SIMULATION ANALYSIS OF THE TOTALLY ASYMETRIC SIMPLE EXCLUSION PROCESS TO DETERMINE THE PROFIL OF THE ONE-BODY CORRELATION FUNCTION, TWO-BODY CORRELATION FUNCTION, AND THREE-BODY CORRELATION FUNCTION AROUND THE ENDS OF THE LATTICE WITH LATTICE NUMBER VARIATION

Abstract

This study aimed to determine the behavior of one-body, two-body, and three-body correlation functions of the model dynamics TASEP with sequential updating rules and open boundary conditions on vehicular traffic around the end of the traffic light. The study began with the determination of algorithm to model the dynamics of TASEP and coding, with the variation of the input rate (α) , the output rate (β), and the number of  lattice sites (N). Then the program  run with specific time limit (t) and number of  systems (M). The value of the one-body correlation function determines the average occupancy of particles in lattice site-i at time t. Two-body correlation function determines the average occupancy of particle at site-i when there is another particle occupying the nearest neighbor lattice, i+1, at time t. Three-body correlation function determines the average occupancy of particles to occupy lattice site-i when there are other particles occupying the nearest and next nearest neighbor lattice sites, i+1 and i+2, at time t. The value of the one-body correlation function turns out to be larger than the value of the two-body correlation function. The value of the two-body correlation function is larger than the value of the three-body correlation function for all phases. The correlation between a vehicle to another vehicle will be even greater.

Keywords:     TASEP, sequential updating, n-body correlation function