This paper presents an investigation of the independent and identically distributed random variate values in Colored Petri Nets nondeterministic network behavior when single and replicated simulations are performed. The results will be utilized and be part of larger research titled "Extended Common Instrument Middleware Architecture toward Heterogeneous Data Sources and the Grid Integration", a proposed architecture extension between remote laboratory instrument connected to the grid for facility sharing aimed at higher communication performance. The nondeterministic characteristics of client-server data transfer is modeled and simulated using Color Petri Nets modified Simplesend for performance analysis. However, the verification and validation of the particular statistics involving random generated variate values must first be investigated; hence independent and identically distributed values must be confirmed by analyzing the results of single versus replicated simulations. © 2010 IEEE.