The Simulation Model

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 presented 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 ëGSM and ëGPRS, 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/µh,GSM for GSM calls and 1/µh,GPRS for GPRS calls. The call durations are

also exponentially distributed with mean values 1/µGSM and 1/µGPRS 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 ëh 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 Âi(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 Ë:

0

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

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

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

arrival rate of packets, ëavg 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 = ë1/ëavg.