IJPAM: Volume 40, No. 2 (2007)

APPROXIMATION OF THE DELAY DISTRIBUTION
IN BATCH ARRIVAL M/G/1 PRIORITY QUEUES

Hideaki Takagi$^1$, Sang-Yong Kim$^2$
$^{1,2}$Graduate School of Systems and Information Engineering
University of Tsukuba
1-1-1 Tennoudai, Tsukuba-Shi, Ibaraki, 305-8573, JAPAN
$^1$e-mail: takagi@sk.tsukuba.ac.jp
$^2$e-mail: sykim@sk.tsukuba.ac.jp


Abstract.We propose new approximate formulas for the distribution functions of the delay in batch arrival M/G/1 nonpreemptive and preemptive resume priority queues. It is assumed that the delay consists of the waiting time and the service time of a whole batch. Our formulas are of the exponential distribution type with the coefficients being matched with the exact mean and second moment of the delay. By numerical examples, they are shown to be useful for evaluating the delay percentile, which may be used as a measure of the quality of service required by the user.

Received: July 6, 2007

AMS Subject Classification: 60K25

Key Words and Phrases: queue, batch arrival, M/G/1, priority

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 2