data serices oer te existing GSM system. In te existing GSM system, eac oice V) call can occupy a single 0140-3664/02/$ - see front matter q 2002 Elseier Science B.V. All rigts resered. PII: S0140-366401)00374-7

J.H. Sarker, S.J. Halme / Computer Communications 25 2002) 522±533 523 traf c cannel for te wole conersation period. A V call is a circuit-switced based, wereas a GPRS call is a packetswitced based transmission system. Traf c cannel utilization is an important measure for te operators. Te users are carged depending on te traf c cannel utilization, implicating te oter parameters. One of te most important criteria for te operators is to keep te existing V calls' blocking probabilitywitin a certain limit. Te GPRS is an effectie solution, wic can transmit data using multiple numbers of traf c cannels dynamically witout increasing V call blocking probability[4±7]. Unfortunately, a GPRS call may suffer from ig delay during congested periods of te network. Some serices suc as ideo stream need to transmit data using multiple traf c cannels wit an almost constant delay. A HSCSD call occupies multiple number of traf c cannels at a time up to completing its wole data transmission time [8]. Tus, te HSCSD proides te solution [9]. Te blocking probabilityof te existing V calls is canged after te implementation of HSCSD calls in te networks. Te blocking probabilities wit HSCSD calls are discussed extensielyin Ref. [10] using a multi-dimensional Marko cain. Te blocking probabilities and teir properties wit a multi-dimensional Marko model are also discussed in Refs. [11±13]. Stasiak carried out excellent work [14], were e deeloped te determined distributions using a combinatorial metod. Te determined distribution enables te calculation of blocking probabilities in multistage switcing networks carrying different multi-cannel traf c streams. Multiple cannels occupied HSCSD calls enance te existing V call blocking probabilities. Fortunately, for te same V call blocking probabilities, te oerall cannel utilization wit continuous multi-cannel occupied HSCSD calls is iger tan tat witout HSCSD calls. Te oerall cannel utilization increases wit increasing number of HSCSD calls pertaining to te same V call blocking probabilities [15]. Suc a result encourages te operators to proide different kinds of serices using HSCSD wit te existing V call serices and, tus, increases te different types of traf c arrial from mobile terminals. Te effectie traf c arrial to te traf c cannel part depends on te output of te random access part. 2. Random access part Te random access part of te GSM network is a slotted ALOHA based, wic is an ef cient algoritm for distributed burstytraf c. Since te access arrial of a GSM base station is burstyin nature, te coice is appropriate. Te slotted ALOHA is used mainlyfor two kinds of purpose: 1) mobile data transmission; and 2) request for a dedicated mobile cannel. In te rst kind of purpose, eac packet sould be receied successfully. So, te retransmissions take place up to te successful reception of eac data packet. On te oter and, for te request of a dedicated mobile cannel, te successful reception of eac data packet is not needed. Terefore, te retransmission cut-off occurs after a certain number of transmissions inoled. Kim [16] studied te frequency-opped spread-spectrum random access slotted ALOHA) considering stabilitywile using te number of re)transmissions, new packet generation rate and te code rate as parameters. A slotted ALOHA system is mono-stable if te number of retransmissions is limited to eigt irrespectie of te offered traf c load [17]. Excellent work regarding te stable operation of slotted ALOHA byusage of te retransmission cut-off as been done in Ref. [18]. It as been sown using computer simulation tat witout anycapture, a maximum of seen retransmissions guarantee te best grade of serice for a new packet generation rate of between 0 and a critical point corresponding to approximately0.35 packets per time slot. Under te same assumptions, it is sown byanalysis [19] tat te retransmission cut-off is not needed wen te new packet generation rate is below e 21 < 0.368) packet per time slot. If te new packet generation rate exceeds tis limit, te number of transmissions as to decrease abruptlywit increasing new packet generation rate for a guaranteed grade of serice. In [20], it is sown tat te alue of te critical point adering to te new packet generation rate, e 21 is te minimum alue of a more general case, comprising a nite number of users and capture effect. Most earlier papers analyzed eiter te traf c cannel part [10±15] or te random access part [16±20] of a TDMA based cellular system. Tis paper combines te two parts togeter. Traditionally, excess random access slots are mapped in pysical cannels of a base station, assuming te base station is always informed of an arrial of a new call. Terefore, te probabilitytat a call is rejected in te random access part as a negligible impact on te traf c cannel part parameters, for instance, cannel utilization and call blocking probability. In particular, te excess random access slot mapped oer te pysical cannel is a waste of te radio resource. In addition, te introduction of new serices increases te oerall traf c arrial and te oerestimated excess) random access slot migt not be a suf cient solution to cope wit te new system. Nowadays, a multiple number of serices wit different Qualityof Serice QoS) are desired from te same mobile network. Tis work migt be a guideline to estimate te parameters in random access and traf c cannel parts wit different QoS of different serices in te same network. Te rest of te paper is organized as follows. Section 3 describes te system model. Te ef ciency of random access cannel is described in Section 4. A xed number of slotted ALOHA based random access slots are mapped onto a normal GSM system for te access of V and HSCSD calls wic is not optimized. Te aerage number of cannels occupied bya single cannel occupied V and multiple cannel occupied HSCSD calls togeter wit te optimization of a number of random access slots can be obtained

