Proc. of the international seminar on Teletraffic analysis and computer performance evaluation
The Cycle Time Distribution of Exponential Cyclic Queues
Journal of the ACM (JACM)
The Distribution of Queuing Network States at Input and Output Instants
Journal of the ACM (JACM)
The Product Form for Sojourn Time Distributions in Cyclic Exponential Queues
Journal of the ACM (JACM)
Passage time distributions in large Markov chains
SIGMETRICS '02 Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
An exact analysis of the distribution of cycle times in a class of queueing networks
SIGMETRICS '83 Proceedings of the 1983 ACM SIGMETRICS conference on Measurement and modeling of computer systems
Queueing Networks and Markov Chains
Queueing Networks and Markov Chains
Ensembles of Models for Automated Diagnosis of System Performance Problems
DSN '05 Proceedings of the 2005 International Conference on Dependable Systems and Networks
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
SLA based resource allocation policies in autonomic environments
Journal of Parallel and Distributed Computing
Approximate transient analysis of large stochastic models with WinPEPSY-QNS
Computer Networks: The International Journal of Computer and Telecommunications Networking
Model-Driven System Capacity Planning under Workload Burstiness
IEEE Transactions on Computers
Bayesian Networks: An Introduction
Bayesian Networks: An Introduction
Approximating discrete probability distributions with dependence trees
IEEE Transactions on Information Theory
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We introduce the Bayesian Expansion (BE), an approximate numerical technique for passage time distribution analysis in queueing networks. BE uses a class of Bayesian networks to approximate the exact joint probability density of the model by a product of conditional marginal probabilities that scales efficiently with the model's size. We show that this naturally leads to decomposing a queueing network into a set of Markov processes that jointly approximate the dynamics of the model and from which passage times are easily computed. Approximation accuracy of BE depends on the specific Bayesian network used to decompose the joint probability density. Hence, we propose a selection algorithm based on the Kullback-Leibler divergence to search for the Bayesian network that provides the most accurate results. Random models and case studies of increasing complexity show the significant accuracy gain of distribution estimates returned by BE compared to Markov and Chebyshev inequalities that are frequently used for percentile estimation in queueing networks.