A queueing model for a wireless GSM/GPRS cell with multiple service classes

Abstract

A novel analytic frameworkis devised for the performance modelling and evaluation of a wireless cell using Global System for Mobile telecommunication (GSM) with General Packet Radio Service (GPRS) supporting both voice and multiple class data services, respectively, under a complete partitioning scheme (CPS). In this context, a queueing model is proposed consisting of two independent queueing systems, namely an M/M/c/c loss system with Poissonian GSM traffic and a {GE/GE/1/N1/FCFS → GE/GE/1/N2/PS} system of access and transfer finite capacity queues in tandem having an external Compound Poisson GPRS traffic with geometrically distributed batches and generalised exponential (GE) service times under first-come-first-served (FCFS) and processor sharing (PS) scheduling rules, respectively. Although the analysis of the former loss system is straightforward, the solution of the GE-type queues in tandem is rather complex. This investigation focuses on the analysis of the tandem GE-type queueing system, which is valid for both uplink and downlink connections and provides multiple class data services with different arrival rates, interarrival-time squared co-efficient of variations (SCVs), file (burst) sizes and PS discrimination service levels. The principle of maximum entropy (ME) is used to characterise a product form approximation, subject to appropriate GE-type queueing theoretic constraints per class, and thus, implying a decomposition of the tandem system into GE/GE/1/N1/FCFS and GE/GE/1/N2/PS building block queues, each of which can be analysed in isolation. Subsequently, closed form expressions for state and blocking probabilities are obtained. Typical numerical examples are included to validate the ME solution against simulation and study the effect of external GPRS bursty traffic upon the performance of the cell.