524 J.H. Sarker, S.J. Halme / Computer Communications 25 2002) 522±533 Fig. 1. System model. from Section 5. Te oerall call success probabilitydepending on two partsðte random access part and te traf c cannel partðare considered in Section 6. Finally, Section 7 deals wit conclusions. 3. System model In te case of a normal GSM transmission system, one mobile terminal initiates te call using Random Access Cannel RACH) [21]. Te RACH is based on slotted ALOHA. After a successful reception of an access packet troug te random access part, te mobile network realizes te nature of te terminals, comprising a maximum of one cannel occupied V call or a multiple usuallyfour) cannels occupied HSCSD call. A single base station is considered, aing M traf c cannels, consisting of maximum M number of V calls and number of HSCSD calls allowed to transmit information at a time. Consider tat te arrial of eac kind of call as Poisson distribution wit a mean l l for V calls and l d for HSCSD calls). Two separate random access parts are used for initial access. Te number of random access slots is x for V and y for HSCSD calls, respectiely. Te selection of a random access slot is random in nature. Terefore, te Poisson arrial traf c is distributed uniformlyoer te random access slots tat are also Poisson distributed. Te output process of different contention packet broadcasting systems is studied in Ref. [22]. Assuming tat te output of eac random access slot is Poisson wit an aerage alue amounting to te slotted ALOHA trougput and te addition of Poisson arrials is also Poisson, te oerall output of te random access part also te input of te traf c cannel part) is Poisson were te mean is te addition of multiple output means corresponding to eac random access slot. Te system model is sown in Fig. 1. After successful reception of a V access packet troug te V random access part, te base station allocates a Traf c CHannel TCH) for tat call to transmit te oice bursts if te network as tat TCH aailable. If all M traf c cannels are full, a successful V call troug te random access part is blocked. On te oter and, a HSCSD call transmits te bursts occupying q ˆ 4) cannels if te number of te base station as tis amount of free cannels aailable to proide tem and te number of existing HSCSD calls is less tan. If eiter of tese two possibilities does not exist during tat time, a successful HSCSD call troug te random access part is blocked. 4. Ef ciency of random access cannel A general approac can be considered for two random access parts and tus te performance of te V random access part is sown below. 4.1. Te number of random access slots Let te traf c arrial from all GSM calls be exponentially distributed wit a mean rate l. In a GSM network, a call generates access packets and transmits tose to te random access slots RACH). Te number access slotted ALOHA based) slot is x. Tere are e different structures of RACH [23] wit approximately400,000 and 780,000n RACH slots per our n ˆ 1, 2, 3, 4). Let us assume tat te arrial packet is uniformlydistributed oer te x random access slots. Tus, te new access arrial rate per slot is l/x packet. We assume tat te access packet arrial rate from any call is equal. If te rst attempt is unsuccessful, te call retransmits te access packet after a random delay. Terefore, te aggregate traf c rst attempt and te retransmitted traf c) generation rate from anycall is greater tan or equal to te access arrial rate. Since te selection of a random access slot is random, te aggregate traf c generation rate from anycall transmitted to anyslot can also be considered as equialent. Te system is assumed to be memoryless, were te probabilityof transmitting a packet in a gien slot is independent of te state of te preious slots). In te case of an in nite number of calls, te distribution of te aggregate packets is Poisson. A packet is successfully

J.H. Sarker, S.J. Halme / Computer Communications 25 2002) 522±533 525 Fig. 2. Random access trougput per slot S ersus aerage access arrial rate l. transmitted if tere is no oter interfering packet in te same time slot and te probabilityof tat is exp2g). Herein, G is te aerage aggregate traf c rst time access arrial and a certain number of retransmission arrials) generation rate from all actie calls per access slot. According to speci cations, maximum r retransmissions are allowed for eac mobile terminal during te access period [21,24]. Te parameter r can be set for four different possible alues 1, 2, 4 or 7. Including te rst transmission, te maximum allowed transmission number is r 1 1). Te retransmission cut-off sceme is studied in Ref. [20] and accordingly, te trougput per slot is rede ned as S ˆ l i 1 2 {1 2 exp 2G }r11 1 x were te new packet arrial rate per random access slot is l/x and te aggregate arrial rate in eac access slot G is related by Gexp 2G l=x ˆ 1 2 {1 2 exp 2G } r11 2 Te trougput or te successful access rate per random access slot is S packets per time slot. Te random access trougput per slot S for different alues ascribed to te number of retransmissions r, is depicted in Fig. 2. Te oerall successful arrial into te traf c cannel part from all actie calls is Sx. Note tat te alue of S sould always be less tan one packet per time slot, but te alue of Fig. 3. Random access part trougput: a) r ˆ 1; b) r ˆ 2; c) r ˆ 4; and d) r ˆ 7.

