Performance Analysis of Queueing Systems for (M/M/C):(GD/∞/∞) and (M/M/∞):(GD/∞/∞) Models

This paper mainly deals with the analysis of multiple server queues (M/M/C):(GD/∞/∞) and (M/M/∞): (GD/∞/∞). c parallel servers for (c≥1) is considered for (M/M/C):(GD/∞/∞), so that, c customers may be in service at the same time. Further, it is assumed that all the channels have the same service (exponential) distribution with mean rate μ per unit time. Since the probability of one service is μh, the probability that one out of n (n≤c) services are completed during h follows a binomial distribution. (M/M/∞): (GD/∞/∞) model describes a situation with state dependent service rates where the number of servers is directly proportional to the number in the system. This unlimited server situations may occur in self-service facilities. Based on the numerical calculations and Graphical representations, the feasibility of the system is analyzed. When the mean system size and the queue size is high, optimized value is obtained so that the total expected cost is minimized. The aim of this study is to compare the properties namely mean service rate and based on the length of the queues. Probability of service of the models (M/M/C):(GD/∞/∞) and (M/M/∞):(GD/∞/∞) have been discussed. By using numerical calculation and graphical representations, analysis of such a queue can be done by solving mean system size and queue size.