Transient and busy period analysis of the GI/G/1 queue: The method of stages

Dimitris J. Bertsimas; Daisuke Nakazato

doi:10.1007/BF01159205

Transient and busy period analysis of the GI/G/1 queue: The method of stages

Dimitris J. Bertsimas, Daisuke Nakazato

Research output: Contribution to journal › Article › peer-review

24 Citations (Scopus)

Abstract

In this paper we study the transient behavior of the MGE_L/MGE_M/1 queueing system, where MGE is the class of mixed generalized Erlang distributions which can approximate an arbitrary distribution. We use the method of stages combined with the separation of variables and root finding techniques together with linear and tensor algebra. We find simple closed form expressions for the Laplace transforms of the queue length distribution and the waiting time distribution under FCFS when the system is initially empty and the busy period distribution. We report computational results by inverting these expressions numerically in the time domain. Because of the simplicity of the expressions derived our algorithm is very fast and robust.

Original language	English
Pages (from-to)	153-184
Number of pages	32
Journal	Queueing Systems
Volume	10
Issue number	3
DOIs	https://doi.org/10.1007/BF01159205
Publication status	Published - 1992 Sep 1
Externally published	Yes

Keywords

Transient analysis
busy period
linear algebra
transform methods

ASJC Scopus subject areas

Statistics and Probability
Computer Science Applications
Management Science and Operations Research
Computational Theory and Mathematics

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N2 - In this paper we study the transient behavior of the MGEL/MGEM/1 queueing system, where MGE is the class of mixed generalized Erlang distributions which can approximate an arbitrary distribution. We use the method of stages combined with the separation of variables and root finding techniques together with linear and tensor algebra. We find simple closed form expressions for the Laplace transforms of the queue length distribution and the waiting time distribution under FCFS when the system is initially empty and the busy period distribution. We report computational results by inverting these expressions numerically in the time domain. Because of the simplicity of the expressions derived our algorithm is very fast and robust.

AB - In this paper we study the transient behavior of the MGEL/MGEM/1 queueing system, where MGE is the class of mixed generalized Erlang distributions which can approximate an arbitrary distribution. We use the method of stages combined with the separation of variables and root finding techniques together with linear and tensor algebra. We find simple closed form expressions for the Laplace transforms of the queue length distribution and the waiting time distribution under FCFS when the system is initially empty and the busy period distribution. We report computational results by inverting these expressions numerically in the time domain. Because of the simplicity of the expressions derived our algorithm is very fast and robust.

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KW - transform methods

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Transient and busy period analysis of the GI/G/1 queue: The method of stages

Abstract

Keywords

ASJC Scopus subject areas

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