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

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