Modelling a Decentralized Constraint Satisfaction Solver for Collision-Free Channel Access

TL;DR

This paper models a decentralized wireless channel access method as a constraint satisfaction problem, analyzing its convergence and performance using Markov chains and validating with simulations.

Contribution

It introduces a novel analytical model for a decentralized collision-free channel access protocol using Markov chains, including error considerations.

Findings

Derived closed-form transition probabilities for the Markov chain

Calculated the expected number of steps to reach a solution

Validated the model through simulations under various conditions

Abstract

In this paper, the problem of assigning channel slots to a number of contending stations is modeled as a Constraint Satisfaction Problem (CSP). A learning MAC protocol that uses deterministic backoffs after successful transmissions is used as a decentralized solver for the CSP. The convergence process of the solver is modeled by an absorbing Markov chain (MC), and analytical, closed-form expressions for its transition probabilities are derived. Using these, the expected number of steps required to reach a solution is found. The analysis is validated by means of simulations and the model is extended to account for the presence of channel errors. The results are applicable in various resource allocation scenarios in wireless networks.