Perfect Sampling of GI/GI/c Queues

TL;DR

This paper presents the first perfect sampling algorithms for the steady-state distribution of multi-server queues with general interarrival and service time distributions, using a coupling from the past approach.

Contribution

It introduces a novel perfect sampling method for GI/GI/c queues based on dominated coupling from the past, with finite expected termination time.

Findings

Algorithm successfully samples from the steady-state distribution.

Finite expected termination time under mild moment conditions.

Applicable to a broad class of multi-server queue models.

Abstract

We introduce the first class of perfect sampling algorithms for the steady-state distribution of multi-server queues with general interarrival time and service time distributions. Our algorithm is built on the classical dominated coupling from the past protocol. In particular, we use a coupled multi-server vacation system as the upper bound process and develop an algorithm to simulate the vacation system backwards in time from stationarity at time zero. The algorithm has finite expected termination time with mild moment assumptions on the interarrival time and service time distributions.