Ruth Williams, San Diego Stochastic Networks with Resource Sharing
Abstract: Stochastic networks are used as models for complex systems involving dynamic interactions subject to uncertainty. Application domains include manufacturing, the service industry, telecommunications, and computer systems. Networks arising in modern applications are often highly complex and heterogeneous, with network features that trascend those of conventional queueing models. The control and analysis of such networks present challenging mathematical problems.
In this talk, a concrete application will be used to illustrate a general approach to the study of stochastic networks using more tractable approximate models. Specifically, we consider a connection-level model of Internet congestion control that represents the randomly varying number of flows present in a network where bandwidth is shared fairly amongst elastic documents. This model, introduced by Massoulie and Roberts, can be viewed as a stochastic network with simultaneous resource possession. Elegant fluid and diffusion approximations will be used to study the stability and performance of this model.
The talk will conclude with a summary of the current status and description of open problems associated with the further development of approximate models for general stochastic networks.
This talk is based in part on joint work with W. Kang, F. P. Kelly, and N. H. Lee.