An efficient two-phase approximation method for exponential tandem queueing systems with blocking

In this paper, an efficient approximation method is proposed for analyzing the performance of exponential tandem queueing systems with blocking. The approximation method decomposes a tandem queueing system into individual queues with revised arrival and service processes and revised queue capacity. Then each queue is analyzed in isolation. The method consists of two phases and each phase can be used separately. Phase One approximates the mean throughput rate of the system in a forward form. The output of Phase One serves as the input to Phase Two. Phase Two approximates the queue-length distributions of each queue by the conservation of flow in a backward form. The mean queue-length and the mean waiting time of the tandem queue are also obtained. The approximate results are compared with exact or simulation solutions to show that the proposed method can perform well with acceptable errors.