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Petri nets are a popular tool for process modeling, formal analysis and design of discrete event systems. This paper introduces the use of timed Petri nets to model a high-throughput screening (HTS) process, specifically automation used for testing biological compounds for drug derivative discovery. This paper also illustrates of the use of a general hybrid simulation tool such as Simulink to implement timed Petri nets. A mathematical description of how we implemented the design of the timed Petri net model is provided. A simulator of the Petri net model in Simulink is implemented and verified. The resulting model can be used to estimate the operation time of the target HTS process and for process planning. The demonstrated approach to Petri net modeling and simulation development may be applicable to other domains involving highly automated processes with time delays dictating product quality.