Analytical Comparison of Different GPRS Introduction Strategies

M. Ermel, K. Begain, T. M¨uller, J. Sch¨uler, M. Schweigel

Chair for Telecommunications, Dresden University of Technology01062 Dresden, Germany

fermel,begain,muellert,schuelj,schweigeg@ifn.et.tu-dresden.de

Abstract

The ongoing introduction of GPRS services in existingGSM networks by mobile network providers raises the ques-tion of the best strategy to partition the available cell ca-pacity. The paper describes three different strategies – com-plete partitioning, partial sharing and complete sharing. Ananalytical call/burst level model of one cell of a homoge-neous multiservice GSM/GPRS network is used to investi-gate these strategies with respect to important performancemeasures like new and handover blocking probabilities, sys-tem utilization and mean data rates of the services. Numer-ical results show, that the complete sharing strategy in con-nection with the proposed admission policy achieves a highsystem utilization while even for low priority data connec-tions some minimum quality of service is guaranteed.

1 Introduction

The General Packet Radio Service (GPRS) is a new ser-vice, that has been added to the traditional Global Systemfor Mobile Communications (GSM), which is the world’smost popular second generation digital cellular system. Theevolution of GSM technology has been led by the EuropeanTelecommunications Standard Institute (ETSI) and can bedivided into three phases. In Phase 1 (1992), the basic com-mercial services, like telephony and short message service,were introduced. Phase 2 (1996) has completed the originalwork and established a framework for future enhancements.In order to satisfy the increasing user requirements and topreserve competitiveness, one major concern of the GSMPhase 2+ has been the specification of GPRS, to accommo-date data connections with high bandwidth efficiency.

With the introduction of GPRS in existing GSM net-works, service providers are able to offer new serviceswith a bursty traffic nature. The GPRS standard [12] pro-vides packet based access, in which resources are efficientlyshared between active users. Scarce radio resources are oc-cupied only when necessary. Using GPRS, many users can

share a radio link by adapting their individual data rates.On the other hand, higher bit rates can be achieved, whenresources are available. Consequently, GPRS is supposedto be the main development trend of GSM networks to-wards third generation mobile systems like UMTS/IMT-2000 [13, 10, 11], which are based on Wideband CDMA.

Although the initial work on GPRS standardization hasbegun in 1994 there are many open questions to be stud-ied. One of the most recent questions is how to divide thecell capacity between traditional GSM and GPRS services.There are very few experiences so that network providerscan follow different introduction strategies. Based on ananalytical call/burst level model and an efficient admissionpolicy originally described in [4], this paper describes andcompares different introduction strategies with respect tocall and burst level performance measures like new and han-dover blocking probabilities, achievable average data ratesand utilization of cell capacity.

From performance point of view, there are some works inthis area like [5, 6]. Both papers present performance anal-ysis using simulation. Analytical studies can be found inmany publications on GSM networks (e.g. [3, 1]), but onlyfew deal with multiple service networks and different par-titioning strategies. In [1], an analytical model of one cellof a GSM network, with voice, data, and video services, alloperating on the traditional circuit switching, is introduced.

2 System Description

The ETSI GSM standard [12] introduces GPRS as aGSM Phase 2+ feature for efficient packet switched datatransfer. With the separate addressing of up- and downlink,bitrates up to 171.2 kbit/s per user can be achieved undergood radio conditions. Specific point-to-point and point-to-multipoint services are defined and the interworking withstandard packet data protocols like X.25 or IP is supported.A quality of service (QoS) profile provides tracking of ser-vice parameters within the entire Public Land Mobile Net-work including the radio link. According to [12] the QoSprofile defines the expected quality of service in terms of the

following attributes: Precedence Class, Delay Class, Relia-bility Class, Peak Throughput Class and Mean ThroughputClass.

A QoS profile is associated with each Packet Data Pro-tocol (PDP) context. A PDP context is the set of parametersrelated to a ‘session’ between the mobile and the PacketData Network, containing the QoS parameters, PDP type,mobile station address, etc. A session will be establishedby initiating a so called PDP context activation procedure.During a session, user packet data are transfered transpar-ently end-to-end between the mobile station and the exter-nal data network using encapsulation and tunneling meth-ods.

