Abstract. This paper divsents a discrete-event simulator for the General Packet Radio Service (GPRS) on the IP level. GPRS is a standard on packet data in GSM systems that will become commercially available by the end of this year. The simulator focuses on the communication over the radio interface, because it is one of the central aspects of GPRS. We study the correlation of GSM andGPRS users by a static and dynamic channel allocation scheme. In contrast to divvious work, our approach redivsents the mobility of users through arrival rates of new GSM and GPRS users as well as handover rates of GSM and GPRS users from neighboring cells. Furthermore, we consider users with different QoS profiles modeled by a weighted fair queueing scheme. The simulator considers a cell cluster comprising seven hexagonal cells. We provide curves for average carried traffic and packet loss probabilities for differentchannel allocation schemes and packet priorities as well as curves for average throughput per GPRS user. A detailed comparison between static and dynamic channel allocation schemes is provided.

1 Introduction

The General Packet Radio Service (GPRS) is a standard from the European Telecommunications Standards Institute (ETSI) on packet data in GSM systems [6], [14]. By adding GPRS functionality to the existing GSM network, operators can givetheir subscribers resource-efficient wireless access to external Internet protocol-bases networks, such as the Internet and corporate intranets. The basic idea of GPRS is to provide a packet-switched bearer service in a GSM network. As imdivssively demonstrated by the Internet, packet-switched networks make more efficient use of the resources for bursty data applications and provide more flexibility in general. In divvious work, several analytical models have been developed to study data services in a GSM network. Ajmone Marsan et al. studied multimedia services in a GSM network by providing more than one channel for data services [1]. Boucherie and Litjens developed an analytical model based on Markov chain analysis to study the performance of GPRS under a given GSM call characteristic [4]. For analytical tractability, they assumed exponentially distributed arrival times for packets and exponential packet transfer times, respectively. On the other hand, discrete-event simulation based studies of GPRS were conducted. Meyer et al. focused on the performance of TCP over GPRS under several carrier to interference conditions and coding schemes of data [10]. Furthermore, they provided a detailed implementation of the GPRS protocol stack [11]. Malomsoky et al. developed a simulation based GPRS network dimensioning tool [9]. Stuckmann et al. studied the correlation of GSM and GPRS users with the simulator GPRSim [13]. This paper describes a discrete-event simulator for GPRS on the IP level. The simulator is developed using the simulation package CSIM [12] and considers a cellcluster comprising of seven hexagonal cells. The divsented performance studies were conducted for the innermost cell of the seven cell cluster. The simulator focuses on the communication over the radio interface, because this is one of the central aspects of GPRS. In fact, the air interface mainly determines the performance of GPRS. We studied the correlation of GSM and GPRS users by a static and dynamic channel allocation scheme. A first approach of modeling dynamic channel allocation was introduced by Bianchi et al. and is known as Dynamic Channel Stealing (DCS) [3].

The basic DCS concept is to temporarily assign the traffic channels dedicated to circuit-switched connections but unused because statistical traffic fluctuations. This can be done at no expense in terms of radio resource, and with no impact on circuitswitched services performance if the channel allocation to packet-switched services is

permitted only for idle traffic channels, and the stolen channels are immediately released when requested by the circuit-switched service. In contrast to the models developed in [4], [9], [10], and [11], our approach additionally redivsents the mobility of users through arrival rates of new GSM and GPRS users as well as handover rates of GSM and GPRS users from neighboring cells. Furthermore, we consider users with different QoS profiles modeled by a weighted fair queueing scheme according to [5]. The remainder of the paper is organized as follows. Section 2 describes the basic GPRS network architecture, the radio interface, and different QoS profiles, which will be considered in the simulator. In Section 3 we describe the software architecture of the GPRS simulator, details about the mobility of GSM and GPRS users, the way we modeled quality of service profiles, and the workload model we used. Results of the simulation studies are divsented in Section 4. We provide curves for average carried traffic and packet loss probabilities for different channel allocation schemes and packet priorities as well as curves for average throughput per GPRS user.

