Customer Entry Behavior and System Regulation Strategy in a Multi-Server Queue with Synchronous Hybrid Vacations

This paper studies customers' entry behavior and regulation strategy formulated accordingly in a multi-server Markovian queue with synchronous hybrid vacations. In case the system becomes empty, partial servers take incomplete vacations whereas the other servers take complete vacations. Unless the queue length does not exceed the number of partial servers at the completion instant of a vacation time, all the servers return and resume normal service. This hybrid vacation mechanism with overflow threshold is widely used in modern communication systems and health-care systems. In view of the four levels of system information visibility: the fully/almost visible and the almost/fully invisible, we obtain the customers' equilibrium entry strategy and their socially optimal entry strategy, respectively. Based on these results, we further discuss the manager's regulation and control strategy for optimizing system performance. We find that the amount of information available to customers is not completely positively correlated with customer utility and system performance in anarchy. After regulation, the servers generally can charge more admission fees and effectively avoid risks of paying compensation by hiding system information from customers. Moreover, regardless of the information level or the composition of social utility, the manager should set up an appropriate number of servers taking incomplete vacations according to specific conditions, which is not simple that the more the better or the less the better