Can car density in a two-lane section depend on the position of the latter in a single-lane road?

TL;DR

This study investigates how the position of a double-chain section in a TASEP network influences car density profiles, revealing that shifting the section alters the flow characteristics and could impact traffic management and biological transport.

Contribution

It introduces the effect of section position on density profiles in TASEP networks, highlighting finite-size influences on flow dynamics and providing new insights into traffic and biological transport modeling.

Findings

Shifting the double-chain section causes sharp changes in density profiles.

Maximum current conditions lead to different phase behaviors based on section position.

Finite-size effects explain the observed profile transformations.

Abstract

We report here results on the study of the totally asymmetric simple exclusion processes (TASEP), defined on an open network, consisting of head and tail simple chain segments with a double-chain section inserted in-between. Results of numerical simulations for relatively short chains reveal an interesting new feature of the network. When the current through the system takes its maximum value, a simple translation of the double-chain section forward or backward along the network, leads to a sharp change in the shape of the density profiles in the parallel chains, thus affecting the total number of cars in that part of the network. In the symmetric case of equal injection and ejection rates (\alpha = \beta >1/2) and equal lengths of the head and tail sections, the density profiles in the two parallel chains are almost linear, characteristic for the coexistence line (shock phase). Upon moving the section forward (backward), their shape changes to the one typical for the high (low) density phases of a simple chain. The total bulk density of cars in a section with a large number of parallel chains is evaluated too. The observed effect might have interesting implications for the traffic flow control as well as for biological transport processes in living cells. An explanation of this phenomenon is offered in terms of finite-size dependence of the effective injection and ejection rates at the ends of the double-chain section.