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Incompleteness of results for the slow-server problem with an unreliable fast server

Abstract

Efrosinin (Ann Oper Res 202:75–102, 2013) examined the optimal allocation of customers in an \(M/M/2\) queueing system with heterogeneous servers differentiated by their service rates and reliability attributes. Specifically, the faster server is subject to partial or complete failures, and the slower server is perfectly reliable. The objective is to determine an optimal allocation policy that minimizes the long-run average number of customers in the system. The purpose of this note is to show that some key arguments in Efrosinin (2013) related to the optimality of a threshold policy are incomplete.

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Acknowledgments

The authors thank Dr. Dmitry Efrosinin for his valuable comments.

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Correspondence to Jeffrey P. Kharoufeh.

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Özkan, E., Kharoufeh, J.P. Incompleteness of results for the slow-server problem with an unreliable fast server. Ann Oper Res 226, 741–745 (2015). https://doi.org/10.1007/s10479-014-1615-5

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Keywords

  • Dynamic control
  • Threshold policy
  • Markov decision processes