A Mean Field Analysis of CSMA/CA Throughput

Due to the fact that Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) protocols are extensively used in commercial wireless networks, the analysis of this family of medium access control protocols has been a topic of great interest for the wireless networking community. In this paper, we present a mean field analysis for the throughput of a slotted CSMA/CA scheme in single-hop networks. The concept of mean field approximation originates in statistical mechanics and it is a widely used approximation method employed to address systems of many interacting particles that cannot be solved exactly. The idea is to simplify the treatment of a many-body system by describing the interaction of one particle with the other interacting particles by an average potential, the so-called mean field. In our analysis, the nodes of a wireless network constitute a set of interacting particles; the interaction of a certain node with the other nodes in the network is reduced to an averaged channel condition. We estimate the amount of busy slots and the network throughput with respect to the offered traffic. Our analysis is of a recursive form, in which at each step the amount of traffic is increased by a specific amount. Also, our model takes into accounts retransmissions of collided packets.