Decomposition of Open Queueing Networks with Batch Service

The decomposition method for non-product form networks with non-exponentially distributed interarrival and service times assumes that nodes within the network can be treated being stochastically independent and internal flows can be approximated by renewal processes. The method consists of three phases to calculate the interarrival times of a node: merging, flow, splitting. Some well-known approximation formulas for ordinary single class open queueing networks calculate the characteristics in each phase for each node as shown by Kuehn, Chylla, Whitt and Pujolle/Ai. Node performance measures such as mean queue length are determined by using approximation formulas for non-Markovian queues. In 2011 the decomposition method was extended to open queueing networks with batch processing using the approximation formula described by Pujolle/Ai. A comparison with discrete event simulation as benchmark shows that the approach provides good results. Thus, the approach was expanded for the approximation given by Kuehn, Chylla and Whitt. Since the method consists of several phases it is possible to combine different formulas. For example, merging will be approximated by Kuehn and flow by Whitt. To perform an evaluation the benchmark was done in regard to the 2011 publication. Approximation formulas with the same approach generate similar results. In some cases, it is apparent that some formulas have advantages over other ones and a few tend to larger errors. Thus, the focus of interest particularly addresses the load and batch size changes within the network and the impact on the accuracy of the decomposition method as a fast solver or pre-evaluation for optimization using simulation.