On time and space decomposition of complex structures
Communications of the ACM
An Aggregation Technique for the Transient Analysis of Stiff Markov Chains
IEEE Transactions on Computers
The perceived effect of breakdown and repair on the performance of multiprocessor systems
Performance Evaluation
The reduction of perturbed Markov generators: an algorithm exposing the role of transient states
Journal of the ACM (JACM)
Numerical transient analysis of Markov models
Computers and Operations Research
Aggregation with an error of O(&egr;2)
Journal of the ACM (JACM)
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Weak D-Markov Chain and its Application to a Queueing Network
Proceedings of the International Workshop on Computer Performance and Reliability
Aggregation Methods for Large Markov Chains
Proceedings of the International Workshop on Computer Performance and Reliability
International Workshop on Timed Petri Nets
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Model-Based Evaluation: From Dependability to Security
IEEE Transactions on Dependable and Secure Computing
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An aggregation method for computing transient cumulative measures of large, stiff Markov models is presented. The method is based on classifying the states of the original problem into slow, fast-transient, and fast-current states. The authors aggregate fast-transient states and fast-recurrent states so that an approximate value to the desired cumulative measure can be obtained by solving a nonstiff set of linear differential equations defined over a reduced subset of slow states only. Several examples are included to illustrate how stiffness arises naturally in actual queuing and reliability models, and to show that cumulative measures provide a better characterization of the time-dependent system behavior.