On finite buffer BMAP/G/1 queue with queue length dependent service

Abstract

This paper deals with the analysis of a finite buffer queueing system where customers are arriving according to the batch Markovian arrival process (BMAP). The service time is considered to be generally distributed and is dependent on the queue length at service initiation epoch. The stationary queue length distribution at various epoch is obtained using the embedded Markov chain technique and the supplementary variable technique. A computational procedure has been discussed by considering phase-type service time distribution. Finally, some numerical results are given to show the numerical compatibility of the analytical results. Also a comparative study is carried out to establish the fact that our model may help in optimizing system performance by controlling the service rate depending on the state of the system. © 2018, Springer Nature Singapore Pte Ltd.