an:06000227
Zbl 1238.60106
Xue, Jungong; Alfa, Attahiru S.
Geometric tail of queue length of low-priority customers in a nonpreemptive priority MAP/PH/1 queue
EN
Queueing Syst. 69, No. 1, 45-76 (2011).
00287336
2011
j
60K25 90B22
priority queue; tail probability; Markovian arrival process; phase-type distribution; decay rate
The authors earlier studied a discrete-time BMAP/PH/1 queue with preemptive service discipline [Stoch. Models 21, No. 2--3, 799--820 (2005; Zbl 1069.60085)]. In this paper, they study the geometric decay of the tail probability of low-priority customers of a priority MAP/PH/1 queue with non-preemptive service discipline. They use a quasi birth and death (QBD) process to describe a queue with the queue length of high-priority customers playing the role of \textit{level} and the queue length of low-priority customers together with the phases of arrival and service processes of both classes describing a \textit{phase} in each level. This treatment make the G-matrix and R-matrix of the QBD block upper triangular with identical blocks on each diagonal. They obtain a generating function equation for the stationary distribution of the queue length of low-priority customers. They also derive a sufficient condition for geometric decay. Numerical methods are presented.
P. R. Parthasarathy (Chennai)
Zbl 1069.60085