Annals of Operations Research

, Volume 226, Issue 1, pp 741–745 | Cite as

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

Article
First Online:

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.

Keywords

Dynamic control Threshold policy Markov decision processes 
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Notes

Acknowledgments

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

References

  1. Efrosinin, D. (2013). Queueing model of a hybrid channel with faster link subject to partial and complete failures. Annals of Operations Research, 202, 75–102.CrossRefGoogle Scholar
  2. Koole, G. (1995). A simple proof of the optimality of a threshold policy in a two-server queueing system. Systems & Control Letters, 26, 301–303.CrossRefGoogle Scholar
  3. Larsen, R. L. (1981). Control of multiple exponential servers with application to computer systems. Ph.D. thesis, University of Maryland, College Park, MD, USA.Google Scholar
  4. Larsen, R. L., & Agrawala, A. K. (1983). Control of a heterogeneous two-server exponential queueing system. IEEE Transactions on Software Engineering, SE–9, 522–526.CrossRefGoogle Scholar
  5. Lin, W., & Kumar, P. R. (1984). Optimal control of a queueing system with two heterogeneous servers. IEEE Transactions on Automatic Control, 29, 696–703.CrossRefGoogle Scholar
  6. Luh, H. P., & Viniotis, I. (2002). Threshold control policies for heterogeneous server systems. Mathematical Methods of Operations Research, 55, 121–142.CrossRefGoogle Scholar
  7. Puterman, M. L. (1994). Markov decision processes: Discrete stochastic dynamic programming. Hoboken, NJ: Wiley.CrossRefGoogle Scholar
  8. Sennott, L. I. (1991). Value iteration in countable state average cost Markov decision processes with unbounded costs. Annals of Operations Research, 28, 261–272.CrossRefGoogle Scholar
  9. Viniotis, I., & Ephremides, A. (1988). Extension of the optimality of the threshold policy in heterogeneous multiserver queueing systems. IEEE Transactions on Automatic Control, 33, 104–109.CrossRefGoogle Scholar
  10. Walrand, J. (1984). A note on “Optimal control of a queuing system with two heterogeneous servers”. Systems & Control Letters, 4, 131–134.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Industrial EngineeringUniversity of PittsburghPittsburghUSA

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