Time-headway distribution for periodic totally asymmetric exclusion process with various updates

• Time-headway distribution for generalized update TASEP is derived analytically.
• Relation between fully-parallel and forward-sequential update is demonstrated.
• Distributions for γ=0and1 are determined by the flow regardless to density.
• The backward genTASEP with attraction corresponds qualitatively to traffic data.

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 characteristic of traffic flow) for the model with generalized update (genTASEP) in both, forward- and backward-sequential representations. The usually used updates, fully-parallel and regular forward- and backward-sequential, are analyzed 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.