Conservation Laws for Single-Server Fluid Networks

Authors:
Nicole Bäuerle;Shaler Stidham
Affiliations:
Department of Operations Research, University of Ulm, D-89069 Ulm, Germany baeuerle@mathematik.uni-ulm.de;Department of Operations Research, University of North Carolina, Chapel Hill, NC 27599-3180, USA sandy@email.unc.edu
Venue:
Queueing Systems: Theory and Applications
Year:
2001

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Abstract

We consider single-server fluid networks with feedback and arbitrary input processes. The server has to be scheduled in order to minimize a linear holding cost. This model is the fluid analogue of the so-called Klimov problem. Using the achievable-region approach, we show that the Gittins index rule is optimal in a strong sense: it minimizes the linear holding cost for arbitrary input processes and for all time points t≥0.