  The totally asymmetric exclusion process (TASEP) with periodic boundaries is
considered as traffic flow model. The large-L approximation of the stationary
state is used for the derivation of the time-headway distribution (an important
microscopic characteristics of traffic flow) for the model with generalized
update (genTASEP) in both, forward- and backward-sequential representation. The
usually used updates, fully-parallel and regular forward- and
backward-sequential, are analysed as special cases of the genTASEP. It is shown
that only for those cases, the time-headway distribution is determined by the
flow regardless to the density. The qualitative comparison of the results with
traffic data demonstrates that the genTASEP with backward order and attractive
interaction evinces similar properties of time-headway distribution as the real
traffic sample.
