The $$MMAP\left[ K \right]/PH\left[ K \right]/1$$ queues with a last-come-first-served preemptive service discipline

This paper studies two queueing systems with a Markov arrival process with marked arrivals and PH-distribution service times for each type of customer. Customers (regardless of their types) are served on a last-come-first-served preemptive resume and repeat basis, respectively. The focus is on the stationary distribution of queue strings in the system and busy periods. Efficient algorithms are developed for computing the stationary distribution of queue strings, the mean numbers of customers served in a busy period, and the mean length of a busy period. Comparison is conducted numerically between performance measures of queueing systems with preemptive resume and preemptive repeat service disciplines. A counter-intuitive observation is that for a class of service time distributions, the repeat discipline performs better than the resume one. This revised version was published online in June 2006 with corrections to the Cover Date.