Computing conditional sojourn time of a randomly chosen tagged customer in a BMAP/MSP/1 queue under random order service discipline

Abstract

This paper deals with the analysis of a single server queue with non-renewal batch arrival and non-renewal service, where the customers are selected randomly for service. The Laplace�Stieltjes transform of the waiting time distribution of a randomly chosen k-type (k?1) customer, i.e., the customer who finds k (?1) other customers in the system at his arrival epoch, is derived using matrix-analytic (RG-factorization) technique. The expression of the expected sojourn time of a k-type (k ? 0) customer is formulated. The detailed computational procedure along with the numerical results is presented in this paper. A comparison among the random order service (ROS), first-come first-serve, egalitarian processor sharing and generalized processor sharing discipline in terms of the expected sojourn time of a k-type (k ? 0) customer is presented in the numerical section. The present study indicates that the ROS discipline may be preferred over other scheduling policies for certain correlated arrival and/or service processes. � Springer Science+Business Media New York 2017.