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[Formula: see text]/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.