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.
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Bäuerle, N., Stidham, S. Conservation Laws for Single-Server Fluid Networks. Queueing Systems 38, 185–194 (2001). https://doi.org/10.1023/A:1010906331066
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DOI: https://doi.org/10.1023/A:1010906331066