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Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 4, Pages 339-356

Sojourn time distributions in a Markovian G-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 Hindawi Publishing Corporation. 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.