STOCHASTIC ORDERS IN RETRIAL QUEUES AND THEIR APPLICATIONS

We consider a Markovian retrial queue with waiting space in which the service rates and retrial rates depend on the number of customers in the service facility and in the orbit, respectively. Each arriving customer from outside or orbit decide either to enter the facility or to join the orbit in Bernoulli manner whose entering probability depend on the number of customers in the service facility. In this paper, a stochastic order relation between two bivariate processes (C(t), N(t)) representing the number of customers C(t) in the service facility and N(t) one in the orbit is deduced in terms of corresponding parameters by constructing the equivalent processes on a common probability space. Some applications of the results to the stochastic bounds of the multi-server retrial model are presented.