The GPRS air interface, which can be assumed to be thebottleneck of the system, provides a maximum date rateof 21.4 kbit/s per occupied packet data channel (PDCH).This data rate includes overhead for the GSM physical layer(synchronization, guard band) as well as protocol overheadfor the GPRS air interface, but excludes additional channelcoding for forward error correction (FEC) and overhead ofhigher protocol layers. FEC channel coding is done adap-tively to the actual measured radio condition and changesdynamically between four proposed schemes. The reach-able bit rate ranges from 9.05 kbit/s (coding scheme 1) upto 21.4 kbit/s (coding scheme 4).

The adaptive FEC mechanism together with the Auto-matic Repeat Request (ARQ) protocol of GPRS makes itimpossible to foresee the net data rates seen by the applica-tions. This strongly depends on the current radio conditions,the geographic environment and the movement behavior ofthe users. Only a long term average data throughput couldbe applied, making more or less realistic assumptions.

For this paper, we decided to base all network related cal-culations on the maximum achievable data rate of one occu-pied PDCH under good radio conditions (21.4 kbit/s). Theadditional overhead for FEC, ARQ and higher layer proto-cols are taken into account at the service description. Thisallows to calculate a service dependent overhead. An appro-priate QoS profile can be specified for every single service,including a reliability class, which indicates the used ARQstrategy. Also, for each application a different user behaviorcan be supposed.

The maximum number of PDCH a single user can oc-cupy is 8, according to the number of timeslots per radiofrequency. This sets the maximum data rate a single usercan achieve to 171.2 kbit/s for unprotected data transmis-sion, if the network resources are available.

3 Classification of Services

The performance in a GSM/GPRS system depends onthe mix of services and the user behavior. However, typicalservices in GPRS differ from those in networks like tradi-

tional GSM, the telephone network or the Internet. The fea-sibility of a service depends on constraints like available bitrate and packet delay.

Possible GPRS services are listed in [5]. Among them,there are typical Internet applications like WWW, FTP,email and telnet as well as real time services like video con-ferencing or Road Traffic and Transport Informatics (RTTI)applications. In the future, there may be many services,which have not been defined yet. For example in the Inter-net, we expect new innovative services to be implementedvery fast, if there is a need for them. Therefore, it is not fea-sible to include every possible service in our investigation.We have considered 3 service classes:

Voice serviceThe voice service is treated as in traditional GSM sys-

tems. Calls arrive according to a state dependent Poissonprocess. The call holding time is negative exponentially dis-tributed.

Road Traffic and Transport Informatics (RTTI)Examples for such services are route guidance, parts of

transport planning applications or positioning systems. Weexpect such applications to become very popular in GPRS.In a circuit switched network, this would mean high over-head and costs for establishing connections for these smallmessages. In the packet oriented GPRS, such services couldbe transported with reduced costs.

We use a modified version of the ETSI railway model[5]. Messages arrive according to a Poisson process. Themessage size is geometrically distributed with mean 170byte. Compared to the original model, our model doesnot include the maximum message size, which would havecomplicated the analysis.

InternetBecause the Internet is very popular, we expect the us-

age of GPRS also for typical Internet applications. Wemodel Internet traffic on burst level. Bursts of geometri-cally distributed size are generated which arrive accordingto a Poisson process. The mean burst size has been chosenaccording to measurements of typical flow lengths [15, 7]to 10 kByte. In reality, heavy tailed burst sizes can be ex-pected, because of the distribution of the file size [9]. How-ever, whether users retrieve large files or not, depends onthe pricing. If pricing is based on volume or time, users willrarely download large files. For the near future, we assumeInternet over GPRS to be more expensive than in a fixednetwork. Therefore, we believe that the assumption of non-heavy tailed distribution of burst size is acceptable. Similareffects have been reported for the holding time of Internetdialup traffic [14]. In general the holding time is shown tobe heavy-tailed, but during expensive periods of the day, themeasurements do not show heavy tails.

All models in this study capture the call or burst level.

