Asymptotic Analysis Retrial Queueing System M/GI/1 with Hyper Exponential Distribution of the Delay Time in the Orbit and Exclusion of Alternative Customers

Abstract

This paper deals with a retrial queueing system in which the arrival flow is described by a stationary Poisson process, the service time is random with a given distribution function, hyper exponential distribution of the delay time of customers in the orbit and exclusion of alternative customers. We examine a retrial queueing system using the method of asymptotic analysis under the condition of long delay in the orbit. For use of this method we write the system of Kolmogorov’s equations for the probability distribution of the number of customers in the orbit and the server state. We have completed the transition to the system of differential equations for partial characteristic function. Using the method of asymptotic analysis we obtain two-dimensional distribution of the number of customers in the orbit in the first and second phases. This distribution can be approximated by the two-dimensional Gaussian distribution. The values of the parameters are found.