B alancing R educes A symptotic V ariance of O utputs. Yoni Nazarathy * EURANDOM, Eindhoven University of Technology, The Netherlands. Based on some joint works with Ahmad Al Hanbali , Michel Mandjes , Gideon Weiss and Ward Whitt. QTNA 2010, Beijing, July 26, 2010.
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EURANDOM, Eindhoven University of Technology,The Netherlands.
Based on some joint works withAhmad Al Hanbali, Michel Mandjes,
Gideon Weiss and Ward Whitt
QTNA 2010, Beijing,
July 26, 2010.
*Supported by NWO-VIDI Grant 639.072.072 of Erjen Lefeber
Balancing Reduces Asymptotic Variance of Outputs
* Squared coefficient of variation:
* Stationary stable M/M/1, D(t) is PoissonProcess( ):
* Stationary M/M/1/1 with . D(t) is RenewalProcess(Erlang(2, )):
* In general, for renewal process with :
* The output process of most queueing systems is NOT renewal
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is approximately the same as when or
Theorem (Al Hanbali, Mandjes, N. , Whitt 2010):For the GI/G/1 queue with , under some further technical conditions:
For GI/G/1/K with :
Numerically Conjectured: GI/G/1/K with light tails