526 J.H. Sarker, S.J. Halme / Computer Communications 25 2002) 522±533 and te number of slots becomes j n ok x ˆ le 12 1 2 e 21 r11 ˆ bwc 3 were bwc is te smallest integer $w. Te numerical representation of Eq. 3) is depicted in Fig. 4. Eidently, te required number of slots x is iger if te number of retransmissions is ig. Remarkably, tis iger number slot implementation stimulates te lower rejection probability and, tus, enances te output traf c of te random access part onlywit te iger number of retransmission number r. In te case of lower number of retransmission number r, te rejection probabilityis ig because of te protocol implementation and te excess random slot implementation is a waste of radio resource. Fig. 4. Required number of random access slots x. Sx migt be more tan one. Howeer, its alue sould be less or equal to l. Fig. 3 depicts te RACH trougput Sx wit te ariation of te number of random access slots x for different alues of access arrial rate l. Te gure sows: a) te random cannel trougput increases almost linearly wit increasing number of random access slots x if te retransmission number r is low r ˆ 1 or 2). If te number of random access slots x is eryig, te output traf c of RACH Sx is almost similar to input traf c l; b) in te case of iger retransmission number r r ˆ 4 or 7), te output traf c of RACH Sx increases abruptlyif te number of random access slots x crosses a certain limit. To obtain te same output Sx as te input traf c l, te retransmission number 7 is most preferable in terms of number of slots x. Operators are interested in tis access state to gie full aailabilityfor all kinds of GSM calls. In te second stage, if all traf c cannels are full and te network is unable to proide anyserice, te network informs te mobile terminal of its blocked call. In contrast, if te call is rejected in te access stage, it cannot receie anymessage from te base station. Pysically, it is unknown to te network tat one terminal tries to access to transmit te information. In tis case, te mobile terminal mayreceie an automatic `access rejection' signal, wic mayrequest te mobile user to tryagain. Te mobile user maytink tat te network is full and it supplicates a call later. Tis is true for te case of call blocking, but not for call rejection. So, call blocked is a better situation tan tat of call rejection. Tus, te operators ae to stimulate more random access slots wit augmenting retransmission number if te aerage access arrial rate of te GSM users is more tan tis limit. It is well known tat te slotted ALOHA sows te maximum trougput wen te aggregate traf c generation rate from all actie GSM calls per random access slot is G ˆ 1. If te aggregate arrial rate is more tan tis alue, te trougput decreases sarplyand te system becomes unstable [20,25]. Considering tis case in te random access part, te optimum relation between te access arrial rate 4.2. Aerage number of retransmissions Te collapse of te RACH is controlled in a GSM system bytwo different parameters: te retransmission number control; and te aerage time between tem. Te aerage number of retransmissions de nes te aerage number of retransmission slots needed for a successful access packet transmission. A GSM call tries to access into te base station immediatelyif it as anyinformation for transmitting. If te rst access transmission is unsuccessful, it retransmits te access packet using a special algoritm. Te time between te two transmissions, measured in units of RACH slots, is an integer random ariable, uniformlydistributed between 1 and a parameter Tx-integer, were Tx-integer can be set to some alues ranging from 3 to 50 slots. In GSM, maximum r r ˆ 1, 2, 4 or 7) time retransmissions is allowed. Te probabilitytat an access