Abstract
This paper considers the equilibrium behavior of customers in a Markovian queue with setup times and partial failures, where the reactivated server must go through a period of setup time to reach the normal working state and a failure can occur at any time during the normal service. When a partial failure occurs, the server continues to serve the customers on spot at a low rate and does not admit a new arrival. Once the system becomes empty, an exponential repair time starts. Assuming that all the customers have the option of joining or balking based on a linear reward-cost structure, the authors analyze the equilibrium strategies of the customers and the average social benefits of the system in the fully observable case and the partially observable case, respectively. And on this basis, the effect of several parameters on customers’ strategic behavior is presented by some numerical examples.
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This research was supported by the National Natural Science Foundation of China under Grant No. 11201408, Key Project of Scientific Research in Higher Education of Hebei Province (Natural Sciences Class) under Grant No. ZD2019079.
This paper was recommended for publication by Editor WANG Shouyang.
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Zhang, S., Xu, X. Equilibrium Customer Strategies in Markovian Queues with Setup Times and Partial Failures. J Syst Sci Complex 33, 1163–1178 (2020). https://doi.org/10.1007/s11424-020-8123-2
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DOI: https://doi.org/10.1007/s11424-020-8123-2