  In this study, we have developed a parallel version of the random time
simulation algorithm.
  Firstly, we gave a rigorous basis of the random time description of the
stochastic process of chemical reaction network time evolution.
  And then we reviewed the random time simulation algorithm and gave the
implementations for the parallel version of next reaction random time
algorithm.
  The discussion of computational complexity suggested a factor of $M$ (which
is the connection number of the network) folds time consuming reduction for
random time simulation algorithm as compared to other exact stochastic
simulation 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 GPGPU
parallel implementation which achieved roughly 100 folds acceleration as
compared with CPU implementations.
  Therefore the stochastic simulation method we developed here can be of great
application value for simulating time evolution process of large-scale network.