packet is successfullytransmitted after te k-t retransmission is P k ˆ {1 2 exp 2G } k exp 2G ; 0 # k # r Unambiguously, Eq. 4) is not te absolute geometric distribution for te access attempt k 0 # k # r). Terefore, te modi ed distribution is P 0 k ˆ X1 P k kˆ0 P k X r P k kˆ0 wic yields a modi ed geometric distribution as P 0 k ˆ {1 2 exp 2G }k exp 2G 1 2 {1 2 exp 2G } r11 5 Finally, te expected number of retransmissions needed for a successful transmission of an access packet is RTx ˆ Xr ˆ kp 0 k kˆ0 exp 2G X r 1 2 {1 2 exp 2G } r11 kˆ0 k{1 2 exp 2G } k 4

J.H. Sarker, S.J. Halme / Computer Communications 25 2002) 522±533 527 Fig. 5. Aerage number of retransmissions. Fig. 7. Call rejection traf c and access part output traf c. After simpli cation RTx ˆ {1 2 exp 2G } 1 2 r 1 1 {1 2 exp 2G } r 1 r{1 2 exp 2G } r11 Š exp 2G 1 2 {1 2 exp 2G } r11 Š 6 were te relationsip between te aggregate traf c arrial rate G packet per time slot and te aerage access packet arrial rate l/x packet per time slot can be obtained from Eq. 2). Te aerage number of retransmissions of a random access call packet) is depicted in Fig. 5. 4.3. Call rejection probability Te interesting parameter in te RACH part is te call rejection probability. It de nes te probability tat an access packet is rejected. If an access packet is rejected, a mobile terminal cannot inform te network of te wanted serice. For tis reason, te network or base station cannot inform te mobile terminal of te access failure. Tis parameter can be calculated in te following way. Te probability tat an access packet is successfullytransmitted after te rst transmission is exp2g). Te probabilityof failure after te rst transmission is {1 2 exp2g)}. Assuming tat te failure probabilityin eac transmission time is independent, and te transmission takes place r 1 1) times maximum limit), te call rejection probabilityis R ˆ {1 2 exp 2G } r11 Te numerical representation of call rejection probabilityis sown in Fig. 6. Clearly, te access arrial traf c l is te sum of two different parts: rejection traf c Rx; and te access part output traf c Sx. Te numerical representation of tese two different traf cs wit te ariation of number of random access slot is depicted in Fig. 7. A careful inspection sows tat most of te arrial traf cs are rejected if te number of random access slots is less tan 20 and most of te arrial traf cs are conerted to a random part output traf c if te number of random access slots is more tan 40. In oter words, te arrial traf c switces linearlyfrom rejected traf c to random access part output traf c wile te number of random access slots aries from 20 to 40. 7 5. Single cannel occupied oice and multi-cannel occupied HSCSD transmission system Fig. 6. Call rejection probability. Te output traf c of random access part directly works as te input traf c of traf c cannel part. Te aggregate of x branc Poisson processes is anoter Poisson process wit a mean arrial rate Sx. Te call blocking probabilityis de ned as te successful random access, but te network as no traf c cannel to sere a new call. Consider onlyv calls, were a V call can old onlyone traf c cannel at a time. Te access

528 J.H. Sarker, S.J. Halme / Computer Communications 25 2002) 522±533 Fig. 8. States from two-dimensional to one-dimensional models. arrial rate of V calls is Poisson wit a mean l.letx random access slots be mapped onto a time period for all V calls in a base station. If te output of eac random access slot is S, ten te aerage arrial rate of te traf c cannel part is S x.ifavcallissuccessful neiter rejected nor blocked), it olds a traf c cannel up to te entire conersation period of te user. Let us consider tat te cannel olding time of eac V call is independent and