MATHEMATICAL ANALYSIS OF PERFORMANCE MEASURES OF M/M/1 QUEUE MODELS.

The goal of this research is to expand existing single server queue models by deriving their performance measures through the application of probability laws. In this paper, we present a server queue model which consists of balking customers whose behaviours are characterised by discouragement and impatience during long queues. The averages number of such customers and response times of the queue system are being used to derive the average time customers have to wait and the number of customers who wait for service. Bayes law of total probability and Laplace-Stieltjes transforms are being applied to derive these parameters in single-server queue systems presented in this research. A numerical example is also presented to validate the model parameters. It is observed that, in order to evaluate the distribution of the response and waiting time, the distribution at the instant a customer joins it must be known. It is also observed that, the model distribution’s parameters from both the theoretical and numerical illustrations of the single server (M/M/1) with balking customers presented in this paper conform to the Little’s theorem on queues.