On the emergence of traffic jams in a stochastic traffic flow driven by additive and multiplicative white Gaussian noise processes

Understanding the influence of random phenomena on the emergence of jams in vehicular traffic flows is a fundamental question in the study of traffic flow dynamics. Motivated by the fact that additive and multiplicative white Gaussian noise processes represent fundamentally distinct sources of randomness that can engender qualitatively different patterns in the dynamics of traffic flow, here we compare and contrast the influences of those two distinct stochastic processes on the formation of traffic jams. Analyzing the macroscopic dynamics of spatially homogeneous single-lane traffic flow using a car distribution function that evolves according to a Fokker–Planck type equation, we first obtain the equilibrium distribution function in closed form for traffic flow driven by additive as well as multiplicative white Gaussian noise. We then derive the mean first passage time (MFPT) for both cases and also present results that elucidate the influence of varying noise strength on both the equilibrium distribution function and the MFPT. Additionally, we obtain fundamental diagrams corresponding to speed versus flux of vehicle flow for both cases that further highlight the distinct effects of the two types of noise. In summary, the results underscore the contrasting influences of additive and multiplicative noise processes on the emergence of traffic jams and thereby contribute to advancing our understanding of this aspect of stochastic traffic flow. The findings could also help improve our understanding of how randomness affects traffic flows that are a combination of human and self-driven vehicles.