Mathematical Analysis of the Packet Delay Statistics in Bluetooth Piconets under Round Robin Polling Regime

Personal Area Network technologies like Bluetooth and its subsequent derivations and evolutions (Bluetooth v1.2, v2.0+EDR) are valid candidates to realize the mobile and pervasive communication paradigm that is considered in several recent research projects. Although the delay performance of the basic Bluetooth network configuration (piconet) has been widely evaluated through numerical simulations, no satisfactory analytical framework has been yet proposed in the literature. In this paper we present an analysis of the packet delay statistic in Bluetooth piconets, for a limited–1 (round robin) polling strategy. The mathematical model proposed in this paper extends the other models presented in the literature by providing more accurate results for a wider range of traffic patterns, under the assumption of a marked Poisson arrival process. Our analysis provides a complete statistical characterization of the packet delay, by means of Laplace-Stieltjes transform, for generic traffic patterns. Furthermore, expressions for the estimation of the average packet delay for unbalanced and asymmetric traffic are derived, thus improving existing results based on the theory of M/G/1 queues with vacations. Such expressions are, however, rather complex. Therefore, we propose an approximation, based on a renewal argument, which leads to a closed–form expression for the access delay statistic. The proposed analysis permits an accurate estimation of the packet delay under a wide range of network load conditions.