Conference on Stochastic Processing Networks

Speaker: Jim Dai Title: Maximum Pressure Policies in Stochastic Processing Networks Abstract: Stochastic processing networks have been introduced in a series of three papers by Harrison (2000, 2002, 2003). These networks are much more general than multi-class queueing networks. The added generality allows one to model skill-based routing in call centers, operator-machine interactions in semiconductor wafer fabrication facilities, and combined inputand output-queued data switches. We introduce a family of maximum pressure policies that can be used to operate a stochastic processing network. Such a policy is shown to be throughput optimal for a wide class of networks. When the holding cost rate is a quadratic function of the buffer contents, we show that a maximum pressure policy asymptotically minimizes the holding cost under a heavy traffic condition and a complete resource pooling condition. [This talk is based on the joint work with Wuqin Lin at Northwestern University.] Speaker: Maury Bramson, University of Minnesota Title: Positive Recurrence of Reflecting Brownian Motion in 3 Dimensions Abstract: Precise conditions are known for positive recurrence of semimartingale reflecting Brown motion (SRBM) in 2 dimensions. The behavior in 4 and more dimensions is largely unexplored. In 3 dimensions, sufficient conditions for positive recurrence are given by El Kharroubi et al. (2002). In joint work with Jim Dai and Mike Harrison, it was recently shown that these results are, in fact, sufficient. In this talk, we summarize the above material. Speaker: Steve Shreve, Carnegie Mellon University Title: Double Skorokhod Map and Reneging Real-Time Queues Abstract: An explicit formula for the Skorokhod map on [0,a] is provided. Specifically, it is shown that on the space of right-continuous functions with left limits taking values in the real numbers, ψ(t)− [ (ψ(0)− a) ∧ inf u∈[0,t] ψ(u) ] ∨ sup s∈[0,t] [ (ψ(s)− a) ∧ inf u∈[s,t] ψ(u) ]