The matrix-form solution for Geo(X)/G/1/N working vacation queue and its application to state-dependent cost control

摘要

This paper studies a finite buffer size Geo(X)/G/1/N queue with single working vacation and different input rates. By combining two classic methods of supplementary variable and embedded Markov chain, the matrix-form solutions of queue-length distributions at departure, arbitrary, pre-arrival and outside observer's observation epochs are obtained. Based on these queue-length distributions, some performance measures are also derived and some numerical experiments are carried out. Then, an optimal control on state-dependent operating cost of a production to order is presented. (C) 2015 Elsevier Ltd. All rights reserved.