Performability Analysis: Measures, an Algorithm, and a Case Study
IEEE Transactions on Computers - Fault-Tolerant Computing
On Evaluating the Cumulative Performance Distribution of Fault-Tolerant Computer Systems
IEEE Transactions on Computers
Performability Analysis: A New Algorithm
IEEE Transactions on Computers
A Rigorous Global Optimization Algorithm for Problems with Ordinary Differential Equations
Journal of Global Optimization
Evaluation of Reward Analysis Methods with MRMSolve 2.0
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Fluid Flow Approximation of PEPA models
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Global Optimization with Nonlinear Ordinary Differential Equations
Journal of Global Optimization
A fluid analysis framework for a Markovian process algebra
Theoretical Computer Science
A unified approach to the moments based distribution estimation – unbounded support
EPEW'05/WS-FM'05 Proceedings of the 2005 international conference on European Performance Engineering, and Web Services and Formal Methods, international conference on Formal Techniques for Computer Systems and Business Processes
A fast algorithm for the transient reward distribution in continuous-time Markov chains
Operations Research Letters
Fluid computation of the performance: energy tradeoff in large scale Markov models
ACM SIGMETRICS Performance Evaluation Review
Mean-field approximations for performance models with generally-timed transitions
ACM SIGMETRICS Performance Evaluation Review
Mean-Field analysis of markov models with reward feedback
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
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Capturing energy consumption directly from a stochastic behavioural model is a computationally expensive process. Using a so-called fluid analysis technique we are able to access accumulated reward measures in much larger scale stochastic systems than has been previously possible.These accumulated rewards are ideal for deriving energy and power consumption from stochastic process models. In previous work, it has been shown how to derive a set of ordinary differential equations (ODEs) whose solutions approximate the moments of component counts in a continuous-time Markov chain(CTMC) described in a stochastic process algebra. In this paper, we show how to extend the method to provide rapid access to moments of accumulated rewards in CTMCs. In addition to measuring the amount of energy used by a system, we are also interested in the time taken to reach a particular level of energy consumption. In reward terms, this is a so-called completion time. In this paper, we are able to use higher moments of rewards to give us access to completion time distributions. We demonstrate the technique on a model of energy consumption in a client-server system with server failure and hibernation. Moreover, we are able to use these new and rapid techniques to capture the trade-off between energy consumption and service level agreement (SLA) compliance. We use a standard optimisation approach to find the precise configuration of the system which minimises the energy consumption while satisfying an operational response-time quantile.