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We represent the results of computer simulation of two effects in Jaynes-Cummings-Hubbard model: dephasing assisted transport and quantum bottleneck. The simulation is performed in the framework of Lindblad- Kossakowsky-Glauber-Sudarshan master equation; it shows the interesting interplay between these two contra-intuitive effects, which comes from the non optimal or optimal choice of JCH parameters.