Stochastic processing networks have been introduced in a series of three papers by Harrison (2000, 2002, 2003). A processing network is a system that takes materials of various kinds as inputs, and uses processing resources to produce other materials as outputs. These networks model complex systems including semiconductor wafer fabrication facilities, networks of data switches, and large-scale call centers. Key performance measures of such a network include throughput and average cycle time. Elements of an operational policy may include input control, sequencing, and routing; the choice of such a policy can dramatically affect network performance.
In this talk, we will first show that even in simple networks, commonly used operational policies such as first-in-first-out sequencing may perform badly, failing to achieve even "throughput optimality." We then introduce a family of policies known as maximum pressure policies. Such a policy needs only local or semi-local congestion information to be implemented. Often, its implementation does not require arrival rate information which can be difficult to be estimated reliably.
We show that maximum pressure policies are always throughput optimal, regardless of the processing network's topology or parameter values. Such a policy is further shown to asymptotically minimize a certain diffusion-scaled quadratic holding cost when the network satisfies a heavy traffic condition and a complete resource pooling condition.
This talk is based on joint works with Wuqin Lin at Kellogg School of Business of Northwestern University.