Optimum Cost Analysis of a Bulk Queueing System with Multiple Vacations and Restricted Admissibility of Arriving Batches
نویسندگان
چکیده
In this paper, a bulk queueing system with multiple vacations under a restricted admissibility policy of arriving batches is considered. Arrivals occur in bulk according to Poisson process. But all the arrivals are not considered for service. During the busy period of the server, the arrivals are admitted with probability ‘ ’, whereas, with probability ‘ ’, they are admitted when the server is idle. Such assumption is quite meaningful in many real life situations. The service is done in bulk with minimum of ‘a’ customers and maximum of ‘b’ customers. The server is assigned for secondary jobs (vacations) repeatedly when the number of waiting jobs is inadequate to process. For the proposed queueing system, the probability generating function of the steady state queue size distribution at an arbitrary time is obtained. Various performance measures are derived. A cost model for the queueing system is developed. To optimize the cost, a numerical illustration is provided. Keywords Bulk queue; Multiple Vacations; Restricted admissibility policy, Queue size
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