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Clouds, Fuzzy Sets and Probability Intervals
 Reliable Computing, Kluwer Academic Publishers
, 2004
"... Clouds are a concept for uncertainty mediating between the concept of a fuzzy set and that of a probability distribution. A cloud is to a random variable more or less what an interval is to a number. We discuss the basic theoretical and numerical properties of clouds, and relate them to histograms, ..."
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Cited by 7 (2 self)
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Clouds are a concept for uncertainty mediating between the concept of a fuzzy set and that of a probability distribution. A cloud is to a random variable more or less what an interval is to a number. We discuss the basic theoretical and numerical properties of clouds, and relate them to histograms, cumulative distribution functions, and likelihood ratios.
Interval matrices for the bottleneck analysis of queuing network models with histogram based parameters
 in In IEEE International Computer Performance & Dependability Symposium
, 1998
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Interval Parameters for Capturing Uncertainties in an EJB Performance Model
, 2000
"... Exact as well as approximate analytical solutions for quantitative performance models of computer systems are usually obtained by performing a series of arithmetical operations on the input parameters of the model. However, especially during early phases of system design and implementation, not a ..."
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Cited by 1 (1 self)
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Exact as well as approximate analytical solutions for quantitative performance models of computer systems are usually obtained by performing a series of arithmetical operations on the input parameters of the model. However, especially during early phases of system design and implementation, not all the parameter values are usually known exactly. In related research contributions, intervals have been proposed as a means to capture parameter uncertainties. Furthermore, methods to adapt existing solution algorithms to parameter intervals have been discussed. In this paper we present the adaptation of an existing performance model to parameter intervals. The approximate solution of a queueing network modelling an Enterprise JavaBeans server implementation is adapted to interval arithmetic in order to represent the uncertainty in some of the parameters of the model. A new interval splitting method is applied to obtain reasonable tight performance measure intervals. Monotonicity p...
Splitting Techniques for Interval Parameters in Performance Models
, 2000
"... During early phases of design and implementation, not all the parameter values of a performance model are usually known exactly. In related research contributions, intervals have been proposed as a means to capture parameter uncertainties. Existing model solution algorithms can be adapted to inte ..."
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Cited by 1 (1 self)
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During early phases of design and implementation, not all the parameter values of a performance model are usually known exactly. In related research contributions, intervals have been proposed as a means to capture parameter uncertainties. Existing model solution algorithms can be adapted to interval parameters by replacing conventional arithmetic by interval arithmetic. However, the socalled dependency problem may cause extremely wide intervals for the computed performance measures. Interval splitting has been proposed as a technique to overcome this problem. In this work we give an overview of existing splitting algorithms and propose a new selective splitting method that signicantly reduces the computational complexity of interval evaluations. Moreover, the exploitation of partial monotonicity properties to further decrease the computational complexity is discussed. The proposed methods are illustrated along the lines of two examples: a small performance model of the MA...