exponentiallydistributed wit a mean 1/ m. Te V call traf c intensityof te traf c cannel part is S x/m. Te number of traf c cannels is M in te considered base station. Te maximum M number of V calls is allowed to transmit oice bursts at a time. Consider a base station were te HSCSD calls arrie at a base station wit a Poisson distribution aing a mean l. Te base station allocates y random access slots for HSCSD calls in te random access part as depicted in Fig. 1. A HSCSD call olds multiple q cannels at a time in a time frame. Assuming tat te multiple q cannels olding by eac HSCSD call is independent and exponentiallydistributed wit a mean 1/m d. Te data traf c intensityof te traf c cannel part for HSCSD calls is S y/m. Te maximum d number of HSCSD calls is allowed to transmit information at a time. Te state i, j) de nes te probabilitytat i number of V calls and j number of HSCSD calls are in te system. Yielding te probabilitytat i number of V calls and j number of HSCSD calls are in te system leads to [26] p i; j ˆ 1 i! S i 1 x=m S j y=m p 0; 0 ; 0 # i # d; 0 # j # M; 0 # iq 1 j # M We consider te two-dimensional system state model as a one-dimensional system state probability model as depicted 8 in Fig. 8. Since tere are M number of traf c cannels in te system, te system states will be from 0 to M. Assuming Qk) as te probabilitytat k cannels are occupied byeiter HSCSD or V calls in Fig. 8, te probabilitytat te system is idle is Q 0 ˆp 0; 0 One HSCSD call needs at least q cannels. Tus, te probabilitytat 1 to q cannels are occupied is Q 1 ˆp 0; 1 ˆQ 0 S x=m 10a Q 2 ˆp 0; 2 ˆQ 0 S 2 x=m 2!. S Q q ˆp 0; q 1 p 1; 0 ˆQ 0 x=m q! ˆ Q 0 X1 S x=m q2qj S y=m j q 2 qj! q 1 S y=m 1! Q q 1 1 ˆp 0; q 1 1 1 p 1; 1 S ˆ Q 0 x=m q11 1 S 1 ) x=m S y=m q 1 1! 1! 1! ˆ Q 0 X1 S x=m q112qj q 1 1 2 qj! S x=m j 9 10b 10c) 10d)

J.H. Sarker, S.J. Halme / Computer Communications 25 2002) 522±533 529 Fig. 9. Cannel utilization wit te ariation of HSCSD traf c arrial rate. M ˆ 100, q ˆ 4, l x ˆ 10, and 1/m ˆ 2 considered for all diagrams. Q 2q ˆp 0; 2q 1 p 1; q 1 p 2; 0 S ˆ Q 0 x=m 2q 1 S q x=m S y=m 1 S 2 ) y=m 2q! q! 1! 2! ˆ Q 0 X2 S x=m 2q2qj 2q 2 qj! S y=m j 10e) Terefore, for te states ranging from 0 to dq, te probabilitytat k cannels are occupied byhscsd and V calls is l m k Q k ˆQ 0 X q iˆ0 S x=m k2qj k 2 qj! S y=m j ; 0 # k # dq 11 were due is te largest integer #u. Let us consider te case wen k. dq. Te probability tat dq 1 1 cannels are occupied is Q dq 1 1 ˆp 0; dq 1 1 1 p 1; dq 1 1 2 q 1 p 2; dq 1 1 2 2q 1 ¼ 1 p d 2 1; q 1 1 1 p d; 1 ˆ Q 0 Xd iˆ0 S x=m dq112qj dq 1 1 2 qj! S y=m j 12a) Similarly, te probability tat dq 1 2 cannels are occupied is Q dq 1 2 ˆp 0; dq 1 2 1 p 1; dq 1 2 2 q 1 p 2; dq 1 2 Q dq 1 2 ˆQ 0 Xd 2 2q 1 ¼ 1 p d 2 1; q 1 2 1 p d; 2 S x=m dq22qj dq 1 2 2 qj! S y=m j 12b) In general, for alues of k between dq and M, te following

530 J.H. Sarker, S.J. Halme / Computer Communications 25 2002) 522±533 Fig. 10. V call blocking probability. a) M ˆ 100, l x ˆ 10, and 1/m ˆ 2. b) M ˆ 100, l y ˆ 5, and 1/m ˆ 20. relation is deeloped Q k ˆQ 0 Xd S x=m k 2 qj! >< Q k ˆ k2qj S y=m j ; dq # k # M 13 Combining Eqs. 11) and 13), te probabilitytat k cannels out of M cannels are occupied is 8 l m k Q 0 X q Q 0 Xd >: S x=m k2qj k 2 qj! S x=m k2qj k 2 qj! S y=m j ; 0 # k # dq S y=m j ; dq # k # M and from Eq. 9) Q 0 ˆp 0; 0 were 8 Q 0 ˆp 0; 0 ˆ Xd S x=m i M X2 iq 9 < S y=m j = : i! ; iˆ0 21 14 15 Traf c cannel utilization or system ef ciency of te traf c cannel part can be de ned as te ratio of te aerage number of traf c cannels to te total number of traf c cannels. Hence, te cannel utilization can be written as U ˆ 1 M X M kˆ0 kq k 16 Fig. 9 sows te numerical results of traf c cannel utilization wit te ariation