Improved lineariser methods for queueing networks with queue dependent centres

A. E. Krzesinski · Jeanie Greyling

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Advanced Queuing Theory Analysis Network Traffic and Congestion Control Interconnection Networks and Systems

Abstract

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 (MNJ 2 ) 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.

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References

1980Mean-Value Analysis of Closed Multichain Queuing Networks 1982Linearizer 1981SCAT

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2010Approximate analysis of load-dependent generally distributed queuing networks with low service time variability 1986A Clustering Approximation Technique for Queueing Network Models with a Large Number of Chains 1986The correction terms in approximate mean value analysis 2015QD-AMVA: Evaluating systems with queue-dependent service requirements 1986Computer System Performance Evaluation Using Queueing Network Models 1986A generalization of mean value analysis to higher moments 1985Multiclass queueing networks with population constrainted subnetworks 1993Network of queues modeling in flexible manufacturing systems : a survey

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