They do not incorporate the data transport itself. However,this has a big influence on the performance, which has beenshown in [6]. The coding mechanism as well as mecha-nisms like ARQ influence the overhead for error correctionand therefore the available net bit rate. For all results of thisinvestigation, this has to be taken into account. In the fol-lowing all types of arrivals (calls and bursts) are commonlydenoted as calls.

4 Partitioning Strategies

Figure 1 shows three strategies that can be used to intro-duce GPRS into an existing GSM network. Partitions arenot created for individual services but for GSM and GPRStraffic. Inside a GPRS or common partition complete shar-ing is used for the different services. Admisson controland resource allocation are done as described in subsection5.2. In common partitions voice service is always given thehighest priority.

GPRS-Handover

GPRS-Partition

GSM-Handover

Common-Handover Common-Handover

GSM-Partition Common-Partition

Common-Partition

GPRS-Partition

GSM-Partition

Compl. Partitioning Complete Sharing Partial Sharing

Figure 1. Partitioning Strategies

Complete Partitioning (CP)Complete partitioning divides the total cell capacity into

two parts, one for GSM and one for GPRS traffic. Fromthe analytical point of view the system behaves like twoseparate systems that can be analyzed separately. In eachpartition resources have to be reserved for incoming han-dover calls. Because there is no sharing of resources acrosspartition borders, the utilization is expected to be low.

Complete Sharing (CS)With complete sharing no capacity is exclusively as-

signed to GSM or GPRS traffic. Only for incoming han-dover calls capacity is reserved. Because voice traffic isassigned the highest priority, it can occupy the whole sys-tem capacity. Therefore, this strategy promises the lowestinfluence of the introduction of GPRS on traditional GSMservice.

Partial Sharing (PS)Partial sharing divides the total cell capacity into three

parts, one for GSM, one for GPRS traffic and one commonpartition. Capacity for incoming handover can be reservedin the individual partitions separately or for all types of han-dover in the common partition. The GPRS partition has to

be big enough to guarantee a certain QoS and small enoughthat no bandwidth is wasted in the case of very low GPRStraffic.

Like with complete partitioning there is a minimum ca-pacity that is exclusively used by GPRS traffic. Therefore,a certain QoS can be guaranteed. On the other hand, the uti-lization is expected to be much higher than with completepartitioning because of the common resources.

5 The Model

5.1 Model Description

A GSM/GPRS cell can be modeled as a loss systemwith total capacityC, offered a finite numberk of trafficstreams, each describing a different service. Depending onthe partitioning strategy,C is divided into at most three par-titions,CGSM , the capacity exclusively used for traditionalGSM voice calls,CGPRS , the capacity exclusively used forGPRS, andCCom, the capacity shared by all services. Thetotal cell capacity of the systemC depends on the actualnumber of frequencies, used in the cell.

Let Xs(t) denote the number of calls of typesin progress in the system at timet. Then X(t) =(X1(t); : : : ; Xk(t)) defines a continuous-time stochasticprocess with finite discrete state space. The set of allowedstates depends on the admission policy to be definedlater. Assuming, the processX(t) reaches a steady state fort ! 1, let p(x);x = (x1; : : : ; xk);x 2 be the steadystate probabilities.

Bit Rate ThresholdsThe vectorb(x) = (b1(x); : : : ; bk(x));x 2 defines

the individual state dependent bit rates, wherebs(x) is thebit rate of one types call in statex. It is assumed, that callsof the same type transmit with the same bit rate somewherebetween0 andb(max)

s . This behavior can be achieved bythe base station, because it has complete control over thecapacity of the system in up- and down link. With the limi-tation, that a mobile station can receive only one frequencyat a time,b(max)

s will not be greater thanCf , withCf as themaximum capacity of one frequency.

