Lumpability of fluid models with heterogeneous agent types

Abstract

Fluid models have gained popularity in the performance modeling of computing systems and communication networks. When the model under study consists of many different types of agents, the size of the associated system of ordinary differential equations (ODEs) increases with the number of types, making the analysis more difficult. We study this problem for a class of models where heterogeneity is expressed as a perturbation of certain parameters of the ODE vector field. We provide an a-priori bound that relates the solutions of the original, heterogenous model with that of an ODE system of smaller size which arises from aggregating system variables concerning different types of agents. By showing that this bound grows linearly with the intensity of the perturbation, we provide a formal justification to the intuitive possibility of neglecting small differences in agents' behavior as a means to reducing the dimensionality of the original system.