On Kleinrock's Power Metric for Queueing Systems

摘要

In a series of papers, Kleinrock proposed a performance metric called power for queueing systems, which captures the tradeoff every queue makes between efficiency and response time. Since then, this metric has been used in different works, all in the area of communication systems. Kleinrock also proved that in the M/GI/1 family of models, the maximal power is obtained when the mean number of customers in the system (the system being in equilibrium) is exactly one. In this paper we show that Kleinrock's definition extends naturally to Jackson product form queueing networks, and that this nice optimality result still holds. We also show that this property of the optimal operating point does not hold in general for single-node models of the GI/GI/1 type (not even for GI/M/1 models), or when the storage capacity of the system is finite.