To introduce as much flexibility as possible into the bitrate allocation, abit rate threshold vectorb(min)

s ;min =(min1; : : : mink) is assigned to each service types. Thethresholdb(mini)

s is called theminimum occupied bit rateof a call of types with respect to calls of typei and is theminimum bit rate, that calls of types have to reduce to infavor of arrivals of typei calls. A value ofb(mini)

s = 0means, an arrival of a typei call can cause a disruption ofan ongoing types call. A softly occupied bit rateof a callof types with respect to calls of typei in statex is definedas the differencebs(x) � b

(mini)s . This difference is the

capacity that can be released immediately. The values of thebit rate threshold vector hold the condition0 � b

(mini)s �

b(max)s ; i = 1; : : : ; k.

Arrival- and Service ProcessThe arrival processes are assumed to be independent

state-dependent Poisson processes with mean arrival rates�(n)s (x) and�(ho)s (x) for new and handover arrivals of types, respectively. The state dependence of the arrival rate fornew calls will be due to the finite number of potential ser-vice types usersM = (M1; : : : ;Mk) in the cell, which areassumed to be constant numbers (as many users entering thecell as many leave it on average). Then, the state dependentarrival rate�(n)s (x) = (Ms�xs)�

(n)s0 with �(n)s0 as the mean

arrival rate for calls of one idle service types user. As canbe seen,�(n)s (x) is proportional to the number of idle usersMs � xs.

Contrarily, the handover arrival rate�(ho)s (x) depends onthe number of active usersxs (if there is no active user,there will be no handover). With the assumption of a ho-mogeneous network structure (adjacent cells have the sameM, the same load and handovers are uniformly distributedamong their neighboring cells), the handover arrival rate canbe expressed as�(ho)s (x) = xs�

(ho)s0 , with �(ho)s0 as the mean

handover rate for one active service types user.Regarding the service time of voice calls it was already

mentioned in section 3, that it is reasonable to assume a neg-ative exponential distribution with parameter�s0. There-fore,�s(x) = xs�s0.

Data services are not described by their holding time dis-tribution, but a geometrically distributed amount of data tobe transmitted. Nevertheless, this can be mapped into a neg-ative exponentially distributed service time with parameter�s0(x) that depends on the statex through the bit rateb(x)of this service. For a high bit rate the service time willbe lower than for a low one. With mean message size ofms0 for types calls, the state dependent mean service rate�s(x) = xs

bs(x)ms0

.

Capacity Reservation ThresholdsThe valuesC(n)

s andC(ho)s for new calls and handover

calls, respectively, are introduced. They are calledcapacityreservation thresholds. A partition, where calls of typescan be admitted is nameds–partition. ThenC(n)

s (C(ho)s )

is the maximum value for the sum of theminimum occu-pied bit ratesof all services in alls–partitions, after theacceptance of a new (handover) types call. For reservingsome capacity for handover arrivals we assume the relationC(n)s < C

(ho)s to be true for all servicess.

Let the voice service be the only one in the GSM–partition, denote it bys = 1 and denote the GPRS servicesby s = 2; : : : ; k. To use the whole system capacity thefollowing conditions must hold:

� Complete PartitioningCGSM = C

(ho)1 and

CGPRS = C(ho)2 ; : : : ; C

(ho)k

� Complete SharingCCom = C

(ho)1 ; : : : ; C

(ho)k

� Partial SharingCGSM + CCom = C

(ho)1 and

CGPRS + CCom = C(ho)2 ; : : : ; C

(ho)k

5.2 Admission Policy

In the following, an admission policy is introduced, thatcan reserve capacity for high priority calls (e.g. handovervoice calls), while maintaining a high utilization of the par-tition resources. The main idea is to utilize the reserved ca-pacity bysoftly occupied bit ratethat can be released uponrequest immediately.

In statex a new arrival of types is accepted, if after itsadmission the sum of theminimum occupied bit ratesof allservices in alls–partitionsis not greater thanC(n)

s . Depend-ing on the admission policy the following conditions musthold

� Complete Partitioning (CP)x1b

(min1)1 � C

(n)1 � b

(min1)1 (GSM)

Pk

i=2 xib(mins)i � C

(n)s � b

(mins)s ; s = 2; : : : ; k

(GPRS)

� Complete Sharing (CS)Pki=1 xib

(mins)i � C

(n)s � b

(mins)s ; s = 1; : : : ; k

(GSM;GPRS)

� Partial Sharing (PS)Pk

i=1 xib(min1)i � CGPRS � C

(n)1 � b

(min1)1 ;

x1b(min1)1 � C

(n)1 � b

(min1)1 (GSM)

Pki=1 xib

(mins)i � CGSM � C

(n)s � b

(mins)s ;

Pk

i=2 xib(mins)i � C

(n)s � b

(mins)s ; s = 2; : : : ; k

(GPRS)

For handover arrivals the same admission conditions ap-ply, except that thecapacity reservation thresholdfor han-doverC(ho)

s is used, instead ofC(n)s .

