Dependence of the transportation time on the sequence in which particles with different hopping probabilities enter a lattice

Smooth transportation has drawn the attention of many researchers and practitioners in several fields. In the present paper, we propose a modified model of a totally asymmetric simple exclusion process (TASEP), which includes multiple species of particles and takes into account the sequence in which the particles enter a lattice. We investigate the dependence of the transportation time on this `entering sequence' and show that for a given collection of particles group sequence in some cases minimizes the transportation time better than a random sequence. We also introduce the `sorting cost' necessary to transform a random sequence into a group sequence and show that when this is included a random sequence can become advantageous in some conditions. We obtain these results not only from numerical simulations but also by theoretical analyses that generalize the simulation results for some special cases.