2012/12/21 by José Blanchet, Jose Blanchet, Jing Dong +2 · 1 citation
Business, Management and Accounting · Mathematics · #Advanced Queuing Theory Analysis #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #math.PR
paper · pdf · doi:10.48550/arxiv.1212.5635
arxiv created 2012/12/21 · openalex publication_date 2012/12/21 · arxiv updated 2012/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.