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In this study, we have developed a parallel version of the random timesimulation algorithm.  Firstly, we gave a rigorous basis of the random time description of thestochastic process of chemical reaction network time evolution.  And then we reviewed the random time simulation algorithm and gave theimplementations for the parallel version of next reaction random timealgorithm.  The discussion of computational complexity suggested a factor of $M$ (whichis the connection number of the network) folds time consuming reduction forrandom time simulation algorithm as compared to other exact stochasticsimulation algorithms, such as the Gillespie algorithm.  For large-scale system, such like the protein-protein interaction network,$M$ is on order of $10^8$.  We further demonstrate the power of random time simulation with a GPGPUparallel implementation which achieved roughly 100 folds acceleration ascompared with CPU implementations.  Therefore the stochastic simulation method we developed here can be of greatapplication value for simulating time evolution process of large-scale network.

Parallel implementations of random time algorithm for chemical network stochastic simulations