There are different approaches to distribute the capac-ity of the system among ongoing calls, whereof the follow-ing is choosen for our investigations. As already mentionedabove, calls of the same type transmit always with the samebit rate. Assume the services are ordered according to theirpriorities in descending order with voice calls having thehighest priority and a state independent constant bit rate.Then the bit rate of one types GPRS call in statex is set to

bs(x) = min�max(A; b(min)

s ); b(max)s

�;

A =C� �

Ps�1i=1 xib

(max)i �

Pk

i=s+1 xib(min)i

xs

whereb(min)i = min(b

(min1)i ; : : : ; b

(mink)i ) and

C� =

8>>><>>>:

CGPRS for CPC � x1b

(max)1 for CS

CGPRS + CCom; x1b(max)1 � CGSM

C � x1b(max)1 ; x1b

(max)1 > CGSM

for PS

This means, at any time there is at maximum one typej ofcalls, transmitting with a bit rate somewhere betweenb

(min)j

andb(max)j . All type i calls with a higher priority than type

j calls transmit with maximum bit rateb(max)i ; i < j and

calls with a lower priority than typej calls transmit withtheir minimum bit rateb(min)

i ; i > j. The total amountof resources occupied in the cell at statex is Cocc(x) =x � b(x).

5.3 Performance Measures

For the evaluation of the different introduction strategiesfollowing performance measures have been observed withrespect to the offered load. A more detailed description canbe found in [4].

New Call Blocking ProbabilityB(n)s , defined as the time

congestion probability regarding new calls of types.Handover Failure ProbabilityB(ho)

s , defined as the timecongestion probability regarding incoming handover re-quests of types.

Cell Utilization U , defined as the ratio of the averageoccupied capacityCocc to the total capacityC.

Average Data Rateb(av)s , defined as the average data rateof a randomly chosen connection of types.

6 Numerical Example

In this section, we give an example on the results, thatcan be obtained using the presented analytical model. Themodel has been written in MOSEL language [2] and theresulting Markov chain has been solved using the SPNPpackage [8]. The examined system has the characteristicsaccording to the ETSI standards as described in section 2.Table 1 summarizes values for the main characteristics ofthe GSM/GPRS system.

TrafficDuring the early phase of GPRS introduction into exist-

ing GSM systems, voice calls are still supposed to be themajor source of traffic. RTTI calls will not contribute a lotto the overall load because they represent short messagesand hence have relatively small holding times. Neverthe-less, they will be much more frequent than voice calls and,

number of frequencies used 3number of channels per frequency 8number of signaling channels 2number of data channels 22gross data rate per PDCH 21.4 kbit/soverall gross bandwidth 470.8 kbit/smax. number of PDCH per single user 8max. gross data rate per single user 171.2 kbit/s

Table 1. Network parameters

therefore, contribute a lot to the signalling load. There isvery few experience about mobile Internet traffic. For theearly phase we assume Internet traffic to contribute aboutone tenth to the overall load. Following this argumentationthe offered traffic for the numerical investigations is com-posed of 90% voice, 1% RTTI and 9% Internet traffic.

PartitioningThe sizes of the individual partitions for the three strate-

gies reflect the offered traffic ratio (90% GSM, 10% GPRS)and the assumptions given in section 4. The values are givenin table 2. There has to be no extra partition for voice ser-vice with partial sharing. Because of the priority schemeused, voice calls can rule out GPRS calls in the commonpartition and, therefore, they have not to be protected.