of HSCSD traf c arrial rate l, were M ˆ 100, q ˆ 4, l x ˆ 5 and 1/m ˆ 2 considered for all four diagrams. Te four diagrams demonstrate four caracteristics. a) Te cannel utilization can be increased byincreasing te number of allowed HSCSD calls amounting to d. After a certain limit of traf c arrial rate l, te cannel utilization U decreases abruptly. Te reason is tat te number of random access slots y ˆ 25) is not enoug and most of te traf cs are rejected in te random access part. b) A gien HSCSD call occupies q ˆ 4) traf c cannels at a time. Terefore, as te HSCSD call cannel olding time 1/ m increases from 10 to 20, te multiple cannels occupy longer time witout canging te arrial or random access part. Higer traf c cannel utilization can be obtained wit a iger number of allowed HSCSD calls equialent to d. c) As mentioned earlier, te abruptlydecreased trougput results from te sudden increasing rejection probability, due to enanced HSCSD traf c arrial rate. Te introduction of more number random access slots x ere y) can sole tis problem. d) If te arrial traf c is suf cientlyig and te number of random access slots x is not suf cient for te iger traf c cannel or te enanced random access output, te reduced number of retransmissions r mayproide te solution. Setting te maximum HSCSD call d to zero indicates tat te base station operates onlyte V calls and te traf c cannel utilization is onlyfor oice traf c. In Fig. 9, te oice traf c is constant and its alue is 10. A similar caracteristic can be obtained if te traf c cannel utilization is justi ed wit te ariation of V traf c arrial rates. If eiter HSCSD calls and/or V calls occupyall M cannels, a new V call is lost or blocked. Te probabilityfor tat is termed as blocking probability for V calls identi ed by B, and can be deried from Eqs. 14) and 15) as B ˆ Q M ˆ X d X d iˆ0 S x=m M2qj M 2 qj! S x=m i! i MX 2 iq S y=m j S y=m j 17 Te V call blocking probabilityis depicted in Fig. 10. According to te aboe mentioned system model, a maximum of dq cannels are aailable for HSCSD calls. Te HSCSD calls are blocked for two different reasons: rstly, if HSCSD calls alreadyoccupydq cannels; secondly, if more tan M 2 q 1 1 cannels are alreadyoccupied, i.e. q cannels are not aailable for one HSCSD call. In te

J.H. Sarker, S.J. Halme / Computer Communications 25 2002) 522±533 531 Fig. 11. HSCSD call blocking probability. a) M ˆ 100, l x ˆ 3, and 1/m ˆ 2. b) M ˆ 100, l y ˆ 2, and 1/m ˆ 5. system state probability diagram, te HSCSD call blocking probabilitystates can be sown in areas A and B, as eoked in Fig. 8, and can be de ned as wit a recourse to call rejection and blocked probabilities concerning te random access and te traf c cannel parts. Considering a general case for V and HSCSD calls, a call is B ˆ M 2X dq 2 q p d; j 1 XM kˆm 2 q 1 1 Q k ˆ S y=m d d! M 2X dq 2 q S x=m j X d iˆ0 S x=m i! 1 XM X d kˆm 2 q 1 1 i MX 2 iq S y=m S x=m k2qj k 2 qj! j S y=m j 18 Fig. 11 exibits te HSCSD call blocking probabilities. A detailed discussion of te call blocking probabilities togeter wit te call rejection probabilities is proided in te next section. 6. Call success probability rejected in te random access part wit a probability R. Consequently, te input probability of te traf c cannel part is 1 2 R). A call is blocked in te traf c cannel part wit a probability B. Terefore, te probabilitytat a call is successfullytransferred neiter rejected nor blocked) is gien by Here, we discuss te subsequent deelopment adances T ˆ 1 2 R 1 2 B 19 Fig. 12. Call rejection, blocking and success probabilities for V calls. Two regions are distinguised for r ˆ 7. If l, xe 21 {1 2 1 2 e 21 ) 8 } 21, ten te rst region and if l $ xe 21 {1 2 1 2 e 21 ) 8 } 21, ten te next region.

