This paper deals with the modeling and the numerical simulation of computational cluster networks (grid) dynamics and is more precisely focused on the management of the computational load offered by transferring jobs from one cluster to another. In order to tackle the complexity arising from dealing with the sheer number of processes existing in the system, we develop a comprehensive model of the global population of jobs using the kinetic theory. It takes into account the main characteristics of the clusters, their interactions and allows for a thorough description of the jobs. We then study the resulting system of macroscopic conservation laws and illustrate numerically its ability to capture some interesting behaviors of the grid. This model allows for real-time insight of the performance of a given policy for load management in the grid.