The heavy-traffic bottleneck phenomenon under splitting and superposition

Since the heavy-traffic bottleneck phenomenon was observed in tandem queues, various attempts have been made to develop better approximation methods for queueing networks. In this paper we present a more general heavy-traffic bottleneck phenomenon which is not explained by current approaches such as the QNA, the variability function, and the innovations method. We show that the variability function could be ineffective for queueing networks with splitting and superposition and propose a new decomposition method based on the variability function and innovations method. Our approach is designed to better approximate the asymptotic squared coefficient of variation of interarrival times at the bottleneck station with the superposed inputs. A numerical experiment shows that our approach approximates the expected waiting time at the bottleneck with about 8% relative errors while others show 40–80% relative errors.