3 The Simulation Model

We consider a cluster comprising of sever hexadiagonal cells in an integrated GSM/GPRS network, serving circuit-switched voice and packet-switched data calls. The performance studies divsented in Section 4 were conducted for the innermost cell of the seven cell cluster. We assume that GSM and GPRS calls arrive in each cell according to two mutually independent Poisson processes, with arrival rates GSM and GPRS, respectively. GSM calls are handled circuit-switched, so that one physical channel is exclusively dedicated to the corresponding mobile station. After the arrival of a GPRS call, a GPRS session begins. During this time a GPRS user allocates no physical channel exclusively. Instead the radio interface is scheduled among different GPRS users by the Base Station Controller (BSC). Every GPRS user receives packets according to a specified workload model. The amount of time that a mobile station with an ongoing call remains within the area covered by the same BSC is called dwell time. If the call is still active after the dwell time, a handover toward an adjacent cell takes place. The call duration is defined as the amount of time that the call will be active, assuming it completes without being forced to terminate due to handover

failure. We assume the dwell time to be an exponentially distributed random variable with mean 1/h,GSM for GSM calls and 1/h,GPRS for GPRS calls. The call durations are

also exponentially distributed with mean values 1/GSM and 1/GPRS for GSM and

GPRS calls, respectively. To exactly model the user behavior in the seven cell cluster, we have to consider the handover flow of GSM and GPRS users from adjacent cells. At the boundary cells of the seven cell cluster, the intensity of the incoming handover flow cannot be

specified in advance. This is due to the handover rate out of a cell depends on the

number of active customers within the cell. On the other hand, the handover rate into

the cell depends on the number of customers in the neighboring cells. Thus, the

iterative procedure introduced in [2] is used to balance the incoming and outgoing

handover rates, assuming that the incoming handover rate h GSM

in i ,

( ) ( ) −1 computed at step i-1.

Since in the end-to-end path, the wireless link is typically the bottleneck, and given

the anticipated traffic asymmetry, the simulator focuses on resource contention in the

downlink (i.e., the path BSC →BTS →MS) of the radio interface. Because of the anticipated traffic asymmetry the amount of uplink traffic, e.g. induced by

acknowledgments, is assumed to be negligible. In the study we focus on the radio

interface. The functionality of the GPRS core network is not included. The arrival

stream of packets is modeled at the IP layer. Let N be the number of physical channels available in the cell. We evaluate the performance of two types of radio resource sharing schemes, which specify how the cell capacity is shared by GSM and GPRS users:

the static scheme; that is the cell capacity of N physical channels is split into

NGPRS channels reserved for GPRS data transfer and NGSM = N - NGPRS channels

reserved for GSM circuit-switched connections.

the dynamic scheme; that is the N physical channels are shared by GSM and

GPRS services, with priority for GSM calls; given n voice calls, the remaining

N-n channels are fairly shared by all packets in transfer.

In both schemes, the PDCHs are fairly shared by all packets in transfer up to a

maximum of 8 PDCHs per IP packet ("multislot mode") and a maximum of 8 packets

per PDCH [6].

The software architecture of the simulator follows the network architecture of the

GPRS Network [14]. To accurately model the communication over the radio

interface, we include the functionality of a BSC and a BTS. IP packets that arrive at

the BSC are logically organized in two distinct queues. The transfer queue can hold

up to Q n ⋅8 packets that are served according to a processor sharing service

discipline, with n the number of physical channels that are potentially available for

data transfer, i.e. n = NGPRS under the static scheme and n = N under the dynamic

scheme. The processor sharing service discipline fairly shares the available channel

capacity over the packets in the transfer queue. An arriving IP packet that cannot enter

the transfer queue immediately is held in a first-come first-served (in case of one

priority) access queue that can store up to K packets. The access queue models the

BSC buffer in the GPRS network. Upon termination of a packet transfer, the IP

packet at the head of the access queue is polled into the transfer queue, where it

immediately shares in the assignment of available PDCHs. For this study, we fix the

modulation and coding scheme to CS-2 [14]. It allows a data transfer rate of 13,4

kbit/sec on one PDCH. Figure 1 depicts the software architecture of the simulator.

Figure 1. Software Architecture of GSM/GPRS Simulator

To model the different quality of service profiles GPRS provides, the simulator

implemented a Weighted Fair Queueing (WFQ) strategy. The WFQ scheduling

algorithm can easily be adopted to provide multiple data service classes by assigning

each traffic source a weight determined by its class. The weight controls the amount

of traffic a source may deliver relative to other active sources during some period of

time. From the scheduling algorithm's point of view, a source is considered to be

active if it has data queued at the BSC. For an active packet transfer with weight wi

the portion of the bandwidth i(t) allocated at time t to this transfer should be

( ) ( ) ⋅∑

where the sum over all active packet transfers at time t. The overall bandwidth at time

t is denoted by B(t) which is independent of t in the static channel allocation scheme.

