Service Rate Control of Tandem Queues With Power Constraints

In this paper, we study the optimal control of service rates of a tandem queue with power constraints. The service rate of a server is determined by the power allocated to that server. The total power of the system is fixed. The system cost is comprised of two parts, the holding cost reflecting the congestion of queues and the operating cost reflecting the power consumed at servers. The optimization objective is to find the optimal power allocation policy among servers, which can minimize the system average cost. We formulate this problem as a Markov decision process with a constrained action space. Sensitivity-based optimization theory is applied to study this problem. The necessary and sufficient condition of optimal service rates, and the optimality of the vertexes of the feasible domain are derived when the operating cost has a linear or concave form. An iterative algorithm is further developed to find the optimal service rates. This algorithm may work well even when the cost function has a general form. The extension to general tandem queues with many servers is also studied. Finally, we conduct numerical experiments under different parameter settings to demonstrate the main idea of this paper.