Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
Performance bound hierarchies for queueing networks
ACM Transactions on Computer Systems (TOCS)
Linearizer: a heuristic algorithm for queueing network models of computing systems
Communications of the ACM
Balanced job bound analysis of queueing networks
Communications of the ACM
Some Extensions to Multiclass Queueing Network Analysis
Proceedings of the Third International Symposium on Modelling and Performance Evaluation of Computer Systems: Performance of Computer Systems
A Reduction Technique for Evaluating Queueing Networks with Serialization Delays
Performance '83 Proceedings of the 9th International Symposium on Computer Performance Modelling, Measurement and Evaluation
Multiple class memory constrained queueing networks
SIGMETRICS '82 Proceedings of the 1982 ACM SIGMETRICS conference on Measurement and modeling of computer systems
Fast approximate solution of multiprogramming models
SIGMETRICS '82 Proceedings of the 1982 ACM SIGMETRICS conference on Measurement and modeling of computer systems
Asymptotic expansions for closed Markovian networks with state-dependent service rates
Journal of the ACM (JACM)
A model of file server performance for a heterogeneous distributed system
SIGCOMM '86 Proceedings of the ACM SIGCOMM conference on Communications architectures & protocols
The inconsistency index method for estimating the accuracy of Schweitzer's approximation
IBM Journal of Research and Development
The correction terms in approximate mean value analysis
Operations Research Letters
Device utilizations in approximate MVA
Operations Research Letters
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Queueing network performance modelling technology has made tremendous strides in recent years. Two of the most important developments in facilitating the modelling of large and complex systems are hierarchical modelling, in which a single load dependent server is used as a surrogate for a subsystem, and approximate mean value analysis, in which reliable approximate solutions of separable models are efficiently obtained. Unfortunately, there has been no successful marriage of these two developments; that is, existing algorithms for approximate mean value analysis do not accommodate load dependent servers reliably. This paper presents a successful technique for incorporating load dependent servers in approximate mean value analysis. We consider multiple class models in which the service rate of each load dependent server is a function of the queue length at that server. In other words, load dependent center k delivers “service units” at a total rate of f@@@@ (n@@@@) when n@@@@ customers are present. We present extensive experimental validation which indicates that our algorithm contributes an average error in response times of less than 1% compared to the (much more expensive) exact solution. In addition to the practical value of our algorithm, several of the techniques that it employs are of independent interest.