STRATEGIC ANALYSIS IN MARKOVIAN QUEUES WITH A SINGLE WORKING VACATION AND MULTIPLE VACATIONS

摘要

This paper considers the customers' equilibrium behavior in Markovian queues with a single working vacation and multiple vacations. That is, if there are customers in the queue upon the end of the working vacation, the new regular busy period will start. Otherwise, the server begins a classical vacation. Arriving customers decide whether to join the system or balk based on the system states and a linear reward-cost structure. Firstly, we study the expected sojourn time of customers in the fully observable and almost observable queues. Secondly, we derive equilibrium strategies for the customers for two cases and analyze the customers' strategic behavior and social welfare under these strategies. Finally, the effect of the information levels as well as system parameters on equilibrium strategies and social welfare are illustrated by numerical examples. We observe that equilibrium thresholds for the almost observable queues are contained within the range between thresholds for the fully observable queues. Moreover, we also find that the state of the server informed to the customers is not necessarily beneficial to social welfare.