Exclusion processes are hot study issues in statistical physics and corresponding complex systems. Among fruitful exclusion processes, totally asymmetric simple exclusion process (namely, TASEP) attracts much attention due to its insight physical mechanisms in understanding such nonequilibrium dynamical processes. However, interactions among isolated TASEP are the core of controlling the dynamics of multiple TASEPs that are composed of a certain amount of isolated one-dimensional TASEP. Different from previous researches, the interaction factor is focused on the critical characteristic parameter used to depict the interaction intensity of these components of TASEPs. In this paper, a much weaker constraint condition ∏Ki=1ωdi=∏Ki=1ωui∏Ki=1ωdi=∏Ki=1ωui is derived as the analytical expression of interaction factor. Self-propelled particles in the subsystem ii of multiple TASEPs can perform hopping forward at pipi, moving into the target site of the (i − 1)th TASEP channel at ωuiωui or updating into the (i + 1)th TASEP channel at ωdiωdi. The comparison of this proposed interaction factor and other previous factors is performed by investigating the computational efficiency of obtaining analytical solutions and simulation ones of order parameters of the proposed TASEP system. Obtained exact solutions are observed to match well with Monte Carlo simulations. This research attempts to have a more comprehensive interpretation of physical mechanisms in the impact of interaction factors on TASEPs, especially corresponding to stochastic dynamics of self-propelled particles in such complex statistical dynamical systems.
