Analysis of a Batch Arrival and Batch Service Queuing System with Multiple Vacations
Journal Title: International Journal of Modern Engineering Research (IJMER) - Year 2015, Vol 5, Issue 2
Abstract
This paper concerns the queuing system MX /G1, B/1, to which the customers are assumed to arrive in batches of random size X according to a compound Poisson process and also are served in batches. As soon as the system becomes empty, the server leaves for a vacation of random length V. If no customers are available for service after returning from that vacation, the server keeps on taking vacations till he finds at least one customer in the queue, then immediately begins to serve the customers up to the service capacity B. If more than B customers are present when the server returns from a vacation, the first B customers are taken into service. If fewer than B customers are present, all waiting customers go into service. Late arrivals are not allowed to join the ongoing service. The steady state behavior of this queuing system is derived by an analytic approach to study the queue size distribution at a random point as well as a departure point of time under multiple vacation policy. It may be noted that the results in [5] and [7] can be obtained as special cases from the results in this paper
Authors and Affiliations
G. S. Mokaddis , S. A. Metwally , B. E. Farahat
Keywords
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