Insensitive bounds for the moments of the sojourn time distribution in the M/G/1 processor-sharing queue

Cheung, Sing-Kong and Berg van den, Hans and Boucherie, Richard J. (2006) Insensitive bounds for the moments of the sojourn time distribution in the M/G/1 processor-sharing queue. Queueing Systems, 53 (1-2). pp. 7-18. ISSN 0257-0130

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Abstract:	This paper studies the M/G/1 processor-sharing (PS) queue, in particular the sojourn time distribution conditioned on the initial job size. Although several expressions for the Laplace-Stieltjes transform (LST) are known, these expressions are not suitable for computational purposes. This paper derives readily applicable insensitive bounds for all moments of the conditional sojourn time distribution. The instantaneous sojourn time, i.e., the sojourn time of an infinitesimally small job, leads to insensitive upper bounds requiring only knowledge of the traffic intensity and the initial job size. Interestingly, the upper bounds involve polynomials with so-called Eulerian numbers as coefficients. In addition, stochastic ordering and moment ordering results for the sojourn time distribution are obtained. (Keywords: M/G/1 PS - Conditional sojourn time - Moments - Insensitive bounds - Instantaneous sojourn time - Euler's number triangle - Moment ordering - Permanent customers)
Item Type:	Article
Copyright:	© 2006 Springer
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Stochastic Operations Research (SOR)
Link to this item:	http://purl.utwente.nl/publications/62864
Official URL:	http://dx.doi.org/10.1007/s11134-006-7583-y
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