Performance analysis of the GI/D-MSP/1 queue with N-policy and its optimal control

Abstract

ABSTRACT This paper investigates a discrete-time GI/D-MSP/1/\\infty queueing system under N-policy with renewal input. The service process is correlated and its structure is constructed through discrete-time Markovian service process. The idle server resumes to serve the customers as soon as the number of waiting customers in the queue reaches a predefined threshold value N and serves the customers exhaustively until the system becomes empty. We use the matrix-geometric method to derive the system-length distribution at prearrival epoch. Employing the Markov renewal theory, we obtain the system-length distribution at random epoch. We also carried out the system-length distributions at outside observer’s, intermediate and post-departure epochs. Further, we find the waiting-time distribution in the queue measured in slots of an arrival customer. An expected linear cost function per unit time is considered to determine the optimal value of N, which minimises the expected cost function. Some numerical results are demonstrated to measure the effects of N, interarrival-time distributions and other model parameters.