Throughput maximization for two station tandem systems: A proof of the Andradóttir-Ayhan conjecture

John J. Hasenbein, Bara Kim

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

We study a tandem queueing network with two stations, M heterogeneous flexible servers, and a finite intermediate buffer. The objective is to dynamically assign the servers to the stations in order to maximize the throughput of the system. The form of the optimal policy for M≤3 was derived in two previous papers. In one of those papers, Andradóttir and Ayhan (Operations Research 53:516-531, 2005) provide a conjecture on the form of the optimal policy for M≥4. We prove their conjecture in this paper, showing that the optimal policy is defined by monotone thresholds and the ratios of the service rates among the servers. For M>1, we also prove that the optimal policy always uses the entire intermediate buffer.

Original languageEnglish
Pages (from-to)365-386
Number of pages22
JournalQueueing Systems
Volume67
Issue number4
DOIs
Publication statusPublished - 2011 Apr

Keywords

  • Flexible servers
  • Markov decision processes
  • Tandem queueing networks
  • Throughput optimality

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics

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