Fluid Approximation of a Processor Sharing Queue with Impatient Customers
Bert Zwart
Department of Mathematics and Computer Science
Eindhoven University of Technology
Wednesday, June 8, 2005
4:30 - 5:45 PM
Terman Engineering Center, Room 453
Abstract:
Motivated by obtaining a better understanding of the impact of
reneging (e.g. aborting the download of a webpage) behavior in
communication networks, we consider the GI/GI/1 PS queue where
customers may leave after a certain amount of time before their
service is finished. Under the PS service discipline, such behavior is
very undesirable, since it implies that some work is done for nothing.
By considering a fluid scaling, we show that the process describing
the number of customers in this Processor Sharing queue can be
approximated by a delay-differential equation. We analyze this
equation in detail; in particular we show convergence to a simple
fixed-point equation. This equation enables us to do performance
analysis and to obtain approximations for the fraction of customers
that renege and the fraction of waisted bandwidth.
This talk is based on ongoing work with Christian Gromoll (Stanford)
and Philippe Robert (INRIA).
Operations Research Colloquia: http://or.stanford.edu/oras_seminars.html