GSM GPRS CommonPar- incl. Par- incl. Par- incl.tition HO tition HO tition HO

CP 20 2 2 1/4 – –CS – – – – 22 2PS – – 1 – 21 2

Table 2. Partition sizes in channels/PDCH

ThresholdsBecause the partitioning strategies are very different,

comparable results are not easy to obtain. When setting thebit rate thresholdsand thecapacity reservation thresholds,the following design goals were in mind. At first, voice callsshould not suffer any disadvantage because of the introduc-tion of GPRS traffic. Furthermore, since data calls (RTTIcalls and Internet bursts) consist of short messages, it is bet-ter to allow these messages to be transmitted as fast as possi-ble. Therefore, data calls are allowed to occupy a part of thechannels reserved for handover. Finally, handover blockingprobabilities should be a factor 5 to 10 lower than new callblocking probabilities. Data call handover are expected tobe very infrequent because of the short holding time. Theresulting values for the systems investigated are given in ta-ble 3.

Strategy Partition Service s bmaxs bmin1

s bmin2s bmin3

s C(n) C(ho) PriorityGSM Voice 1 21.4 21.4 – – 385.2 428.0

Compl. Partitioning GPRS RTTI 2 42.8 – 5.35 5.35 37.45 42.8 1GPRS Internet 3 42.8 – 5.35 5.35 37.45 42.8 2

Common Voice 1 21.4 21.4 21.4 21.4 428.0 470.8 1Complete Sharing Common RTTI 2 171.2 10.7 10.7 10.7 449.4 470.8 2

Common Internet 3 171.2 10.7 10.7 10.7 449.4 470.8 3GSM/Com. Voice 1 21.4 21.4 21.4 21.4 406.6 449.4 1

Partial Sharing GPRS/Com. RTTI 2 171.2 10.7 10.7 10.7 449.4 470.8 2GPRS/Com. Internet 3 171.2 10.7 10.7 10.7 449.4 470.8 3

Table 3. Data rate and capacity reservation threshold values in kbit/s

ServicesNumerical results are given for three classes of services

as discussed in section 3. The first traffic class representsvoicecalls, which are treated in a similar manner as in tra-ditional GSM circuit switched networks. As can be seen intable 3 the bit rate thresholds of this class are always set insuch a way, that the bitrate of voice calls is not influencedby the current load of the cell. Therefore, the values are setto the gross data rate of one PDCH. This class is associatedto the highest priority. Furthermore, the values for the ca-pacity reservation thresholds are set to give incoming voicehandovers priority over new calls. For the voice service, weassume a mean call duration of 100 s, a dwell time of 80 sand that there are 500 users per cell (Table 4).

s Service 1=�s0 1=�(ho)s0 ms0

1 Voice 100 s 80 s –2 RTTI – 40 s 170 Byte3 Internet – 600 s 10 kByte

Table 4. Service parameters

We considerRTTI as the second class of service. Withsimilar argumentation and the assumptions of section 3, theparameters of this service class are set to the values given intable 4.

As a third class of service, theInternet traffic as dis-cussed in section 3 is considered. The maximum data rate ofone user is set to the gross data rate of one frequency (171.2kbit/s), while the minimum PDCH data rate for this classdepends on the partitioning strategy (see table 3). The ac-tual minimum data rate of the service depends on the codingscheme used, according to transmission conditions in thecell. For Internet traffic, we assume an exponentially dis-tributed burst interarrival time with constant intensity anda geometrically distributed burst length with an average of10 kByte. Furthermore, the handover of Internet bursts is

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2U

tiliz

atio

nNormalized offered load

Complete PartitioningComplete Sharing

Partial Sharing

Figure 2. Utilization

assumed not to be frequent (Table 4).

ResultsAll results in the following figures are given with respect

to the normalized offered load. Anormalized offered loadof 1.0 means, that the offered bitrate traffic equals the capac-ity of the system. This point is calledcritical load. Also wedefine anormal loadas the normalized offered load whitha voice call blocking probability of 1%.