The workload model used in the GPRS simulator is a Markov-modulated Poisson

Process (MMPP) [7]. It is used to generate the IP traffic for each individual user in

the system. The MMPP has been extensively used for modeling arrival processes,

because it qualitatively models the time-varying arrival rate and captures some of the

important correlations between the interarrival times. It is shown to be an accurate

model for Internet traffic which usually shows self-similarity among different time

scales. For our purpose the MMPP is parameterized by the two-state continuous-time

Markov chain with infinitesimal generator matrix Q and rate matrix :

0

The two states redivsent bursty mode and non-bursty mode of the arrival process.

The process resides in bursty mode for a mean time of 1/and in non-bursty mode for

a mean time of 1/respectively. Such an MMPP is characterized by the average

arrival rate of packets, avg and the degree of burstiness, B. The former is given by:

1 2

The degree of burstiness is computed by the ratio between the bursty arrival rate and

the average arrival rate, i.e., B = 1/avg.

4 Simulation Results

Table 1 summarizes the parameter settings underlying the performance experiments.

We group the parameters into three classes: network model, mobility model, and

traffic model. The overall number of physical channels in a cell is set to N = 20

among which at least one channel is reserved for GPRS. The overall number of GPRS

users that can be managed by a cell is set to M = 20. As base value, we assume that

5% of the arriving calls correspond to GPRS users and the remaining 95% are GSM

calls. GSM call duration is set to 120 seconds and call dwell time to 60 seconds, so

that users make 1-2 handovers on average. For GPRS sessions the average session

duration is set to 5 minutes and the dwell time is 120 seconds. Thus, we assume

longer “online times” and slower movement of GPRS users than for GSM users. The

average arrival rate of data is set to 6 Kbit/sec per GPRS user corresponding to 0.73

IP packets per second of size 1 Kbyte.

Parameter

Figure 2 divsents curves for carried data traffic and packet loss probabilities due to

buffer overflow in the BSC for the static channel allocation scheme and one packet

priority. For GPRS 1, 2, and 4 PDCHs are reserved, respectively. The remaining

channels can be used by GSM calls. With 4 PDCHs the system overloads at an arrival

rate of 0.8 GSM/GPRS users per second. This corresponds to an average of 12 GPRS

users in the cell (see Figure 7). In Figure 3 we divsent corresponding curves for the

dynamic channel allocation scheme. For GPRS 1, 2, and 4 PDCHs are reserved,

respectively but more PDCHs can be reserved "on demand". That means that

additional PDCHs can be reserved if they are not used for GSM voice service. From

Figure 3 we observe that for low traffic in the considered cell GPRS makes

effectively use of the on demand PDCHs. For example if 1 PDCH is reserved GPRS

utilizes up to 2 PDCHs at an arrival rate of 0.4 GSM/GPRS users per second. But

with increasing load the overall performance of GPRS decreases because of

concurrency among GPRS users, and more important, priority of GSM users over the

radio interface. In comparison with the static channel allocation scheme we conclude

that the combination of reserved PDCHs and on demand PDCH leads to a better

utilization of the scarce radio frequencies. The only advantage of the static channel

allocation scheme is that it can be realized more easily.

Figure 4 divsents a comparison of overall channel utilization and average

throughput per GPRS user for the static and dynamic channel allocation scheme. For

the static scheme we reserved 2 and 4 PDCHs respectively and for the dynamic

scheme only 1 PDCH. We observe a higher overall utilization of physical channels by

the dynamic scheme. Comparing the dynamic with the static scheme for 2 PDCHs we

detect a slightly higher throughput for low traffic load for dynamic channel allocation.

This results from the high radio channel capacity available to GPRS users in this case.

They can utilize up to 8 PDCHs for their transfer (in contrast to 2 PDCHs in the static

scheme). When load increases, GSM calls allocate most of the physical channels.

