Time dependent retrial queueing model with orbital search under non-preemptive priority services

Abstract

Transient solution of Single server Non-preemptive priority Retrial model with orbital search is studied using eigenvalues and eigenvectors. In this model, customers are arriving in Poisson process.  Arrival rates of low priority and high priority customers are respectively λ₁ and λ₂. The service times for low and high priority customers follow exponential distribution with parameters µ₁ and µ₂ respectively. Customer finding the system busy, on arrival, goes to the orbit and form a virtual queue. In this model of orbital search, when the server becomes free, he has two options. Either the server search for the customer in the orbit with probability p to provide  service for a customer in the orbit or remains idle with the probability 1-p. Whenever the server is free, customer from orbit try for service,  under classical retrial policy with rate σ which follows  Poisson process.  In this paper, transient solution of average number of customers in the orbit and high priority queue, the probability of server being idle, the probabilities of server being busy with low and high priority customers for various values of λ_1, λ_2, µ_{1 ,} µ₂, σ, p and t are estimated.