In this numerical example, the blocking probabilities ofthe RTTI calls and Internet bursts (Figures 3, 4, 5) are equalfor all three strategies, because of the equal thresholds ofthe two services (Table 3). As can be seen in the figures,the results forcomplete sharing(CS) andpartial sharing(PS) are very similiar, PS having slightly better blockingprobabilities than CS for data calls because of the individualGPRS-partition.

Complete partitioning(CP) can be evaluated as two inde-pendent systems. The small GPRS-partition promises lowblocking probabilities for low load, whereas it becomes notacceptable for high load (Figure 3). Because of the smallGPRS-partition (2 PDCH), RTTI calls and Internet burstsget a low average data rate (Figure 6), resulting in longer

holding times. This is reflected in the higher mean numberof RTTI calls and Internet bursts, as calculations had shown.Whereas the mean number of voice calls lies in the same re-gion for all strategies, for data calls (bursts) this number isa factor 5 to 7 higher with CP.

As expected, CP has the lowest utilization. Comparingthe strategies regarding the utilization at thenormal load(CP: 0.369; PS: 0.404; CS: 0.427) the utilization for CP isabout 6.4% lower, for PS around 2.4% and for CS around9.1% higher. Whereas the carried traffic of the system wasabout 90% voice, 1% RTTI and 9% Internet, in terms of thenumber of calls the ratio was about 5% voice, 83% RTTIand 12% Internet bursts.

Summarizing it can be said, that thecomplete sharingstrategy in combination with the proposed admission policygives the best results in terms of utilization of the systemresources.

Additionally, the CS strategy was investigated with al-lowing voice calls to push out data calls completely. Thiswas achieved by setting the bandwidth thresholdsb

(min1)2 =

0 andb(min1)3 = 0. At normal load, Internet bursts (RTTI

calls) did not get any bandwidth for 0.07% (0.0002%) of thetime on average. These values change to 2.8% (0.008%) forthe critical load. The distribution of these time periods isof great interest for investigations of the interactions withlower layers, e.g. outrunning timer of the TCP layer dur-ing such periods could cause retransmissions and hence in-crease the load to the system. This can be considered as amajor drawback of such an approach.

7 Conclusions

The contribution of the paper is threefold. First, an effi-cient call admission policy has been proposed for multiser-vice GSM/GPRS networks, comprising voice and differentdata services. Secondly, an analytical model, based on amulti-dimensional Markov chain, has been introduced. Themodel is quite general and capable of capturing interestingcall and burst level dynamics of the GSM/GPRS system.Thirdly, three different strategies of introducing GPRS traf-fic into existing GSM networks have been described andinvestigated.

The results of the numerical examples allow a compari-son of the three strategies. They have verified the efficiencyof the proposed call admission policy and have shown, thatwith an appropriate setting of the parameters individualblocking probabilities and QoS requirements of the differ-ent service types can be achieved. It has also been shown,that with the use of thepartial sharingor complete sharingstrategy the flexible GPRS service contributes to a betterutilization of the GSM system.

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8 1 1.2

Blo

ckin

g Pr

obab

ility

Normalized offered load

VoiceRTTI

InternetVoice HORTTI HO

Internet HO

Figure 3. Blocking and handover blockingprobabilities for Complete Partitioning

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8 1 1.2

Blo

ckin

g Pr

obab

ility

Normalized offered load

VoiceRTTI

InternetVoice HORTTI HO

Internet HO

Figure 4. Blocking and handover blockingprobabilities for Partial Sharing

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8 1 1.2

Blo

ckin

g Pr

obab

ility

Normalized offered load

VoiceRTTI

InternetVoice HORTTI HO

Internet HO

Figure 5. Blocking and handover blockingprobabilities for Complete Sharing

0

20

40

60

80

100

120

140

160

180

0 0.2 0.4 0.6 0.8 1 1.2

Ave

rage

Dat

a R

ate

[kB

it/s]

Normalized offered load

VoiceRTTI

Internet

Figure 6. Average data rates for Complete Par-titioning

0

20

40

60

80

100

120

140

160

180

0 0.2 0.4 0.6 0.8 1 1.2

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Figure 7. Average data rates for Partial Shar-ing

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Figure 8. Average data rates for CompleteSharing

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