Reversible Models for Wireless Multi-Channel Multiple Access

Abstract

This paper presents a network layer model for a wireless multiple access system with both persistent and non-persistent users. There is a single access point with multiple identical channels. Each user who wants to send a file first scans a subset of the channels to find one that is idle. If at least one idle channel is found, the user transmits a file over that channel. If no idle channel is found, a persistent user will repeat the access attempt at a later time, while a non-persistent user will leave. This is a useful mathematical model for "coffee shop" situations where a group of persistent users stay near an access point for an extended period of time while non-persistent users come and go. Users have heterogeneous activity behavior, file upload rates, and service durations. The system is a complex multi-dimensional Markov chain. The steady state probabilities are found by exploiting a latent reversibility property. This enables simple expressions for throughput and blocking probability.