On the execution of parallel programs on multiprocessor systems—a queuing theory approach
Journal of the ACM (JACM)
Stochastic Bounds on Execution Times of Parallel Programs
IEEE Transactions on Software Engineering
An Efficient Kronecker Representation for PEPA Models
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
An Algorithmic Approach to Stochastic Bounds
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
Acyclic discrete phase type distributions: properties and a parameter estimation algorithm
Performance Evaluation
PEPA nets: a structured performance modelling formalism
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
SFM'07 Proceedings of the 7th international conference on Formal methods for performance evaluation
Closed form absorption time bounds
EPEW'07 Proceedings of the 4th European performance engineering conference on Formal methods and stochastic models for performance evaluation
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We propose new techniques to simplify the computation of the cycle times and the absorption times for a large class of PEPA models. These techniques allow us to simplify the model description to reduce the number of states of the underlying Markov chain. The simplification processes are associated with stochastic comparisons of random variables. Thus the simplified models are stochastic bounds for the original ones