Perfect Sampling and Gradient Simulation for Fork-Join Networks

TL;DR

This paper introduces a perfect sampling algorithm for fork-join networks that accurately captures steady-state distributions and enables unbiased gradient estimation, aiding performance analysis and optimization.

Contribution

It develops a novel simulation method combining CFTP and IPA techniques for exact steady-state sampling and derivative estimation in complex fork-join networks.

Findings

Successfully generates i.i.d. samples of job sojourn times

Provides unbiased estimators for derivatives of sojourn times

Demonstrates effectiveness on networks with known and unknown steady-states

Abstract

Fork-join network is a class of queueing networks with applications in manufactory, healthcare and computation systems. In this paper, we develop a simulation algorithm that (1) generates i.i.d. samples of the job sojourn time, jointly with the number of waiting tasks, exactly following the steady-state distribution, and (2) unbiased estimators of the derivatives of the job sojourn time with respect to the service rates of the servers in the network. The algorithm is designed based on the Coupling from the Past (CFTP) and Infinitesimal Perturbation Analysis (IPA) techniques. Two numerical examples are reported, including the special 2-station case where analytic results on the steady-state distribution is known and a 10-station network with a bottleneck.