Moment Closures for Performance Models with Highly Non-linear Rates

Fluid analysis of Population CTMCs with non-linear evolution rates requires moment closures to transform a linear system with infinitely many ordinary differential equations (ODEs) into a non-linear one with a finite number of ODEs. Due to the ubiquity of kinetics with quadratic rates in physical processes, various closure techniques have been discussed in the context of systems biology and performance analysis. However, little research effort has been put into moment closures for higher-order moments of models with piecewise linear and higher-order polynomial evolution rates. In this paper, we investigate moment closure techniques applied to such models. In particular we look at moment closures based on normal and log-normal distributions. We compare the accuracy of the moment approximating ODEs with the exact results obtained from simulations. We confirm that by incorporating higher-order moment ODEs, the moment closure techniques give accurate approximations to the standard deviation of populations. Moreover, they often improve the accuracy of mean approximations over the traditional mean-field techniques.