Reversible Models for Wireless Multi-Channel Multiple Access

TL;DR

This paper models a wireless multi-channel access system with persistent and non-persistent users, using a reversible Markov chain to analyze throughput and blocking probabilities in complex, heterogeneous user scenarios.

Contribution

It introduces a reversible Markov chain model for wireless multi-channel access with heterogeneous user behaviors, enabling simplified analysis of system performance.

Findings

Steady state probabilities derived using latent reversibility.

Explicit expressions for throughput and blocking probability.

Model applicable to real-world scenarios like coffee shops.

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.