Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 4, Pages 339-356
Sojourn time distributions in a Markovian -queue with batch arrival and batch removal
Changwon National University, Department of Statistics, 9 Sarim-dong, Kyung-nam, Changwon 641-773, Korea
Received 1 November 1997; Revised 1 January 1999
Copyright © 1999 Yang Woo Shin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider a single server Markovian queue with two types of customers;
positive and negative, where positive customers arrive in batches and arrivals of negative customers remove positive customers in batches. Only
positive customers form a queue and negative customers just reduce the
system congestion by removing positive ones upon their arrivals. We derive the LSTs of sojourn time distributions for a single server Markovian
queue with positive customers and negative customers by using the first
passage time arguments for Markov chains.