The Nonpreemptive Priority Map/G/1 Queue

Authors:
José Manuel Campa;Mauro F. Guillén;Gila E. Fruchter;Tetsuya Takine
Affiliations:
-;-;-;-
Venue:
Operations Research
Year:
1999

Citing 0
Cited 9

Distributional Form of Little's Law for FIFO Queues with Multiple Markovian Arrival Streams and Its Application to Queues with Vacations

Queueing Systems: Theory and Applications
Queue Length Distribution in a FIFO Single-Server Queue with Multiple Arrival Streams Having Different Service Time Distributions

Queueing Systems: Theory and Applications
Optimal Policies for Multi-server Non-preemptive Priority Queues

Queueing Systems: Theory and Applications
Single-Server Queues with Markov-Modulated Arrivals and Service Speed

Queueing Systems: Theory and Applications
Stationary delays for a two-class priority queue with impatient customers

Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Unified analysis of BMAP/G/1 cyclic polling models

Queueing Systems: Theory and Applications
Performance analysis of priority queueing systems in discrete time

Network performance engineering
Geometric tail of queue length of low-priority customers in a nonpreemptive priority MAP/PH/1 queue

Queueing Systems: Theory and Applications
Efficient analysis of the queue length moments of the MMAP/MAP/1 preemptive priority queue

Performance Evaluation

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.