Stochastic simulation for in silico studies of large biochemical networks requires a great amount of computational time. We recently proposed a new exact simulation algorithm, called the rejection-based stochastic simulation algorithm (RSSA) [Thanh et al., J. Chem. Phys. 141(13), 134116 (2014)], to improve simulation performance by postponing and collapsing as much as possible the propensity updates. In this paper, we analyze the performance of this algorithm in detail, and improve it for simulating large-scale biochemical reaction networks. We also present a new algorithm, called simultaneous RSSA (SRSSA), which generates many independent trajectories simultaneously for the analysis of the biochemical behavior. SRSSA improves simulation performance by utilizing a single data structure across simulations to select reaction firings and forming trajectories. The memory requirement for building and storing the data structure is thus independent of the number of trajectories. The updating of the data structure when needed is performed collectively in a single operation across the simulations. The trajectories generated by SRSSA are exact and independent of each other by exploiting the rejection-based mechanism. We test our new improvement on real biological systems with a wide range of reaction networks to demonstrate its applicability and efficiency.

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