Analytic and computational analysis of the discrete-time GI/D-MSP/1 queue using roots

Computers & Operations Research, 56 (2015), 33–40
http://dx.doi.org/10.1016/j.cor.2014.10.017

This paper presents a simple closed-form analysis for evaluating system-length distributions at various epochs of the discrete-time GI/D-MSP/1 queue. The proposed analysis is based on roots of the associated characteristic equation of the vector-generating function of system-length distribution at prearrival epochs. We provide the steady-state system-length distribution at random epoch by using the classical argument based on Markov renewal theory. The queueing-time distribution has also been investigated. Numerical aspects have been tested for a variety of interarrival- and service-time distributions and a sample of numerical outputs is presented.