Abstract
This article studies an infinite-buffer single server queue with versatile bulk service policy, where the service rates depend on the service batch sizes. Such queueing systems have potential applications in manufacturing, computer and telecommunication systems, semiconductor industry, group testing etc. Also from our present analysis, the results for several batch-service models can be derived. We use the matrix-geometric method to obtain joint distribution of the number of customers in the queue and the number of customers undergoing service, in steady-state. Based on these limiting probabilities, we present various performance measures, which are useful in determining optimal service policy and controlling congestion in the system. Some optimal policies has also been suggested based on a cost structure and the threshold values of the sensitive parameters.
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