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Abstract

Queueing models where services are offered in groups (or blocks or batches) have shown to be very helpful in real-world applications and these queues have been well studied in the literature. In this paper we see one such group service queueing model with soft failure and reneging; here, by soft failure, we mean an emergency arrival. The arrival process is a Markovian arrival, whereas the emergency arrival follows an exponential distribution. Customers are served in groups ranging in size from 1 to a fixed constant, let’s say N. A batch’s service time is determined by the phase-type distribution that corresponds to each group size. The service time for a group is calculated as the highest of all the customers who make up the group. The emergency arrival can occur at any time and when the emergency arrival occurs the batch which is in the service station will be placed at the head of the queue. Service to the emergency arrival follows exponential distribution. The customers in the pool may renege when the server is busy with an emergency. The matrix geometric method was used to obtain the steady state probabilities and we generated few performance measures. We have studied the busy time and calculated the distribution of waiting times. Results are illustrated with some graphical representations.

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