Control policies for a two-stage queueing system with parallel and single server options

TL;DR

This paper models and analyzes optimal control policies for a two-stage queueing system with parallel and single-server options, using Markov decision processes to improve decision-making and system performance.

Contribution

It provides a full characterization of the structural properties of optimal policies based on service rate relationships, enhancing understanding of queue control strategies.

Findings

Optimal policies depend on service rate relationships.

Numerical results show the benefits of optimal control over heuristics.

Structural properties guide decision-making in two-stage queues.

Abstract

We study a two-stage tandem service queue attended by two servers. Each job-server pair must complete both service phases together, with the server unable to begin a new job until the current one is fully processed after two stages. Immediately after the first phase of service, the server decides whether to send the job/customer to a downstream station that allows parallel processing or to a single-service facility that offers faster or higher-quality service but handles only one job at a time. This choice determines whether the second phase commences immediately or (potentially) after waiting in a queue for the single-service facility to become available. The decision-making scenario is modeled via a Markov decision process formulation, of a clearing system with holding costs at each station. We fully characterize the structural properties of an optimal control policy based on the relationship between the service rates at the downstream stations. A numerical study highlights the significance of optimal control by comparing its performance against several natural heuristic policies.