Analysis of the GI/M/c queue with N-threshold policy

ABSTRACT We consider an infinite buffer queueing system consisting of multiple number of identical servers and a common queue. The customers’ arrival into the system follows renewal process, whereas the service time is exponentially distributed. The servers provide service according to threshold policy where all the servers together go to an idle state when the system becomes empty and they resume service only when customers are accumulated in the queue. We perform the steady-state analysis of the model using two well-known methods namely, supplementary variable and difference equation technique, to evaluate the probability distribution of the system-content at different epochs. We also obtain the Laplace-Stieltjes transform of waiting time distribution along with other system characteristics. The expected cost model is also formulated and dealt with numerically in order to obtain the optimum threshold value. Finally, with the help of certain numerical examples, the influence of model parameters on the system behavior is studied and the managerial implications of the model is discussed.