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Optimal Choice of Threshold in Two Level Processor Sharing Konstantin Avrachenkova, Patrick Brownb, Natalia Osipovac, 1
 

Summary: Optimal Choice of Threshold in Two Level Processor Sharing
Konstantin Avrachenkova, Patrick Brownb, Natalia Osipovac, 1
a
INRIA Sophia Antipolis, France, e-mail: K.Avrachenkov@sophia.inria.fr,
address: 2004, route des Lucioles, 06902, INRIA Sophia Antipolis, France, tel: +33.04.92.38.77.51
b
France Telecom R&D, France, e-mail: Patrick.Brown@orange-ftgroup.com
c
INRIA Sophia Antipolis, France, e-mail: Natalia.Osipova@sophia.inria.fr
Abstract
We analyze the Two Level Processor Sharing (TLPS) scheduling discipline with the hyper-
exponential job size distribution and with the Poisson arrival process. TLPS is a convenient
model to study the benefit of the file size based differentiation in TCP/IP networks. In the case
of the hyper-exponential job size distribution with two phases, we find a closed form analytic
expression for the expected sojourn time and an approximation for the optimal value of the
threshold that minimizes the expected sojourn time. In the case of the hyper-exponential job
size distribution with more than two phases, we derive a tight upper bound for the expected
sojourn time conditioned on the job size. We show that when the variance of the job size
distribution increases, the gain in system performance increases and the sensitivity to the
choice of the threshold near its optimal value decreases.

  

Source: Avrachenkov, Konstantin - INRIA Sophia Antipolis

 

Collections: Computer Technologies and Information Sciences