Sojourn time distributions in a Markovian G-queue with batch arrival and batch removal (Q1566515)

Summary: 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.