Ghosh S.Banik A.D.2025-02-172017http://dx.doi.org/10.1007/s10479-017-2534-zhttps://idr.iitbbs.ac.in/handle/2008/1436This 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 ((Formula presented.)) customer, i.e., the customer who finds k ((Formula presented.)) 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 ((Formula presented.)) 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 ((Formula presented.)) 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. � 2017 Springer Science+Business Media New YorkenBatch Markovian arrival process (BMAP)Expected sojourn timeMarkovian service process (MSP)Random order service (ROS)RG-factorizationArticle in Press