Parametric Analysis of Queueing Networks with Blocking

摘要

We already observed in the investigation of queueing networks with blocking that the throughput is a non-decreasing function of the number of jobs (3), i.e., the blocking events have the effect of violating the throughput results. Two questions arose from this observation: 1) How to distribute the total buffer capacity to the stations such that no deadlock will occur and a maximum (optional) throughput will be achieved; and 2) Given the buffer capacity of each station in the network, how to select the total number of jobs in the network such that the throughput will be maximum (optimum). To answer these questions first we assumed that all stations have infinite capacity and derived new formulas for optimal throughput and response times based on the well-known mean value analysis approach (4). Then in (5) we found necessary and sufficient conditions for buffer allocation in the cyclic networks with blocking such that an optimal throughput will be achieved. (kr)