The article investigates a M/M/1 queuing model with impatient customers. The size of a batch taken up for service depends on the number of customers present in the waiting line. The server serves a minimum of “a” and a maximum of “b” customers at a time. The service time is assumed to be exponentially distributed with mean dependent on the batch size. Customers arrive to the system as a Poisson process, and may leave on finding a long queue or may renege after waiting in the queue for an exponentially distributed time. The model is analyzed to find different measures of effectiveness of the system. A new measure of performance is also discussed. The approach adopted for analysis of the model is based on embedded Markov chain.
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