Antonio Gomez-Corral. On the applicability of the number of collisions in p-persistent CSMA/CD protocols

Abstract. Blocked mobile terminals in wireless networks such as wireless LANs (WLANs) commonly assume repeated attempts. The medium access control (MAC) protocol employed by the 802.11 WLAN belongs to the class termed CSMA (carrier sense multiple access). In particular, the 802.11 WLAN MAC protocol has been shown to be closely approximated by a p-persistent CSMA, where the transmit power consumption of a WLAN can be reduced by optimizing the access probability p. Classically, WLANs have been analyzed using Poisson arrivals and deterministic transmission times. In this context, the most commonly used approach is based on throughput-delay characteristics.

In this talk, we seek to show how the value of p can be evaluated, in an alternative manner, from the use of the number of collisions. To that end, we focus on the p-persistent CSMA protocol with collision detection (CSMA/CD) and an infinite number of terminals. More specifically, we first note that this protocol can be thought of as a level-dependent Markov chain of M/G/1-type. The Markovian framework is formulated in terms of a D-BMAP, discrete phase-type transmission and collision-recovery times, and a binomial process for retransmission times. The length of the slot is fixed as a function of the propagation delay. Based on the time to reach the maximum number of blocked terminals, we derive iterative schemes for the mass function and moments of the number of collisions. Numerical results are presented to illustrate the effect of the number of collisions on the duration of a slot.