Approximating class-departure variability in tandem queues with downtime events: Regression-based variability function

Predicting queue performance by approximating class-departure variability in tandem queues with downtime events via existing decomposition methods is neither accurate enough nor efficient enough. Analytic approximations, if conducted alone, lack accuracy but attempting to increase accuracy by incorporating simulation to analytic approximation has proved to require significant computation efforts. The aim of this paper is to reduce the latter inefficiency by modeling the Regression-Based Variability Function (RBVF) designed to approximate the between-class effect by exploiting the departure process from a single queue. The new approach predicts performance of n-tandem queues by reducing the focus to two-tandem queues for each traffic intensity level, as well as by modeling different policies of downtimes (e.g. first-come-first-served or priority). Numerical experiments demonstrate that the proposed RBVF delivers both accuracy and efficiency improvements: the relative errors associated with RBVF are about three times smaller than the best existing analytic procedures and the computation efforts associated with RBVF are about five times smaller than existing analytic procedure combined with simulation.