The nonpreemptive priority MAP/G/1 queue

This paper considers the nonpreemptive priority queue with MAP (Markovian A rrival Process) arrivals. Since MAP is weakly dense in the class of station ary point processes, it is a fairly general arrival process. Service times of customers of each priority class are independent and identically distrib uted according to a general distribution function that may differ among pri ority classes. Using both the generating function technique and the matrix analytic method, we derive various formulas for the marginal queue length d istribution of each class. Further, we provide the delay cycle analysis of the waiting lime distribution of each class and characterize its Laplace-St ieltjes transform.