Pointwise Stationary Fluid Models for Stochastic Processing Networks

Achal Bassamboo, J. Michael Harrison, Assaf Zeevi

Manufacturing & Service Operations Management · 2009 · Volume 11 · Issue 1

Abstract

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.

Keywords

admission control, dynamic routing, doubly stochastic arrivals, approximation, pointwise stationary, fluid models, abandonments, stochastic networks

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