IEICE TRANSACTIONS on Communications
Mean Approximate Formulas for GI/G/1 Processor-Sharing System
Summary :
The processor-sharing (PS) rule arises as a natural paradigm in a variety of practical situations, including time-shared computer systems. Although there has been much work on Poisson-input queueing analysis for the PS rule, there have been few results for renewal-input GI/G/1 (PS) systems. We consider the GI/G/1 (PS) system to provide develop a two-moment approximation for the mean performance measures. We derive the relationship between the mean unfinished work and the conditional mean sojourn time for the GI/G/1 (PS) system. Using this relationship, we derive approximate formulas for the mean conditional sojourn time, mean sojourn time, and the mean number of customers in the GI/G/1 (PS) system. Numerical examples are presented to compare the approximation with exact and simulated results. We show that the proposed approximate formulas have good accuracy.
- Publication
- IEICE TRANSACTIONS on Communications Vol.E94-B No.8 pp.2247-2253
- Publication Date
- 2011/08/01
- Publicized
- Online ISSN
- 1745-1345
- DOI
- 10.1587/transcom.E94.B.2247
- Type of Manuscript
- PAPER
- Category
- Fundamental Theories for Communications
Authors
Keyword
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Kentaro HOSHI, Yoshiaki SHIKATA, Yoshitaka TAKAHASHI, Naohisa KOMATSU, "Mean Approximate Formulas for GI/G/1 Processor-Sharing System" in IEICE TRANSACTIONS on Communications,
vol. E94-B, no. 8, pp. 2247-2253, August 2011, doi: 10.1587/transcom.E94.B.2247.
Abstract: The processor-sharing (PS) rule arises as a natural paradigm in a variety of practical situations, including time-shared computer systems. Although there has been much work on Poisson-input queueing analysis for the PS rule, there have been few results for renewal-input GI/G/1 (PS) systems. We consider the GI/G/1 (PS) system to provide develop a two-moment approximation for the mean performance measures. We derive the relationship between the mean unfinished work and the conditional mean sojourn time for the GI/G/1 (PS) system. Using this relationship, we derive approximate formulas for the mean conditional sojourn time, mean sojourn time, and the mean number of customers in the GI/G/1 (PS) system. Numerical examples are presented to compare the approximation with exact and simulated results. We show that the proposed approximate formulas have good accuracy.
URL: https://global.ieice.org/en_transactions/communications/10.1587/transcom.E94.B.2247/_p
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@ARTICLE{e94-b_8_2247,
author={Kentaro HOSHI, Yoshiaki SHIKATA, Yoshitaka TAKAHASHI, Naohisa KOMATSU, },
journal={IEICE TRANSACTIONS on Communications},
title={Mean Approximate Formulas for GI/G/1 Processor-Sharing System},
year={2011},
volume={E94-B},
number={8},
pages={2247-2253},
abstract={The processor-sharing (PS) rule arises as a natural paradigm in a variety of practical situations, including time-shared computer systems. Although there has been much work on Poisson-input queueing analysis for the PS rule, there have been few results for renewal-input GI/G/1 (PS) systems. We consider the GI/G/1 (PS) system to provide develop a two-moment approximation for the mean performance measures. We derive the relationship between the mean unfinished work and the conditional mean sojourn time for the GI/G/1 (PS) system. Using this relationship, we derive approximate formulas for the mean conditional sojourn time, mean sojourn time, and the mean number of customers in the GI/G/1 (PS) system. Numerical examples are presented to compare the approximation with exact and simulated results. We show that the proposed approximate formulas have good accuracy.},
keywords={},
doi={10.1587/transcom.E94.B.2247},
ISSN={1745-1345},
month={August},}
Copy
TY - JOUR
TI - Mean Approximate Formulas for GI/G/1 Processor-Sharing System
T2 - IEICE TRANSACTIONS on Communications
SP - 2247
EP - 2253
AU - Kentaro HOSHI
AU - Yoshiaki SHIKATA
AU - Yoshitaka TAKAHASHI
AU - Naohisa KOMATSU
PY - 2011
DO - 10.1587/transcom.E94.B.2247
JO - IEICE TRANSACTIONS on Communications
SN - 1745-1345
VL - E94-B
IS - 8
JA - IEICE TRANSACTIONS on Communications
Y1 - August 2011
AB - The processor-sharing (PS) rule arises as a natural paradigm in a variety of practical situations, including time-shared computer systems. Although there has been much work on Poisson-input queueing analysis for the PS rule, there have been few results for renewal-input GI/G/1 (PS) systems. We consider the GI/G/1 (PS) system to provide develop a two-moment approximation for the mean performance measures. We derive the relationship between the mean unfinished work and the conditional mean sojourn time for the GI/G/1 (PS) system. Using this relationship, we derive approximate formulas for the mean conditional sojourn time, mean sojourn time, and the mean number of customers in the GI/G/1 (PS) system. Numerical examples are presented to compare the approximation with exact and simulated results. We show that the proposed approximate formulas have good accuracy.
ER -
English
