Simulation study of satisfaction rate in the mixed traffic flow with open boundary conditions

In this paper, we propose a single-lane cellular automata (CA) traffic model which takes into account the disorder in the length and the maximal speed of the vehicles (i.e. slow and fast) to study the satisfaction rate of the fast vehicles (i.e. the number of vehicles that run with their desired speed) with open boundary conditions in the case of a chain of one entry; where α is the injecting rate of vehicles independent of their nature and β is the extracting rate. The slow vehicles are injected with the conditional probability αs, where 0≤αs=χα≤α and χ is the concentration of the slow vehicles. It is found that for the low value of the injecting rate α and for the high extraction rate β, the satisfaction rate takes higher values. It also depends on the concentration of the slow vehicles injected on the road. Furthermore, we have shown that, in the case when α=β, the satisfaction rate undergoes a transition from the maximal value to the minimal one and it takes a value near to zero in the case of α>β. We have also found that the satisfaction rate depends strongly on the probability of overtaking, also the phase diagrams (α,β) are established for the different values of the slow vehicles concentrations χ.