Date: Oct. 1, 3:30 pm in 3355 Engr. Hall Title: Worst Case and Probabilistic Analysis of Integrated Services Networks Speaker: Rajeev Agrawal, ECE Department Abstract: We consider a network model in which the basic queueing elements are regulators and schedulers. Regulators reshape the arrival process to a burstiness constraint, while schedulers ensure a certain level of service to individual flows (through some scheduling mechanism). We introduce a unified queueing model for these elements that may be viewed as a linear system with a time-varying impulse response in the (min,+) algebra. We then consider fork-join networks of such elements that allow us to model end-to-end or hop-by-hop window flow control mechanisms as well as both unicast and multicast session topologies. These networks may be viewed as parallel, series, and feedback interconnections in the (min,+) algebra. We obtain a number of pathwise, worst case, and probabilistic results for this queueing model. We show how the departure processes from such networks may be explicitly obtained in terms of the exogenous arrival and service processes. We obtain worst case bounds on the queue lengths, delay and burstiness of departure processes. We use these bounds to show how regulation may be used inside the network to reduce buffering requirements without affecting the worst case delay. When the arrival and service processes are stationary ergodic we obtain the throughputs in terms of the arrival and service rates, and we also obtain necessary and sufficient conditions for the stability of the system. These results may be used to investigate the support of different types of service classes for integrated services networks. In particular, we may consider three distinct classes. The first and second provide worst case and probabilistic guarantees, respectively, on the loss and delay received in return for imposing constraints on the traffic. The third provides no guarantees but uses feedback flow control to ensure that the traffic utilizes the available bandwidth without causing congestion. Hybrid service categories that combine these may also be designed. These service classes may be viewed as ways of realizing the guaranteed, controlled load, and best effort service categories defined by the integrated services working group of the Internet Engineering Task Force. (This is joint work with Francois Baccelli and Rajendran Rajan)