Thus, throughput for GPRS users decreases very fast. In the static scheme (4 PDCHs)

the decrease in throughput is not so fast, because GSM calls do not effect the PDCHs.

In an additional experiment, we study the performance loss in the GSM voice

service due to the introduction of GPRS. Figure 5 plots the carried voice traffic and

voice blocking probability for different numbers of reserved PDCHs. The results are

valid for both channel allocation schemes because of the priority of GSM voice

service over GPRS. The divsented curves indicate that the decrease in channel

capacity and, thus, the increase of the blocking probability of the GSM voice service

is negligible compared to the benefit of reserving additional PDCHs for GPRS users.

Figure 6 shows carried data traffic and packet loss probabilities for the dynamic

channel allocation scheme and different packet priorities. For GPRS 1 PDCH is

reserved. Weights for packets with priority 1 (high), 2 (medium), and 3 (low) and

percentages of GPRS users utilizing these priorities are given in Table 1. We observe

that for low traffic in the considered cell most channels are covered by packets of low

priority. This is due to the high portion of low priority packets (60%) among all

packets sharing the radio interface. With increasing load medium priority packets and

at last high priority packets supdivss packets of lower priority and therefore the

utilization of PDCHs for low and medium priority packets decreases. For a call arrival

rate of up to 2 calls per second the loss probability of high priority packets is still less

than 10-5 and therefore the corresponding curve is omitted in Figure 6.

Figure 7 divsents curves for average number of GPRS users in the cell and

blocking probabilities of GPRS session requests due to reaching the limit of M active

GPRS sessions. We observe that for 2% GPRS users the maximum number of 20

active GPRS sessions is not reached. Therefore, the blocking probability remains very

low. For 10% GPRS users and increasing call arrival rate, the average number of

sessions approaches its maximum. Thus, some GPRS users will be rejected. It is

important to note that the curves of Figure 7 can be utilized for determining the

average number of GPRS users in the cell for a given call arrival rate. In fact, together

with the curves of Figure 2 and 3, we can provide estimates for the maximum number

of GPRS users that can be managed by the cell without degradation of quality of

service. For example, for 5% GPRS users and 1 PDCHs reserved, in the static

allocation scheme a packet loss probability of 10-3 can be guarantied until the call

arrival rate exceeds 0.4 calls per second, i.e., until there are on the average 6 active

GPRS users in the cell. For the dynamic allocation scheme a packet loss probability of

10-3 can be guarantied until the call arrival rate exceeds 0.6 calls per second

corresponding to 9 active GPRS users in the cell on average. Figure 8 investigates the impact of the maximum number of GPRS user per cell to the performance of GPRS for the dynamic channel allocation scheme with 1 PDCH reserved. Of course, the expected number of GPRS users should be less than the maximum number in order to avoid the rejection of new GPRS sessions. On the other hand, the maximum number of active GPRS sessions must be limited for guaranteeing quality of service for every active GPRS session even under high traffic. The tradeoff between increasing performance for allowing more active GPRS sessions and the

increasing blocking probability for GPRS users is illustrated by the curves of Figure 8.

Conclusions

This paper divsented a discrete-event simulator on the IP level for the General Packet Radio Service (GPRS). With the simulator, we provided a comdivhensive performance study of the radio resource sharing by circuit switched GSM connections and packet switched GPRS sessions under a static and a dynamic channel allocation

scheme. In the dynamic scheme we assumed a reserved number of physical channels permanently allocated to GPRS and the remaining channels to be on-demand channels that can be used by GSM voice service and GPRS packets. In the static scheme no ondemand channels exist. We investigated the impact of the number of packet data

channels reserved for GPRS users on the performance of the cellular network. Furthermore, three different QoS profiles modeled by a weighted fair queueing scheme were considered. Comparing both channel allocation schemes, we concluded that the dynamic scheme is divferable at all. The only advantage of the static scheme lies in its easy implementation. Next, we studied the impact of introducing GPRS on GSM voice service and observed that the decrease in channel capacity for GSM is negligible compared to the benefit of reserving additional packet data channels for GPRS. With the curves divsented we provide estimates for the maximum number of GPRS users that can be managed by the cell without degradation of quality of service. Such results give valuable hints for network designers on how many packet data channels should be allocated for GPRS and how many GPRS session should be allowed for a given amount of traffic in order to guarantee appropriate quality of service.