TY - JOUR
T1 - Mean approximate formulas for GI/G/1 processor-sharing system
AU - Hoshi, Kentaro
AU - Shikata, Yoshiaki
AU - Takahashi, Yoshitaka
AU - Komatsu, Naohisa
PY - 2011/8
Y1 - 2011/8
N2 - 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 renewalinput 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.
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 renewalinput 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.
KW - Processor-sharing
KW - Queues
KW - Renewal input
KW - Sojourn-time
KW - Tele-traffic analysis
KW - Unfinished-work
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U2 - 10.1587/transcom.E94.B.2247
DO - 10.1587/transcom.E94.B.2247
M3 - Article
AN - SCOPUS:79961077742
VL - E94-B
SP - 2247
EP - 2253
JO - IEICE Transactions on Communications
JF - IEICE Transactions on Communications
SN - 0916-8516
IS - 8
ER -