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

TL;DR

This paper derives the time-headway distribution for a generalized TASEP traffic model with periodic boundaries, analyzing various update schemes and comparing results with real traffic data.

Contribution

It introduces a generalized update framework for TASEP and derives the time-headway distribution, highlighting cases where flow determines distribution and comparing with empirical traffic data.

Findings

Time-headway distribution depends on update scheme and flow.

Backward order with attractive interaction mimics real traffic headway distribution.

Special update cases show flow-independent headway distribution.

Abstract

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.