Asymptotic approximation and bottleneck analysis in product form queueing networks with large populations

摘要

Asymptotic approximations are constructed for the performance measures of product form queueing networks consisting of single server, fixed rate nodes with large populations. The approximations are constructed by applying singular perturbation methods to the recursion equations of Mean Value Analysis. Networks with a single job class are studied first to illustrate the use of perturbation techniques. The leading term in the approximation is related to bottleneck analysis, but fails to be accurate if there is more than one bottleneck node. accurate if there is more one bottleneck node.