Perfect sampling of stochastic matching models with reneging

TL;DR

This paper presents a novel perfect sampling algorithm tailored for stochastic matching models with bounded patience, enabling exact steady-state distribution estimation where traditional methods struggle.

Contribution

It introduces a modified DCFTP algorithm suitable for non-monotonic stochastic recursions in matching models with bounded patience.

Findings

The algorithm effectively controls the Markov chain via an infinite-server queue.

It handles deterministic patience times with an ad-hoc control technique.

The method allows accurate estimation of loss probabilities in equilibrium.

Abstract

In this paper, we introduce a slight variation of the Dominated Coupling From the Past algorithm (DCFTP) of Kendall, for bounded Markov chains. It is based on the control of a (typically non-monotonic) stochastic recursion by a (typically monotonic) one. We show that this algorithm is particularly suitable for stochastic matching models with bounded patience, a class of models for which the steady state distribution of the system is in general unknown in closed form. We first show that the Markov chain of this model can be easily controlled by an infinite-server queue. We then investigate the particular case where patience times are deterministic, and this control argument may fail. in that case we resort to an ad-hoc technique that can also be seen as a control (this time, by the arrival sequence). We then compare this algorithm to the classical CFTP one, and show how our perfect simulation results can be used to estimate, and compare, the loss probabilities of various systems in equilibrium.