Dependence among tandem queues and the second moment result on the theory of constraints

Due to the analytical intractability of general tandem queues, we develop innovative methods to quantify the dependence among stations through simulation. Dependence is defined by the contribution queue time at each station, and contribution factors are developed based on the insight from Friedman's reduction method and Jackson networks. In a tandem queue, the dependence among stations can be either diffusion or blocking, and their impact depends on the positions relative to the bottlenecks. Based on these results, we show that improving the performance of the system bottleneck may not be the most effective place to reduce system cycle time. Rather than making independence assumptions, the proposed method points out a promising direction and sheds light on the insights of the dependence in practical systems.