A Two-State M/M/1 Retrial Queueing Model with Feedback

Abstract

This paper examined a M/M/1 retrial queueing model with feedback. A primary arriving customer, who cannot experience service immediately then the customer may join a virtual queue and replicate his/her request after some random amount of time until he/she gets service. Once a regular service of the customer is complete then the unsatisfied customer may re-enter the orbit to receive service as a feedback customer. The primary and repeating calls both follow the Poisson distribution. Service times are exponentially distributed. Through recursively solving the difference-differential equations, we obtained the time dependent probabilities of the number of exact arrivals and departures at when we assume the server is free or busy from the system. Some system performance measures are computed. Numerical illustrations are also presented with potential applications.

Keywords: Arrivals, Departures, Feedback, Probability, Queueing, Retrial.