Modelling and analysis of D-BMAP/D-MSP/1 queue using RG-factorization

Abstract

ABSTRACT The current investigation of our paper is concentrated on an infinite-buffer single-server queueing model with discrete-time batch Markovian arrival process and Markovian service process. The steady-state behaviour of this discrete-time queueing system at various significant time epochs are presented. We first analyze the system-length distribution at outside observer’s epoch using the -factorization technique combined with the spectral expansion method to compute the stochastic matrix . For the purpose of comparative study, a comprehensive analysis of the system-length distribution at outside observer’s epoch is also carried out using the roots method. Next, we obtain the explicit closed-form expressions of the system-length distributions at pre-arrival, intermediate, post-departure and random epochs by developing the relations among them in equilibrium state. The analysis of waiting-time distribution in the queue measured in slots of an arbitrary customer in an arriving batch is also discussed. Computational experiences with adequate numerical results are conferred in the structure of tables and graphs. Finally, we suggest that our queueing model seems to be fitted for outpatient service of any specialized hospital in a smart city.