MANAGERIAL ECONOMICS & DECISION SCIENCES; OPERATIONS
Assistant Professor of Managerial Economics and Decision Sciences
Queuing Systems
We consider a class of stochastic processing networks. Assume that the networks satisfy a complete resource pooling condition. We prove that \emph{each} maximum pressure policy asymptotically minimizes the workload process in a stochastic processing network in heavy traffic. We also show that, under each quadratic holding cost structure, there is a maximum pressure policy that asymptotically minimizes the holding cost. A key to the optimality proofs is to prove a state space collapse result and a heavy traffic limit theorem for the network processes under a maximum pressure policy. We extend a framework of Bramson (1998) and Williams (1998) from the multiclass queueing network setting to the stochastic processing network setting to prove the state space collapse result and the heavy traffic limit theorem. The extension can be adapted to other studies of stochastic processing networks.
A class of open processing networks operating under a maximum pressure policy is considered in the heavy traffic regime. We prove that the diffusion-scaled workload process for a network with several bottleneck resources converges to a semimartingale reflecting Brownian motion (SRBM) living in a polyhedral cone. We also establish a state space collapse result that the queue length process can be lifted from the lower-dimensional workload process.
Stochasitc Calculus and Control w/ Applications
Stochastic Calculus and Control With Applications (OPNS-463-0)
Stochastic Calculus and Control With Applications
This course counts toward the following majors:Operations.
Operations management is the management of business processes--that is, the management of the recurring activities of a firm. This course aims to familiarize students with the problems and issues confronting operations managers, and to provide the language, concepts, insights and tools to deal with these issues to gain competitive advantage through operations. We examine how different business strategies require different business processes and how different operational capabilities allow and support different strategies to gain competitive advantage. A process view of operations is used to analyze different key operational dimensions such as capacity management, cycle time management, supply chain and logistics management, and quality management. Finally, we connect to recent developments such as lean or world-class manufacturing, just-in-time operations, time-based competition and business re-engineering.
Prerequisite: DECS-433 or DECS-436.
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