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Optimal routing to parallel heterogeneous servers-small arrival rates

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2 Author(s)
Rosberg, Z. ; Dept. of Comput. Sci., Technion-Israel Inst. of Technol., Haifa, Israel ; Makowski, A.M.

Consider a set of k(⩾2) heterogeneous and exponential servers that operate in parallel. Customers arrive into a single infinite capacity buffer according to a Poisson process, and are routed to available servers in accordance with some routing policy. It is shown that for arrival rates in some possible interval (0,λ0), ever routing policy which minimizes the long-run expected holding cost is contained in the set of routing policies that minimize the expected flow time for a system with fixed initial population and no new arrivals

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Automatic Control, IEEE Transactions on  (Volume:35 ,  Issue: 7 )