Computational analysis of MMAP[K]/PH[>K]/ 1 queues with a mixed FCFS and LCFS service discipline

This paper studies a queueing system 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 mixed first-come-first-served (FCFS) and last-come-first-served (LCFS) nonpreemptive basis. That is, when the queue length is N (a positive integer) or less, customers are served on an FCFS basis; otherwise, customers are served on an LCFS basis. The focus is on the stationary distribution of queue strings, busy periods, and waiting times of individual types of customers. A computational approach is developed for computing the stationary distribution of queue strings, the mean of busy period, and the means and variances of waiting times. The relationship between these performance measures and the threshold number N is analyzed in depth numerically. It is found that the variance of the virtual (actual) waiting time of an arbitrary customer can be reduced by increasing N.