An approximate analysis of open tandem queueing networks with blocking and general service times

An approximation algorithm is presented for open tandem queueing networks with finite buffers and with general service times. The algorithm decomposes the system into individual queues with revised arrival and service processes and revised queue capacity. Then, each queue is analyzed in isolation. The service process is revised to reflect the additional delay a unit might undergo due to blocking. Unlike previous algorithms, the arrival process to each decomposed queue is described by a C2 distribution. The parameters of the service and the arrival processes are computed approximately using an iterative scheme. The approximation procedure yields the steady-state queue-length distribution of each queue. From this, other more commonly sought performance measures, such as mean queue-length, probability that a queue is empty, throughput, etc., can be easily computed. Comparisons of the approximate results with simulation results showed that the proposed algorithm has a good error-level.