Output variance asymptotics of service systems stabilized by customer loss

Output variance asymptotics of service systems stabilized by customer loss

D J Daley
University of Melbourne

Monday, October 14
3:15 - 4:00 PM
Spilker 143

Abstract:

The output of a stable Poisson queue is Poisson at the same rate as the input process. When the input rate exceeds the service rate stability can be achieved via a loss mechanism --- a buffer, or balking, or reneging --- and the output is again (approximately) Poisson. Nazarathy and Weiss (QUESTA, 2008) showed that for a single-server system with a large buffer, the variance rate of the output process is consistent with a Poisson process rate except when the input and service rates are equal. This phenomenon persists in many-server systems, and in many-server systems with reneging provided there is also a buffer.

I shall attempt an explanation via Ornstein--Uhlenbeck and Brownian diffusions, and speculate on the wider implications for the output of networks. This is joint work with Yoni Nazarathy (UQ) and Johan van Leeuwaarden (TU Eindhoven)]

Operations Research Colloquia: http://or.stanford.edu/oras_seminars.html