The nonpreemptive priority MAP/G/1 queue. (English) Zbl 0986.60087

Takine, Tetsuya

Oper. Res. 47, No. 6, 917-927 (1999).

Summary: This paper considers the nonpreemptive priority queue with MAP (Markovian arrival process) arrivals. Since MAP is weakly dense in the class of stationary point processes, it is a fairly general arrival process. Service times of customers of each priority class are independent and identically distributed according to a general distribution function that may differ among priority classes. Using both the generating function technique and the matrix analytic method, we derive various formulas for the marginal queue length distribution of each class. Further, we provide the delay cycle analysis of the waiting time distribution of each class and characterize its Laplace-Stieltjes transform.

MSC:

60K25	Queueing theory (aspects of probability theory)
90B22	Queues and service in operations research

Keywords:

Markovian arrival process; nonpreemptive priority queue; generating function technique; matrix analytic method; queue length distribution; delay cycle analysis; Laplace-Stieltjes transform