Interpolation approximations for the steady-state distribution in multi-class resource-sharing systems

International audienceWe consider a single-server multi-class queue that implements relative priorities among customers of the various classes. The discipline might serve one customer at a time in a non-preemptive way, or serve all customers simultaneously. The analysis of the steady-state distribution of the queue-length and the waiting time in such systems is complex and closed-form results are available only in particular cases. We therefore set out to develop approximations for the steady-state distribution of these performance metrics. We first analyze the performance in light traffic. Using known results in the heavy-traffic regime, we then show how to develop an interpolation-based approximation that is valid for any load in the system. An advantage of the approach taken is that it is not model dependent and hence could potentially be applied to other complex queueing models. We numerically assess the accuracy of the interpolation approximation through the first and second moments