Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
Linearizer: a heuristic algorithm for queueing network models of computing systems
Communications of the ACM
SCAT: A heuristic algorithm for queueing network models of computing systems
SIGMETRICS '81 Proceedings of the 1981 ACM SIGMETRICS conference on Measurement and modeling of computer systems
A Clustering Approximation Technique for Queueing Network Models with a Large Number of Chains
IEEE Transactions on Computers
The inconsistency index method for estimating the accuracy of Schweitzer's approximation
IBM Journal of Research and Development
On the properties of approximate mean value analysis algorithms for queueing networks
SIGMETRICS '88 Proceedings of the 1988 ACM SIGMETRICS conference on Measurement and modeling of computer systems
SIQUEUE-PET: an environment for queueing network modelling
ACM SIGMETRICS Performance Evaluation Review
The mathematics of product form queuing networks
ACM Computing Surveys (CSUR)
A generalization of mean value analysis to higher moments: moment analysis
SIGMETRICS '86/PERFORMANCE '86 Proceedings of the 1986 ACM SIGMETRICS joint international conference on Computer performance modelling, measurement and evaluation
Multiclass queueing networks with population constrainted subnetworks
SIGMETRICS '85 Proceedings of the 1985 ACM SIGMETRICS conference on Measurement and modeling of computer systems
The correction terms in approximate mean value analysis
Operations Research Letters
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The Lineariser is an MVA-based technique developed for the approximate solution of large multiclass product form queueing networks. The Lineariser is capable of computing accurate solutions for networks of fixed rate centres. However, problems arise when the Lineariser is applied to networks containing centres with queue dependent service rates. Thus networks exist which seem well suited (a large number of lightly loaded centres, large numbers of customers in each closed chain) for Lineariser solution but whose queue dependent centres cannot be solved accurately by the Lineariser method. Examples have also been found where the Lineariser computes accurate values for the queue lengths, waiting times and throughputs though the values computed for the queue length distributions are totally in error. This paper presents an Improved Lineariser which computes accurate approximate solutions for multiclass networks containing an arbitrary number of queue dependent centres. The Improved Lineariser is based on MVA results and is therefore simple to implement and numerically well behaved. The Improved Lineariser has storage and computation requirements of order (MN) locations and (MNJ2) arithmetic operations where M is the number of centres, N the total number of customers and J the number of closed chains. Results from 130 randomly generated test networks are used to compare the accuracy of the standard and Improved Linearisers. The Improved Lineariser is consistently more accurate (tolerance errors on all performance measures less than 2 per cent) than the standard Lineariser and its accuracy is insensitive to the size of the network model. In addition, the Improved Lineariser computes accurate solutions for networks which cause the standard Lineariser to fail.