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Calculating equilibrium probabilities for λ(n)/C_k/1/N queues

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PERFORMANCE '80: Proceedings of the 1980 international symposium on Computer performance modelling, measurement and evaluation

Pages 117 - 125

https://doi.org/10.1145/800199.806155

Published: 28 May 1980 Publication History

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Abstract

Equilibrium state distributions are determined for queues with load-dependent Poisson arrivals and service time distributions representable by Cox's generalized method of stages. The solution is obtained by identifying a birth-death process that has the same equilibrium state distribution as the original queue. Special cases of two-stage (C₂) and Erlang-k (E_k) service processes permit particularly efficient algorithms for calculating the load - dependent service rates of the birth-death process corresponding to the original queue. Knowing the parameters of the birth-death process, the equilibrium state probabilities can be calculated straight-forwardly. This technique is particularly useful when subsystems are reduced to flow-equivalent servers representing the complementary network.

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Bies AHermanns HKöhl MSchmidt A(2023)Matching Distributions Under Structural ConstraintsQuantitative Evaluation of Systems10.1007/978-3-031-43835-6_16(221-237)Online publication date: 15-Sep-2023
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Niu ZCasale G(2021)A Mixture Density Network Approach to Predicting Response Times in Layered Systems2021 29th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS)10.1109/MASCOTS53633.2021.9614286(1-8)Online publication date: 3-Nov-2021
https://doi.org/10.1109/MASCOTS53633.2021.9614286
Gorbunova AVishnevsky V(2021)Evaluation of the Performance Parameters of a Closed Queuing Network Using Artificial Neural NetworksDistributed Computer and Communication Networks: Control, Computation, Communications10.1007/978-3-030-92507-9_22(265-278)Online publication date: 15-Dec-2021
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Index Terms

Calculating equilibrium probabilities for λ(n)/C_k/1/N queues
1. Mathematics of computing
  1. Probability and statistics
    1. Statistical paradigms
      1. Queueing theory

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Published In

PERFORMANCE '80: Proceedings of the 1980 international symposium on Computer performance modelling, measurement and evaluation

May 1980

289 pages

ISBN:0897910192

DOI:10.1145/800199

ACM SIGMETRICS Performance Evaluation Review Volume 9, Issue 2
Summer 1980
274 pages
ISSN:0163-5999
DOI:10.1145/1009375
Issue’s Table of Contents

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 28 May 1980

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Cited By

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Bies AHermanns HKöhl MSchmidt A(2023)Matching Distributions Under Structural ConstraintsQuantitative Evaluation of Systems10.1007/978-3-031-43835-6_16(221-237)Online publication date: 15-Sep-2023
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https://doi.org/10.1109/MASCOTS53633.2021.9614286
Gorbunova AVishnevsky V(2021)Evaluation of the Performance Parameters of a Closed Queuing Network Using Artificial Neural NetworksDistributed Computer and Communication Networks: Control, Computation, Communications10.1007/978-3-030-92507-9_22(265-278)Online publication date: 15-Dec-2021
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Al Hanbali AAlvarez EHeijden M(2015)Approximations for the waiting-time distribution in an $$M/PH/c$$M/PH/c priority queueOR Spectrum10.1007/s00291-015-0388-937:2(529-552)Online publication date: 1-Mar-2015
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Park CLee H(2014)Approximation analysis of multi-class closed queueing maintenance networks with a parts inventory system and two-phase Coxian time distributionsComputers and Operations Research10.1016/j.cor.2013.12.01446(23-37)Online publication date: 1-Jun-2014
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