Computing performance measures in a multi-class multi-resource processor-shared loss system

This paper develops methods to compute performance measures in a specific type of loss system with multiple classes of customers sharing the same processor. Such systems arise in the modeling of a call center, where the performance measures of interest are the blocking probability of a call and the reneging probability of customers that are put on hold. Expressions for these performance measures have been derived in previous work by the authors. Given the difficulty of computing these performance measures for realistic systems, this paper proposes two different approaches to simplify this computation. The first method introduces the idea of multi-dimensional convolutions, and uses this approach to compute exact blocking and reneging probabilities. The second method establishes an adaptation of the Monte Carlo summation technique in order to obtain good estimates of blocking and reneging probabilities in large systems along with their associated confidence intervals.