532 J.H. Sarker, S.J. Halme / Computer Communications 25 2002) 522±533 Fig. 13. Call rejection, blocking and success probabilities for H calls. Two regions are eident for r ˆ 7. If l, xe 21 {1 2 1 2 e 21 ) 8 } 21, ten te rst region and if l $ xe 21 {1 2 1 2 e 21 ) 8 } 21, ten te next region. A numerical representation of Eq. 19) is depicted in Fig. 12 for V calls and Fig. 13 for HSCSD calls, respectiely, for a few sets of speci c alues of different parameters tat constitute two separate iews. 1. Call rejection probabilityincreases almost linearlyafter a certain limit of arrial rate l if te number of retransmissions r is low 1 or 2). Call blocking probabilitydepends on oter parameters. Te oerall call success probability follows te relation represented byeq. 19). 2. In te case of iger number of retransmissions r $7), two separate regions are distinguised. If l, xor y)e 21 {1 2 1 2 e 21 ) r11 } 21 : a) te call rejection probabilityis almost zero; b) te call blocking probability depends on oter parameters; and c) te oerall call success probabilityis inerselyproportional to te call blocking probabilitybecause of almost zero call rejection probability. If l $ xor y)e 21 {1 2 1 2 e 21 ) r11 } 21 : a) te call rejection probabilityincreases abruptly; b) tus, most of te calls are rejected in te random access part; c) te arrials to te traf c cannel part decrease and tus te call blocking probabilityalso decreases; and d) te oerall call success probabilitydecreases abruptlybecause of a sarp increase in te call rejection probability. Finally, it must be empasized tat te oerall call success probabilitycan de nitelybe calculated using an multi-dimensional Erlang formula if and onlyif te number of random access slots x or y) is more tan ble 21 {1 2 1 2 e 21 ) r11 }c: were r $ 7. 7. Conclusions Te estimation of random access slots in a GSM based network is analyzed. Te call rejection probability of random access part depends on te number of retransmissions r. Ifr is low 1 or 2), te call rejection probabilityis almost linear after a certain limit of call arrial rate l. If te maximum number of retransmissions r is more tan 7, te call rejection probabilityof te random access part depends on te number of random access slots x or y). Te required number of random access slots is directlyproportional to te aerage access arrial rate. A reduction in te retransmissions r can extenuate te requisite random access slots x or y) at te expense of a iger rejection probability. Te anticipated number of random access slots x is obtained byadjusting te optimum aggregate traf c generation rate per time slot G ˆ 1. Te reasoning is as follows. Retransmission cut-off is stronglyrecommended for te stable operation of random access if te aerage access arrial rate per time slot l/x, is more tan e 21, oterwise te trougput decreases abruptly[20,25]. Tis transition point is obtained from te optimum aggregate traf c generation rate. Tus, te required/optimum number of random access slots can be calculated from te optimum aggregate traf c generation rate tat maximizes te random access trougput. Traf c cannel utilization for different numbers of random access slots is deried. Te utilization deteriorates if less random access slots are inoled, particularlywit a iger number of retransmissions. Te reason is tat more access is rejected in te access part. `Excess' number of random access slots can decrease te call rejection probabilityand, ence, increase te traf c cannel utilization, entangling an acceleration to te blocking probability. Te traf c cannel utilization depreciates if less retransmissions r are used. Te reason is tat a moderate amount of traf c is rejected in te access part. A iger number of retransmissions $7) accompanied byte `excess' number of random access slots can decrease te call rejection probability, rectifying te traf c cannel utilization and, ence, expanding te blocking probability. Te oerall call success probabilityexperiences

J.H. Sarker, S.J. Halme / Computer Communications 25 2002) 522±533 533 detrimental effect if te number of access slots is less tan ble 21 {1 2 1 2 e 21 ) r11 }c, were bwc is te smallest integer $x. Te number of random access slots in te random access part depends exclusielyon te aerage access arrial rate l and te number of retransmissions r. References [1] P. Caudury, W. Mor, S. Onoe, Te 3GPP proposal for IMT-2000, IEEE Communications Magazine 37 12) 1999) 72±81. [2] T. OjanperaÈ, R. Prasad Eds.), Wideband CDMA for Tird Generation Mobile Communications, Artec House, Boston, 1998. [3] U. Amin, S. Cennakesu, Te eolution of TDMA to 3G, IEEE Personal Communications 1999) 6±7. [4] S. Faccin, H. Liangci, R. Koodli, L. Kiem, R. Purnadi, GPRS and IS-136 integration for exible network and serices eolution, IEEE Personal Communications 6 3) 1999) 