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Pointwise Stationary Fluid Models for Stochastic Processing Networks

Kellogg School of Management, Northwestern University, Evanston, Illinois 60208
Graduate School of Business, Stanford University, Stanford, California 94305
Graduate School of Business, Columbia University, New York, New York 10027
a-bassamboo{at}nwu.edu
harrison_michael{at}gsb.stanford.edu
assaf{at}gsb.columbia.edu

Generalizing earlier work on staffing and routing in telephone call centers, we consider a processing network model with large server pools and doubly stochastic input flows. In this model the processing of a job may involve several distinct operations. Alternative processing modes are also allowed. Given a finite planning horizon, attention is focused on the two-level problem of capacity choice and dynamic system control. A pointwise stationary fluid model (PSFM) is used to approximate system dynamics, which allows development of practical policies with a manageable computational burden. Earlier work in more restrictive settings suggests that our method is asymptotically optimal in a parameter regime of practical interest, but this paper contains no formal limit theory. Rather, it develops a PSFM calculus that is broadly accessible, with an emphasis on modeling and practical computation.

Key Words: admission control; dynamic routing; doubly stochastic arrivals; approximation; pointwise stationary; fluid models; abandonments; stochastic networks
History: Received: August 1, 2005; accepted: July 20, 2007.