Operational Research

, Volume 18, Issue 2, pp 273–292 | Cite as

Equilibrium strategic behavior of customers in the M/M/1 queue with partial failures and repairs

Original Paper
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Abstract

This paper analyzes the customers’ equilibrium strategic behavior in the M/M/1 queue subject to Poisson generated partial failures and repairs. In such a queueing system, whenever a partial failure occurs, the system does not admit any customer and continues the service at a lower rate instead of stopping working completely. This goes on till the system becomes empty and, at that point, an exponential repair time is sent on. The arriving customer’s dilemma is whether to enter or balk based on a linear reward-cost structure. We discuss the fully observable and fully unobservable queues respectively. For each type of queue, the corresponding equilibrium balking strategies of customers and the expected social benefits per time unit are derived. Finally, we illustrate the theoretical results by presenting some numerical examples.

Keywords

M/M/1 queue Equilibrium strategies Partial failures Repairs Social benefits 
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Notes

Acknowledgments

The authors would like to thank the anonymous referees for their useful comments and valuable suggestions to help us improve the quality of this paper. This work is support from National Natural Science Foundation of China #11201408 and #71671011 as well as Natural Science Foundation of Hebei Province, China #A2013203148.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.College of ScienceYanshan UniversityQinhuangdaoChina
  2. 2.School of Economics and ManagementBeihang UniversityBeijingChina

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