  The totally asymmetric simple exclusion process (TASEP) is a stochastic model
for the unidirectional dynamics of interacting particles on a $1$D-lattice that
is much used in systems biology and statistical physics. Its master equation
describes the evolution of the probability distribution on the state space. The
size of the master equation grows exponentially with the length of the lattice.
It is known that the complexity of the system may be reduced using mean field
approximations. We provide a rigorous derivation and a stochastic
interpretation of these approximations and present numerical results on their
accuracy for a number of relevant cases.
