A Simulation Perspective: Error Analysis in the Distributed Simulation of Continuous System

To construct a corresponding distributed system from a continuous system, the most convenient way is to partition the system into parts according to its topology and deploy the parts on separated nodes directly. However, system error will be introduced during this process because the computing pattern is changed from the sequential to the parallel. In this paper, the mathematical expression of the introduced error is studied. A theorem is proposed to prove that a distributed system preserving the stability property of the continuous system can be found if the system error is limited to be small enough. Then, the compositions of the system error are analyzed one by one and the complete expression is deduced, where the advancing step T in distributed environment is one of the key factors associated. At last, the general steps to determine the step T are given. The significance of this study lies in the fact that the maximum T can be calculated without exceeding the expected error threshold, and a larger T can reduce the simulation cost effectively without causing too much performance degradation compared to the original continuous system.