A Two-State Retrial Queueing Model with Batch Departures

Abstract

This paper presents an overview of a retrial queueing model contains single server with departures
occurs in batches. The one of the customers join the system and start its service if they find the server
is free. Upon arrival, if the server is unaccessible then all the customers join the retrial group. The
customer arrives in the system according to the Poisson flow. The customers retry from the orbit for
getting service after some time and also follow the Poisson flow. Service time follows an exponential
distribution. By solving the difference-differential equations recursively we obtained transient
probabilities of number of exact arrivals and number of exact departures at whenever the server is
free or busy from the system. Performance measures have been derived and some of the existing
results in the form of special cases have been deduced.