Effect of self-deflection on a totally asymmetric simple exclusion process with functions of site assignments

This study proposes a model of a totally asymmetric simple exclusion process on a single-channel lane with functions of site assignments along the pit lane. The system model attempts to insert a new particle to the leftmost site at a certain probability by randomly selecting one of the empty sites in the pit lane, and reserving it for the particle. Thereafter, the particle is directed to stop at the site only once during its travel. Recently, the system was determined to show a self-deflection effect, in which the site usage distribution biases spontaneously toward the leftmost site, and the throughput becomes maximum when the site usage distribution is slightly biased to the rightmost site. Our exact analysis describes this deflection effect and show a good agreement with simulations.

Figure 1

Schematic view of the proposed model.

Figure 2

Dependence of throughput $Q$ on the number of sites (left side) and number of time steps (right side) in case of setting the probability $\alpha$ to the different twenty values in the range of 0.05 to 1.0 and setting the number of sites $L$ in the right side to 100.

Figure 3

Dependence of throughput $Q$ on probabilities $\alpha$ and $\gamma$.

Figure 4

Dependence of throughput $Q$ on probability $\alpha$ in case of being (b) biased toward the leftmost site (left column) and (c) biased toward the rightmost site (right column).

Figure 5

Dependence of throughput $Q$ on distribution parameter $\lambda$.

Figure 6

Site usage distribution according to each simulation result: (a) uniform random distribution, (b) bias toward the leftmost site, and (c) bias toward the rightmost site in Fig. 5.

Figure 7

(a) The dependence of throughput $Q$ on the skewness $S_k$ of the site usage distribution for different values of parameter $\lambda$ between $-2$ and 0, and (b) the result of same measurement as in (a) for different values of the number of sites $L$ between 4 and 10.

Figure 8

The 20 possible states (left column) and master equations of the proposed system (right column).

Figure 9

Dependence of the expected throughput $E_Q$ on distribution probability $q$.

Figure 10

Comparison of the expected value $E_S$ of the site usage for left site (red line) and right site (blue line) in the pit lane.