Comparisons of site-clearing and non-site-clearing Markovian queues with server failures and unreliable repairer

Abstract

This paper compares the customers’ balking behavior in site-clearing and non-site-clearing Markovian queues with server failures and unreliable repairer. That is, the system is subject to failures (catastrophes or normal failures) that occur when the server is at a functioning state, and it carries out the site-clearing mechanism if catastrophes occur while it carries out the non-site-clearing mechanism if normal failures occur. At a failure epoch, the server is turned off and all present customers are forced to leave the system in a site-clearing queue, whereas they start to experience a repair process in a non-site-clearing queue. After an exponential repair time, the server can be reactivated only with a probability p $(p<1)$. Once the server fails to be repaired, all present customers leave the system, and meanwhile the next repair time begins. Comparing the equilibrium and optimal balking strategies of customers for the two types of queues, we find that although customers more possibly face the bad outcome that can not be served eventually, they still prefer to select a site-clearing queue but not a non-site-clearing queue, which coincides with the social planner’s preference. Moreover, the customers’ equilibrium behavior more deviates from their socially optimal behavior in the site-clearing queues.

Keywords:

• Markovian queues
• server failures
• catastrophes
• unreliable repairer
• balking strategy

Acknowledgements

The authors would like to thank the anonymous reviewers for their useful comments and suggestions on this work.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 71671159], [grant number 71301139], [grant number 61672448]; the Humanity and Social Science Foundation of Ministry of Education of China [grant number 16YJC630106]; the Natural Science Foundation of Hebei Province [grant number G2016203236]; the China Postdoctoral Science Foundation [grant number 2016M600196]; and the project Funded by Hebei Education Department [grant number BJ2016063], [grant number BJ2017029].