Number Of States In Model Research Articles

Integrating Simulation and Numerical Analysis in the Evaluation of Generalized Stochastic Petri Nets

The standard existing performance evaluation methods for discrete-state stochastic models such as Petri nets either generate the reachability graph followed by a numerical solution of equations or use some variant of simulation. Both methods have characteristic advantages and disadvantages depending on the size of the reachability graph and type of performance measure. This article proposes a hybrid performance evaluation algorithm for the steady-state solution of Generalized Stochastic Petri Nets that integrates elements of both methods. It automatically adapts its behavior depending on the available size of main memory and number of model states. As such, the algorithm unifies simulation and numerical analysis in a joint framework. It is proved to result in an unbiased estimator whose variance tends to zero with increasing simulation time. The article extends earlier results with an algorithm variant that starts with a small maximum number of particles and increases them during the run to increase the efficiency in cases that are rapidly solved by regular simulation. The algorithm’s applicability is demonstrated through case studies, including an example where it outperforms the standard methods.

Leveraging Quantum Annealing for Election Forecasting

Accurate, reliable sampling from fully-connected graphs with arbitrary correlations is a difficult problem. Such sampling requires knowledge of the probabilities of observing every possible state of a graph. As graph size grows, the number of model states becomes intractably large and efficient computation requires full sampling be replaced with heuristics and algorithms that are only approximations of full sampling. This work investigates the potential impact of quantum annealing for sampling purposes, building on recent successes training Boltzmann machines using a quantum device. We investigate the use case of quantum annealing to train Boltzmann machines for predicting the 2016 Presidential election.

Fast Passivity Assessment for $S$-Parameter Rational Models Via a Half-Size Test Matrix

Rational models must be passive in order to ensure stable time domain simulations. The assessment of passivity properties is usually done via a Hamiltonian matrix that is associated with the state-space model, allowing precise characterization of passivity violations from its imaginary eigenvalues. The calculation of eigenvalues can be time consuming for large models as the matrix size is equal to twice the number of model states. In this paper, we derive for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameter models a new test matrix which is only half the size of the Hamiltonian matrix. This leads to savings in the eigenvalue computation time by a factor of nearly eight. The new test matrix takes into account that the model is symmetrical, in pole-residue form. Its application is demonstrated by three examples: a microwave filter, a package, and a synthetic model.

REAL-TIME OPTIMISATION OF NATURAL GAS PIPELINE SYSTEMS-A SIMPLIFIED APPROACH

Natural gas pipeline systems are very complicated. From a dynamic modelling, control and optimisation perspective, the number of model states is typically many thousands, the number of disturbance variables can be several hundred and the length of the prediction horizon for predictive control and optimsation must be long enough to include the very slow dynamics and the predicted important future events – typically gas consumption changes- in the system. Simplifications and approximations made to the original large-scale real-time optimisation problem results in a simplified receding horizon quadratic programming problem.