Computing the renaming functions of a ρ-reversible Markov chain

Abstract

A Markov process is a stochastic process where the probability distribution of the future states depend only on the information that we have about the current time, not on the information we have on the past states. Markov models find use in many areas, they are applied to model communication networks, they can be used to prove many of the theorems of the queuing theory and are also applied to study cruise control systems, lines of customers, search engines and much more. The importance of ρ-reversible Markov models is related to the fact that this type of chains don’t require the solution of the system of global balance equation for the computation of their stationary distribution. We propose an heuristic algorithm that is able to find all the possible renaming functions of a ρ-reversible continuous time Markov chain (CTMC). We show an application of the algorithm to a real problem, the fair allocation of resources in a Wireless Sensor Network (WSN). The algorithm is used to show that the underlying Markov chain of a distributed algorithm for bandwidth allocation in a WSN is dynamically reversible