ALGORITHMS FOR COMPUTING WAITING TIME DISTRIBUTIONS UNDER DIFFERENT QUEUE DISCIPLINES FOR THE D-BMAP PH/1/

A queueing system characterized by the discrete batch Markovian arriva l process (D-BMAP) and a probability of phase type distribution for th e service time is one that arises frequently in the area of telecommun ications. Under this arrival process and service time distribution we derive the waiting time distribution for three queue disciplines: firs t in first out (FIFO), last in first out (LIFO), and service in random order (SIRO). We also outline efficient algorithmic procedures for co mputing the waiting time distributions under each discipline. (C) 1997 John Wiley & Sons, Inc.