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Smooth transportation has drawn the attention of many researchers andpractitioners in several fields. In the present paper, we propose a modifiedmodel of a totally asymmetric simple exclusion process (TASEP), which includesmultiple species of particles and takes into account the sequence in which theparticles enter a lattice. We investigate the dependence of the transportationtime on this `entering sequence' and show that for a given collection ofparticles group sequence in some cases minimizes the transportation time betterthan a random sequence. We also introduce the `sorting cost' necessary totransform a random sequence into a group sequence and show that when this isincluded a random sequence can become advantageous in some conditions. Weobtain these results not only from numerical simulations but also bytheoretical analyses that generalize the simulation results for some specialcases.

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