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Title: Two tandem queues with general renewal input. 2: Asymptotic expansions for the diffusion model

Abstract

In Part 1 the authors formulated and solved a diffusion model for two tandem queues with exponential servers and general renewal arrivals. They thus obtained the easy traffic diffusion approximation to the steady state joint queue length distribution for this network. Here they study asymptotic and numerical properties of the diffusion approximation. In particular, analytical expressions are obtained for the tail probabilities. Both the joint distribution of the two queues and the marginal distribution of the second queue are considered. They also give numerical illustrations of how this marginal is affected by changes in the arrival and service processes.

Authors:
;
Publication Date:
Research Org.:
Univ. of Illinois, Chicago, IL (US)
Sponsoring Org.:
USDOE
OSTI Identifier:
20005556
Resource Type:
Journal Article
Journal Name:
SIAM Journal on Applied Mathematics (Society for Industrial and Applied Mathematics)
Additional Journal Information:
Journal Volume: 59; Journal Issue: 6; Other Information: PBD: Oct 1999; Journal ID: ISSN 0036-1399
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; QUEUES; MATHEMATICAL MODELS; INTEGRAL EQUATIONS; MATHEMATICS

Citation Formats

Knessl, C, and Tier, C. Two tandem queues with general renewal input. 2: Asymptotic expansions for the diffusion model. United States: N. p., 1999. Web. doi:10.1137/S0036139997328477.
Knessl, C, & Tier, C. Two tandem queues with general renewal input. 2: Asymptotic expansions for the diffusion model. United States. https://doi.org/10.1137/S0036139997328477
Knessl, C, and Tier, C. 1999. "Two tandem queues with general renewal input. 2: Asymptotic expansions for the diffusion model". United States. https://doi.org/10.1137/S0036139997328477.
@article{osti_20005556,
title = {Two tandem queues with general renewal input. 2: Asymptotic expansions for the diffusion model},
author = {Knessl, C and Tier, C},
abstractNote = {In Part 1 the authors formulated and solved a diffusion model for two tandem queues with exponential servers and general renewal arrivals. They thus obtained the easy traffic diffusion approximation to the steady state joint queue length distribution for this network. Here they study asymptotic and numerical properties of the diffusion approximation. In particular, analytical expressions are obtained for the tail probabilities. Both the joint distribution of the two queues and the marginal distribution of the second queue are considered. They also give numerical illustrations of how this marginal is affected by changes in the arrival and service processes.},
doi = {10.1137/S0036139997328477},
url = {https://www.osti.gov/biblio/20005556}, journal = {SIAM Journal on Applied Mathematics (Society for Industrial and Applied Mathematics)},
issn = {0036-1399},
number = 6,
volume = 59,
place = {United States},
year = {Fri Oct 01 00:00:00 EDT 1999},
month = {Fri Oct 01 00:00:00 EDT 1999}
}