Max-Min optimality of service rates in queueing systems with customer-average performance criterion

In this paper, we consider the optimization of service rates in queueing systems, especially in closed Jackson networks. The optimization criterion is the customer-average performance, which is another important performance metric compared with the traditional time-average performance. Based on the methodology of perturbation analysis, we can derive a performance difference equation when the service rates are changed. With this difference equation, we find the optimal service rates have a max-min property, i.e., the optimal service rates can be chosen from its maximal or minimal value. This property can reduce the complexity of this type of optimization problems. Moreover, we also prove the max-min optimality is valid for both state-dependent service rates and load-dependent service rates in queueing systems.