Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 4, Pages 339-356
doi:10.1155/S1048953399000301
Abstract
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.