Position dependence of the particle density in a double-chain section of a linear network in a totally asymmetric simple exclusion process

Abstract

We report here results on the study of the totally asymmetric simple exclusion process, 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 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 particles in that part of the network. In the symmetric case of equal injection and ejection rates α=β>1/2 and equal lengths of the head and tail sections, the density profiles in the two parallel chains are almost linear, characteristic of 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 particles 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 a finite-size dependence of the effective injection and ejection rates at the ends of the double-chain section.