Discrete-Time Markov Model for EDGE/GPRS Radio Engineering with Finite-length Sessions

GPRS is now deployed and commercially open in a vast number of networks worldwide. The forthcoming generalization of multimedia mobiles with advanced capabilities, along with continuing efforts to optimize the end-to-end performance, are expected to trigger an exponential soaring of traffic. EDGE or UMTS are the possible network evolutions to handle it. A number of important technical challenges are facing the industry. In this paper, we focus on a simple yet important objective: to provide mathematical models for GPRS/EDGE radio engineering. To this end, we develop a constructive model based on an original discrete-time Markov process that captures the detailed behavior of the radio allocator when a finite number of users are performing finite-length ON/OFF sessions in the cell. A number of typical applications are presented. 1. INTRODUCTION As the packet-based data traffic is becoming a commercial reality over wide area wireless networks, some new and interesting technical challenges are facing the industry. Among them, how to make optimal usage of the radio link is essential since it is both the performance bottleneck and the most expensive resource. And contrarily to the voice traffic, which is well understood and for which the simple model developed in the early 1900's by Erlang is still the key tool for resource dimensioning, there does not exist a simple and robust mathematical model allowing to characterize packet traffic over wireless networks. Several papers have been published on performance evaluation of GPRS or EDGE systems. A number of them were based on simulations (see e.g. [11], [18], [19]). Performance evaluation using analytical models were proposed in [5], [16], [17]. In these papers, GPRS session duration was supposed to be infinite. Finite GPRS sessions were investigated in [12], [13], [14] and [15]. In particular, Vornefeld proposes in [12] a marked Markovian arrival process that aims to model the arriving process of data