An exclusion process on a tree with constant aggregate hopping rate

作者：Mottishaw Peter^*; Waclaw Bartlomiej; Evans Martin R

来源：Journal of Physics A-Mathematical and Theoretical, 2013, 46(40): 405003.

DOI：10.1088/1751-8113/46/40/405003

We introduce a model of a totally asymmetric simple exclusion process (TASEP) on a tree network where the aggregate hopping rate is constant from level to level. With this choice for hopping rates the model shows the same phase diagram as the one-dimensional case. The potential applications of our model are in the area of distribution networks, where a single large source supplies material to a large number of small sinks via a hierarchical network. We show that mean-field theory (MFT) for our model is identical to that of the one-dimensional TASEP and that this MFT is exact for the TASEP on a tree in the limit of large branching ratio, b (or equivalently large coordination number). We then present an exact solution for the two level tree (or star network) that allows the computation of any correlation function and confirm how mean-field results are recovered as b -> infinity. As an example we compute the steady-state current as a function of branching ratio. We present simulation results that confirm these results and indicate that the convergence to MFT with large branching ratio is quite rapid.

• 出版日期2013-10-11