Colloquium| Institute of Mathematical Sciences
Time：14:00-15:00, December 12 Thursday
Location：Room S408, IMS
Speaker: Wei You from Hong Kong University of Science and Technology.
Abstract: We study the stationary customer flows in an open queueing network with general arrival and service distributions. The flows are the point processes counting customers flowing from one queue to another or out of the network. We establish the existence of unique stationary flows in generalized Jackson networks and convergence to the stationary flows as time increases. We further establish heavy-traffic limits for the stationary flows, allowing an arbitrary subset of the queues to be critically loaded. Based on the heavy-traffic limits, we show that the variance function of the stationary flow can be approximately characterized as a linear function of the variance functions of related flows, with a time-dependent weight function. This leads to a set of linear equations from which we solve for approximations of the variance function of each flow. We prove that this set of equations is asymptotically exact in heavy traffic. Finally, we demonstrate how the variance functions of the stationary flows can be applied to obtain performance approximation in open queueing networks. This algorithm is referred to as the Robust Queueing Network Analyzer.