Equilibrium threshold strategies and social benefits in the fully observable Markovian queues with partial breakdowns and interruptible setup/closedown policy

ABSTRACT

This paper studies the equilibrium balking strategies in the single-server Markovian queues with partial breakdowns and interruptible/setup closedown policy. That means the server may fail at any point in time, no matter the server is idle or busy and the service continues at a slower rate instead of stopping service totally. When the system becomes empty, the server ceases to operate by a closedown time. If a customer arrives during the closedown period, the system starts the service immediately without a setup time. After the closedown period, the server needs a setup time before providing the service upon arrival. We presume that the customers decide whether to join or balk immediately after their arrival based on the reward-cost structure of the system. The fully observable case is discussed and the equilibrium threshold strategies and the equilibrium social benefits for all customers are derived. A numerical example and a case study for a bank system are investigated in this regard. Eventually, the effects of several parameters on the equilibrium thresholds, social benefits, balking probability, probability of empty system and stationary distribution are expressed.

KEYWORDS:

• M/M/1 queue
• equilibrium balking strategies
• social benefits
• partial breakdowns
• interruptible set up/closedown policy

Acknowledgements

The authors would like to thank the editor-in-chief and the anonymous reviewers for their valuable comments and helpful suggestions on a previous draft of this paper to improve its quality. This work was supported by the Iranian National Science Foundation (91049559).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Amir Aghsami

Amir Aghsami is currently a PhD candidate of Industrial Engineering at the School of Industrial Engineering, Khaje Nasir Toosi University of Technology. His main scientific interests include operations research, stochastic process, queueing systems, mathematical ‌modelling, inventory control, finance and engineering economics.

Fariborz Jolai

Fariborz Jolai is a Professor of Industrial Engineering at the School of Industrial and Systems Engineering, College of Engineering, University of Tehran. His current research interests are Supply chain management, Scheduling and Production Planning optimization problems.