The versatility of MMAP[K] and the MMAP[K]/G[K]/1 queue

This paper studies a single server queueing system with multiple types of customers. The first part of the paper discusses some modeling issues associated with the Markov arrival processes with marked arrivals (MMAP[K], where K is an integer representing the number of types of customers). The usefulness of MMAP[K] in modeling point processes is shown by a number of interesting examples. The second part of the paper studies a single server queueing system with an MMAP[K] as its input process. The busy period, virtual waiting time, and actual waiting times are studied. The focus is on the actual waiting times of individual types of customers. Explicit formulas are obtained for the Laplace–Stieltjes transforms of these actual waiting times.