Single-Server Queue with Markov-Dependent Inter-Arrival and Service Times

Authors:
I. J. B. F. Adan;V. G. Kulkarni
Affiliations:
Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands 5600 MB;Department of Operations Research, University of North Carolina, Chapel Hill, USA 27599
Venue:
Queueing Systems: Theory and Applications
Year:
2003

Citing 0
Cited 11

A BMAP/SM/1 Queueing System with Hybrid Operation Mechanism

Automation and Remote Control
On Queues with Markov Modulated Service Rates

Queueing Systems: Theory and Applications
Fundamental characteristics of queues with fluctuating load

SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
M/M/C queues with Markov modulated service processes

valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
The Gerber-Shiu discounted penalty functions for a risk model with two classes of claims

Journal of Computational and Applied Mathematics
System-theoretical algorithmic solution to waiting times in semi-Markov queues

Performance Evaluation
The Gerber-Shiu penalty functions for two classes of renewal risk processes

Journal of Computational and Applied Mathematics
Analysis of scheduling policies under correlated job sizes

Performance Evaluation
A matrix geometric representation for the queue length distribution of multitype semi-Markovian queues

Performance Evaluation
Analysis of a versatile batch-service queueing model with correlation in the arrival process

Performance Evaluation
Corrected phase-type approximations for the workload of the MAP/G/1 queue with heavy-tailed service times

ACM SIGMETRICS Performance Evaluation Review - Special issue on the 31st international symposium on computer performance, modeling, measurements and evaluation (IFIPWG 7.3 Performance 2013)

Quantified Score

Hi-index	0.01

Visualization

Abstract

In this paper we study a single-server queue where the inter-arrival times and the service times depend on a common discrete time Markov chain. This model generalizes the well-known MAP/G/1 queue by allowing dependencies between inter-arrival and service times. The waiting time process is directly analyzed by solving Lindley's equation by transform methods. The Laplace---Stieltjes transforms (LST) of the steady-state waiting time and queue length distribution are both derived, and used to obtain recursive equations for the calculation of the moments. Numerical examples are included to demonstrate the effect of the autocorrelation of and the cross-correlation between the inter-arrival and service times.