Computational Algorithms for the Product Form Solution of Closed Queuing Networks with Finite Buffers and Skip-Over Policy

Abstract

Closed queuing networks with finite capacity buffers and skip-over policies are fundamental models in the performance evaluation of computer and communication systems. This technical report presents the details of computational algorithms to derive the key performance metrics for such networks. The primary focus is on the efficient computation of the normalization constant, which is critical for determining the steady-state probabilities of the network states under investigation. A convolution algorithm is proposed, which paves the way for the computation of key performance indices, such as queue length distribution and throughput, accommodating the intricacies introduced by finite capacity constraints and skip-over mechanisms. Finally, an extension of the traditional Mean Value Analysis algorithm addressing numerical stability is provided. The approaches discussed here allow make the investigation of large-scale networks feasible and enable the development of robust implementations of these techniques for practical use.