Performance analysis of load based M/M/3 transient queueing system with finite capacity

Abstract

This paper deals with the investigation of M/M/3 queueing model under the provision of service rates of jobs depend upon the load of the jobs arrived in the system. The customers (jobs) arrive in the system in Poisson fashion and they are served in the chronological order of their arrival. Differential equations of transient probability distribution functions by using a transition diagram have been set up. Laplace Transform, probability generating function, and Rouchey’s Theorem have been applied to get the probability of n customer in time t. Various performance indices such as the mean number of customers in the system, expected number of customers in a queue, probability that one has not to wait, expected mean time spent in a system, expected mean time spent in a queue, probability that the queue size being greater than or equal to N have been obtained analytically. Finally, the analytical results are validated graphically with the help of computing software.