On the use of iterative approximations in queueing networks : with simple applications

Networks of queues which have a productform solution can be analyzed easily by the convolution method or with mean value analysis. Regrettably, however, many practical queueing network models do not possess a productform solution. In this paper the following approach is advocated for models with alight deviations from the productform conditions: approximate the model interatively by a sequence of models which satisfy conditions for simple analysis. Quite often aggregation and mean value analysis provide the natural approach for de signing an iteration step. Applications which are mentioned are: two-phase servers where the first phase is a preparatory one; a type of priorities; blocking; many-chains networks; FCFS-servers with different workloads for different types of customers