M X / G/1 queuing system with balking, startup and vacation interruption]]>

摘要

In this paper, a batch arrival single server queuing system with startup, balking and vacation interruption is considered. During the busy period, the customers may join the queue with probability α or may balk with probability 1?. On completion of service, the server goes for vacation when there are no customers available in the queue, otherwise, it resumes service. After a vacation, the server stays idle until the customer arrives and when an arrival occurs, the server begins the startup followed by service. Furthermore, vacation is interrupted suddenly when a customer arrives during vacation and goes for startup and then starts service. The probability generating function of the system size at an arbitrary time epoch is obtained. Various performance measures, some particular cases and cost model are discussed. Moreover, maximum entropy approach is employed and the results are compared with the analytical results, and validated through numerical illustration.