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The shot-noise driven microbunching instability can significantly degrade electron beam quality in x-ray free electron laser light sources. Experiments were carried out at the Linac Coherent Light Source (LCLS) to study this instability. In this paper, we present start-to-end simulations of the shot-noise driven microbunching instability experiment at the LCLS using the real number of electrons. The simulation results reproduce the measurements quite well. A microbunching self-heating mechanism is also illustrated in the simulation, which helps explain the experimental observation.