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.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price includes VAT (USA)
Tax calculation will be finalised during checkout.
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.
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.
Larsen, R. L. (1981). Control of multiple exponential servers with application to computer systems. Ph.D. thesis, University of Maryland, College Park, MD, USA.
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.
Lin, W., & Kumar, P. R. (1984). Optimal control of a queueing system with two heterogeneous servers. IEEE Transactions on Automatic Control, 29, 696–703.
Luh, H. P., & Viniotis, I. (2002). Threshold control policies for heterogeneous server systems. Mathematical Methods of Operations Research, 55, 121–142.
Puterman, M. L. (1994). Markov decision processes: Discrete stochastic dynamic programming. Hoboken, NJ: Wiley.
Sennott, L. I. (1991). Value iteration in countable state average cost Markov decision processes with unbounded costs. Annals of Operations Research, 28, 261–272.
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.
Walrand, J. (1984). A note on “Optimal control of a queuing system with two heterogeneous servers”. Systems & Control Letters, 4, 131–134.
The authors thank Dr. Dmitry Efrosinin for his valuable comments.
About this article
Cite this article
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
- Dynamic control
- Threshold policy
- Markov decision processes