Sampling Point Processes on Stable Unbounded Regions and Exam Simulation of Queues

TL;DR

This paper introduces efficient algorithms for sampling finite points in stable unbounded regions of marked renewal point processes and demonstrates their application to simulating and optimizing infinite server queue performance.

Contribution

It provides novel algorithms for exact simulation of stable regions in point processes and applies these to queue simulation and performance measure optimization.

Findings

Algorithms are theoretically sound and practically efficient.

Exact simulation of steady-state queue measures is achieved.

Successful application to gradient estimation in performance optimization.

Abstract

Given a marked renewal point process (assuming that the marks are i.i.d.) we say that an unbounded region is stable if it contains finitely many points of the point process with probability one. In this paper we provide algorithms that allow to sample these finitely many points efficiently. We explain how exact simulation of the steady-state measure valued state descriptor of the infinite server queue follows as a simple corollary of our algorithms. We provide numerical evidence supporting that our algorithms are not only theoretically sound but also practical. Finally, having simulation optimization in mind, we also apply our results to gradient estimation of steady-state performance measures.