Performance Analysis of M/M ( a,b ) /1 Queuing Model with Balking and State-dependent Reneging and Service

Abstract

The article investigates a M/M $^{(a, b)}$ /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.

Keywords

Bulk service Balking and reneging Poisson arrival embedded Markov chain performance measures

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