A new perspective on the normalization of invariant measures for loss networks and other product form systems

Authors:
N.G Bean;M.A Stewart
Affiliations:
Teletraffic Research Centre, Department of Applied Mathematics University of Adelaide, Australia;Teletraffic Research Centre, Department of Applied Mathematics University of Adelaide, Australia
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2000

Citing 4
Cited 0

Calculating normalization constants of closed queueing networks by numerically inverting their generating functions

Journal of the ACM (JACM)
An inversion algorithm to compute blocking probabilities in loss networks with state-dependent rates

IEEE/ACM Transactions on Networking (TON)
Computational algorithms for closed queueing networks with exponential servers

Communications of the ACM
Multiservice Loss Models for Broadband Telecommunication Networks

Multiservice Loss Models for Broadband Telecommunication Networks

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Abstract

Loss networks have proved to be a vital tool in the study of telecommunication networks, computer performance, and resource allocation problems. For a large subset of these models, the invariant measure is of a product form. The existence of efficient procedures to normalize a product-form invariant measure is essential for analysis of the underlying system. Choudhury et al. [1-4] have recently presented a number of algorithms based upon Fourier analysis for the normalization of product-form invariant measures for specific systems. Bean and Stewart [5] discussed related work for the normalization of product-form invariant measures for closed queueing networks. In this paper, we present a simple unifying framework within which to study these algorithms. This framework is significant as it suggests a number of extensions to these algorithms and simplifies their derivation.