Mobile Networks and Applications 9, 63–72, 2004  2004 Kluwer Academic Publishers. Manufactured in The Netherlands. Performance Evaluation of Bluetooth Polling Schemes: An Analytical Approach ∗ DANIELE MIORANDI, ANDREA ZANELLA and GIANFRANCO PIEROBON Department of Information Engineering, University of Padova, v. Gradenigo 6/B, 35131 Padova, Italy Abstract. In the recent years, many polling schemes for Bluetooth networks have been proposed and evaluated. To the authors knowledge, however, analysis has been carried out mainly through computer simulations and, up to now, no mathematical treatment of this topic has been presented. In this paper, we propose an analytical framework for performance evaluation of polling algorithms in Bluetooth piconets. The analysis is carried out by resorting to an effective and simple mathematical method, called Equilibrium Point Analysis. The system is modelled as a multidimensional finite Markov chain and performance metrics are evaluated at the equilibrium state. The analysis is focused on three classical polling schemes, namely Pure Round Robin, Gated Round Robin and Exhaustive Round Robin, which are compared in terms of packet delay, channel utilization, and fairness among users. Both analytical and simulation results are presented for three relevant scenarios, in order to validate the accuracy of the analysis proposed. Keywords: Bluetooth, polling schemes, equilibrium point analysis, performance evaluation 1. Introduction Originally born as a wireless replacement for cables connect- ing electronic devices, Bluetooth has been gaining a lot of consideration and attention by the scientific community in the last few years. The ability of Bluetooth devices to form small networks called piconets, opens up a whole new arena for ap- plications where information may be exchanged seamlessly among the devices in the piconet. Typically, such a network, referred to as a WPAN (Wireless Personal Area Network), may consist of a mobile phone, laptop, palmtop, headset, and other electronic devices that a person carries around in his every day life. The WPAN may, from time to time, also in- clude devices that are not carried along with the user, e.g., an access point for Internet connection or sensors located in a room. Moreover, devices from other WPANs may also be in- terconnected to enable information sharing. The commercial success of WPANs is intimately linked to their ability to sup- port advanced digital services, like audio and video stream- ing, web browsing, etc. In such a scenario, the performance aspects of the radio technologies involved appear of primary importance. For Bluetooth, in particular, the design of effec- tive polling schemes is an attractive issue, due to its poten- tially dramatic impact on system performance. Polling schemes have been extensively studied in the last decades and exact analysis has been performed for many poli- cies [12,14,15]. Nevertheless, the application of such results to the specific case of Bluetooth appears rather difficult be- cause of the Time Division Duplex (TDD) nature of Blue- tooth links. This consideration has driven many researchers to investigate the performance achieved by classic polling schemes in Bluetooth piconets, and has fostered the design of new, effective polling strategies [3,5,7,8,18] for Bluetooth. To ∗ This work was supported by the Department of Information Engineering (DEI) of the University of Padova (Italy). the knowledge of the authors, however, no theoretical treat- ment of Bluetooth polling schemes has been presented in the literature. In this paper, we provide a simple mathematical model for a Bluetooth piconet. Our primary interest is to evaluate, by analytical methods, the performance of exhaustive and semi- exhaustive polling schemes for a Bluetooth piconet. It is, in- deed, widely acknowledged that exhaustive disciplines are a valuable choice [13] when aggregated throughput and chan- nel utilization are of primary interest. In particular, we con- sider three basic disciplines: Pure Round Robin (PRR), Gated Round Robin (GRR) and Exhaustive Round Robin (ERR). Unfortunately, the exact analysis of such polling strategies for a Bluetooth-like TDD system may result practically un- tractable. For instance, given a piconet with N active slaves, the delay analysis for the exhaustive polling strategy (using the so-called buffer occupancy method [12]) would require the solution of order of (2N) 3 equations. To overcome this drawback, we resort to an approximate method, based on the so-called Equilibrium Point Analysis (EPA). The EPA was first introduced by Tasaka [16] to study the dynamic behavior of the R-ALOHA protocol, generalizing a concept introduced by Kleinrock and Lam [11] and, indepen- dently, by Carleial and Hellman [4]. The EPA method is gen- erally used to obtain an estimation of the performance yielded by Markovian systems. The basic idea is to evaluate the per- formance of the system in its equilibrium point. An equi- librium point may be described as an attractive point in the state space of the system. At the equilibrium, the sum of the stochastic forces that act on the system is, on average, zero. Hence, the system statistically tends to gravitate around that point [17]. This intuitive notion of equilibrium can be given a precise mathematical setting by considering a random vector,