Generalizing earlier work on staffing and routing in telephone call centers, we consider a processing network with multiple server pools, jobs that may require several processing operations, doubly stochastic input flows, differentiated processing modes, and other features as well. Given a finite planning horizon, we address the two-level problem of capacity choice and dynamic system control. A tractable modeling framework is proposed, in which a pointwise stationary fluid model (PSFM) is used

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... o approximate the system's dynamics. This framework allows one to develop practical policies with a computational burden that is manageable. 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. Short Title: Pointwise Stationary Fluid Models