Document Type

Article

Publication Date

2025

DOI

10.1287/stsy.2024.0061

Publication Title

Stochastic Systems

Volume

15

Issue

3

Pages

220-251

Abstract

Consider a Markovian tandem line with finite intermediate buffers and an equal number of stations and servers. Servers are flexible but noncollaborative, so that a job can be processed by at most one server at any time. When a job is being processed, it can be damaged and wasted depending on the proficiency of the server. We identify the dynamic server assignment policy that maximizes the long-run average throughput of the system with two stations and two servers. We find that the optimal policy is either a single or a double threshold policy on the number of jobs in the buffer, where the thresholds depend on the service rates and defect probabilities of the two servers at the two stations. For larger systems, we show that the optimal policy may involve server idling and that improving the service rate at any station is always beneficial. Finally, we propose heuristic server assignment policies motivated by experimentation for small systems with finite buffers and analysis of larger systems with infinite buffers. Numerical results suggest that our heuristics yield near-optimal performance.

Rights

© 2025 The Authors.

This work is licensed under a Creative Commons Attribution 4.0 International License. You are free to copy, distribute, transmit and adapt this work, but you must attribute this work as: "Stochastic Systems. Copyright © 2025 The Authors. https://doi.org/10.1287/stsy.2024.0061, used under a Creative Commons Attribution 4.0 International (CC BY 4.0) License: https://creativecommons.org/licenses/by/4.0."

Funding: This research was supported by the National Science Foundation [Grants CMMI-1536990 andCMMI-2127778]. S. Andradottir was also supported by the National Science Foundation [GrantCMMI-2348409]

ORCID

0000-0002-3598-907X (Hu)

Original Publication Citation

Hu, J., Andradóttir, S., & Ayhan, H. (2025). Optimal control of queueing systems with error-prone servers. Stochastic Systems. 15(3), 220-251. https://doi.org/10.1287/stsy.2024.0061

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