Asymptotic Approximations and Bottleneck Analysis in Product Form Queueing Networks with Large Populations

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. A uniform approximation is constructed which is valid for networks with many bottleneck nodes. The accuracy of the uniform approximation is demonstrated for both small and large population sizes. Next, multiclass networks are considered. The leading term in the asymptotic approximation is again related to bottleneck analysis but fails to be valid across “switching surfaces”. Across these the bottleneck nodes of the network change as a function ...

• Type: Journal
• Year: 1998
• Where: PE
• Authors: Charles Knessl, Charles Tier
• Keywords: Approximation, Asymptotic Approximation, Bottleneck, Optimization, PE 1998