Optimal Control of Queueing Systems with Error-Prone Servers
Year: 2025
Type: article
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. Funding: This research was supported by the National Science Foundation [Grants CMMI-1536990 and CMMI-2127778]. S. Andradóttir was also supported by the National Science Foundation [Grant CMMI-2348409].
Source: Stochastic Systems
Authors: Junqi Hu, Sigrún Andradóttir, Hayriye Ayhan
Institutions: Old Dominion University, Georgia Institute of Technology
Language: English
Subfield: Management Information Systems
Domain: Social Sciences
Open Access status: diamond
OpenAlex ID: W4413219445