article

Two finite-difference methods for solving MAP(t)/PH(t)/1/K queueing models

Authors:

Darryl Wayne Dormuth,

Attahiru Sule AlfaAuthors Info & Claims

Queueing Systems: Theory and Applications, Volume 27, Issue 1/2

Pages 55 - 78

https://doi.org/10.1023/A:1019101828857

Published: 14 December 1997 Publication History

Abstract

In this paper two solution methods to the MAP(t)/PH(t)/1/K queueing model are introduced, one based on the Backwards Euler Method and the other on the Uniformization Method. Both methods use finite-differencing with a discretized, adaptive time-mesh to obtain time-dependent values for the entire state probability vector. From this vector, most performance parameters such as expected waiting time and expected number in the system can be computed. Also presented is a technique to compute the entire waiting (sojourn) time distribution as a function of transient time. With these two solution methods one can examine any transient associated with the MAP(t)/PH(t)/1/K model including time-varying arrival and/or service patterns. Four test cases are used to demonstrate the effectiveness of these methods. Results from these cases indicate that both methods provide fast and accurate solutions to a wide range of transient scenarios.

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Cited By

Efrosinin DStepanova N(2019)On Optimal Control Policy of MAP(t)/M/2 Queueing System with Heterogeneous Servers and Periodic Arrival ProcessDistributed Computer and Communication Networks10.1007/978-3-030-36614-8_14(179-194)Online publication date: 23-Sep-2019
https://dl.acm.org/doi/10.1007/978-3-030-36614-8_14
vanDijk NvanBrummelen SBoucherie R(2018)UniformizationPerformance Evaluation10.1016/j.peva.2017.09.008118:C(8-32)Online publication date: 1-Feb-2018
https://dl.acm.org/doi/10.1016/j.peva.2017.09.008
Cerdà-Alabern LHorvath ABuchholz PCortellessa VMuscariello LSquillante M(2013)Closed form transient solution of continuous time Markov chains through uniformizationProceedings of the 7th International Conference on Performance Evaluation Methodologies and Tools10.4108/icst.valuetools.2013.254376(263-272)Online publication date: 10-Dec-2013
https://dl.acm.org/doi/10.4108/icst.valuetools.2013.254376
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cover image Queueing Systems: Theory and Applications

Queueing Systems: Theory and Applications Volume 27, Issue 1/2

1997

199 pages

ISSN:0257-0130

Issue’s Table of Contents

Copyright © Copyright © 1997 Kluwer Academic Publishers.

Publisher

J. C. Baltzer AG, Science Publishers

United States

Publication History

Published: 14 December 1997

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Cited By

Efrosinin DStepanova N(2019)On Optimal Control Policy of MAP(t)/M/2 Queueing System with Heterogeneous Servers and Periodic Arrival ProcessDistributed Computer and Communication Networks10.1007/978-3-030-36614-8_14(179-194)Online publication date: 23-Sep-2019
https://dl.acm.org/doi/10.1007/978-3-030-36614-8_14
vanDijk NvanBrummelen SBoucherie R(2018)UniformizationPerformance Evaluation10.1016/j.peva.2017.09.008118:C(8-32)Online publication date: 1-Feb-2018
https://dl.acm.org/doi/10.1016/j.peva.2017.09.008
Cerdà-Alabern LHorvath ABuchholz PCortellessa VMuscariello LSquillante M(2013)Closed form transient solution of continuous time Markov chains through uniformizationProceedings of the 7th International Conference on Performance Evaluation Methodologies and Tools10.4108/icst.valuetools.2013.254376(263-272)Online publication date: 10-Dec-2013
https://dl.acm.org/doi/10.4108/icst.valuetools.2013.254376
Niyato DHossain E(2006)Queue-Aware Uplink Bandwidth Allocation and Rate Control for Polling Service in IEEE 802.16 Broadband Wireless NetworksIEEE Transactions on Mobile Computing10.1109/TMC.2006.855:6(668-679)Online publication date: 1-Jun-2006
https://dl.acm.org/doi/10.1109/TMC.2006.85

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