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A direct approach to decentralized control of service rates in a closed Jackson network

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2 Author(s)
Dye-Jyun Ma ; Nat. Chung-Hsing Univ., Taichung, Taiwan ; Xi-Ren Ao

In this note, we consider a problem of decentralized control of service rates in a closed Jackson network under the long-run time-average expected cost criterion. We use a direct approach to solving the problem. The approach is based on an intrinsic property of the product-form solution: if the cost function is an affine function of a service rate, then the long-run average expected cost is always monotone in that service rate. This intrinsic property leads immediately to the optimality of bang-bang or threshold policies. The result extends the existing result obtained by linear programming, to more general cost functions

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Automatic Control, IEEE Transactions on  (Volume:39 ,  Issue: 7 )