摘要：AbstractPricing control is an important problem in service systems. In this paper, we study a dynamic pricing and control problem in an open Jackson network. The goal is to determine the optimal admission prices and the optimal service rates at every state such that the long-run average welfare of the whole system is maximized. We prove that the original problem is equivalent to a rate-setting problem plus a price-setting problem. To solve the rate-setting problem, we derive a difference formula based on the sensitivity-based optimization theory. When the cost rate function is convex in service rates and the value rate function is concave in arrival rates, we decompose the rate-setting problem into a series of convex optimization sub problems. When the rate functions have linear structure, these sub problems are even simpler and a bang-bang control is optimal. For the price-setting problem, we determine the state-dependent prices so as to induce the optimal arrival rates obtained by the rate-setting problem. We propose a recursive algorithm to numerically compute the expected delays at every state. Finally, we conduct numerical experiments to explore properties of the optimal arrival rates, service rates, prices, and expected delays obtained by our approach.
