Omnithermal Perfect Simulation for Multi-server Queues

TL;DR

This paper extends existing perfect simulation algorithms for multi-server queues, enabling simultaneous sampling for a range of server counts using modified domCFTP methods, improving efficiency in queue analysis.

Contribution

It demonstrates how to modify existing domCFTP algorithms to perform perfect simulation for multiple server counts simultaneously.

Findings

Algorithms now support simultaneous simulation for various server numbers.

Enhanced efficiency in sampling from multi-server queue distributions.

Addresses a previously open question about extending domCFTP methods.

Abstract

A number of perfect simulation algorithms for multi-server First Come First Served queues have recently been developed. Those of Connor and Kendall (2015) and Blanchet, Pei, and Sigman (2015) use dominated Coupling from the Past (domCFTP) to sample from the equilibrium distribution of the Kiefer-Wolfowitz workload vector for stable M/G/c and GI/GI/c queues respectively, using Random Assignment queues as dominating processes. In this note we answer a question posed by Connor and Kendall (2015), by demonstrating how these algorithms may be modified in order to carry out domCFTP simultaneously for a range of values of c (the number of servers).