A Retrial Queueing System with Abandonment and Search for Priority Customers

Abstract

We consider a single server retrial queueing model with two types of customers, abandonment of customers and search for priority customers. Two types of customers namely type I and type II arrive according to two independent Poisson processes and upon arrival, if the server is busy, join orbits I and II respectively. Orbit I is of finite capacity while orbit II is of Infinite capacity. Retrial attempts are made by both types of customers at constant rates and each unsuccessful retrial attempt is followed by abandonment of customers from the respective orbits with some probability. Type I customer has higher priority over type II customers. Search for customers in orbit 1 is introduced to reduce their waiting time and also to minimize the loss of such customers due to abandonment. Condition for stability is established and the system state distribution is computed. Several performance measures of the system that influences the efficiency are derived and are illustrated graphically/numerically.