48±54. [5] C. Jain, D.J. Goodman, General packet radio serice in GSM, IEEE Communications Magazine 35 10) 1997) 122±131. [6] G. Brasce, B. Walke, Concepts, serices and protocols of te new GSM pase 2 1 general packet radio serice, IEEE Communications Magazine 35 8) 1997) 94±104. [7] GSM 03.64, V5.1.0, Digital cellular telecommunication system pase 2 1 ); general packet radio serice GPRS); oerall description of te GPRS radio interface stage 2), Noember 1997. [8] GSM 02.34, V5.1.0, Digital cellular telecommunication system pase 2 1 ); ig speed circuit switced data HSCSD)Ðstage 1, Marc 1997. [9] J. Dunlop, Potential for compressed ideo transmission oer te GSM HSCSD serice, Electronics Letters 33 2) 1997) 121±122. [10] D. Calin, D. Zeglace, Analysis of GSM HSCSD serice wit cannel allocation constraints, in: K. Leung, B. Vojcic Eds.), Multiaccess, Mobility, and Teletraf c for Wireless Communications, ol. 3, Kluwer Academic, Boston, 1999, pp. 237±252. [11] A.A. Nilsson, M. Perry, A. Gerst, V.B. Iersen, On multi-rate Erlang-B computations, Proc. ITC 16 1999) 1051±1060. [12] J.S. Kaufman, Blocking in a sared resource enironment, IEEE Transactions on Communications COM-29 10) 1981) 1474±1481. [13] J.M. Aein, A multi-class, blocked-calls-cleared, demand access model, IEEE Transactions on Communications COM-26 3) 1978) 374±385. [14] M. Stasiak, Combinatorial considerations for switcing systems carrying multi-cannel traf c streams, Proc. ITC 14 1994) 1229± 1238. [15] J.H. Sarker, S.H. Halme, M. Rinne, Performance analysis of GSM traf c cannel capacitywitout) ig speed circuit switced data, IEEE VTC2000 Fall, September 24±28, Boston, USA, 2000, pp. 1603±1609. [16] S.W. Kim, Frequency-opped speed-spectrum random access wit retransmission cutoff and code rate adjustment, IEEE Journal of Selected Areas in Communication 10 2) 1992) 344±349. [17] K. Sakakibara, H. Muta, Y. Yuba, Te effect of limiting te number of retransmission trials on te stabilityof slotted ALOHA systems, IEEE Transactions on Veicular Tecnology47 4) 2000) 1449±1453. [18] C. Luders, R. Haferbeck, Te performance of te GSM random access procedure, IEEE 44t Ve. Tec. Conference 94 VTC'94), Stockolm, Sweden, June 8-10, 1994, pp. 1165±1169. [19] J.H. Sarker, S.J. Halme, Te prudence transmission metod I PTM 1): a retransmission cut-off metod for contention based multipleaccess communication systems, IEEE 47t Ve. Tec. Conference 97 VTC'97), Poenix, AZ, USA, May4±7, 1997, pp. 397±401. [20] J.H. Sarker, S.J. Halme, An optimum retransmission cut-off sceme for slotted ALOHA, Wireless Personal Communication 131±2) 2000) 185±202. [21] M. Mouly, M.-B. Pautet, Te GSM for Mobile Communications, Publised byte autors, 1992. [22] H. Takagi, L. Kleinrock, Output process in contention packet broadcasting systems, IEEE Transactions on Communications COM-33 11) 1985) 1191±1199. [23] ETSI-GSM Tecnical Speci cation, GSM 05.02, Version 4.2.0, Pysical Layer on te Radio Pat, Multiplexing and Multiple Access on te Radio Pat, April 1993. [24] ETSI-GSM Tecnical Speci cation, GSM 04.08, Version 4.4.0, Mobile Radio InterfaceÐLayer 3 Speci cation, April 1993. [25] B. Bing, Stabilization of te randomized slotted ALOHA protocol witout te use of cannel feedback information, IEEE Communications Letters 2000) 249±251. [26] H. Akimaru, K. Kawasima, Teletraf c: Teoryand Applications, Springer-Verlag, Berlin, 1993. FX1. Jaangir H. Sarker was born in Daka, Banglades, on Noember 12, 1967. He receied is BSc degree in electrical and electronics engineering form Banglades Uniersity of Engineering and Tecnology, Daka, Banglades, in 1991, and MSc and Licentiate degrees in electrical and communication engineering from Helsinki Uniersity of Tecnology, Finland, in 1996 and 2000, respectiely. From July 1994 to September 1996, e was a researc assistant in communication laboratory of Helsinki Uniersity of Tecnology. Since October 1996, e as been sering as a researc scientist in communication laboratory of Helsinki Uniersity of Tecnology. Currently, e is inoled in one of te GETA projects, SYTE project, and ACCESS project. His researc interests include packet access, radio resource allocation, and queueing teory. He is a member of IEEE. FX2. Seppo J. Halme was born in Ruokolati, Finland, on May 17, 1938. He receied te degree of Diploma Engineering Honors) in 1962, and te degree of Licentiate in Engineering in 1966, bot in electrical engineering, from te Helsinki Uniersity of Tecnology, Helsinki, Finland, and te PD degree in communications from te Massacusetts Institute of Tecnology, Cambridge, in 1970. He was nominated Assistant Professor in 1970and Professor of Communication Engineering in 1972. He as also sered as Dean of Electrical Engineering Department in Helsinki Uniersity of Tecnology. Dr Halme as publised oer 500 articles, reports, and books.