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We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…
The proliferation of connected and automated vehicles (CAVs) has positioned mixed traffic environments, which encompass both CAVs and human driven vehicles (HDVs), as critical components of emerging mobility systems. Signalized…
A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity and acceleration with an…
In this paper we study dependencies of fundamental diagrams, time gap distributions, and velocity-distance relations on vehicle types, lanes and/or measurement sites. We also propose measurement and aggregation methods that have more…
We consider a one-dimensional stochastic reaction-diffusion generalizing the totally asymmetric simple exclusion process, and aiming at describing single lane roads with vehicles that can change speed. To each particle is associated a jump…
Vehicle-infrastructure communication opens up new ways to improve traffic flow efficiency at signalized intersections. In this study, we assume that equipped vehicles can obtain information about switching times of relevant traffic lights…
During the attempt to line up into a dense traffic people have necessarily to share a limited space under turbulent conditions. From the statistical point view it generally leads to a probability distribution of the distances between the…
Observed accidents have been the main resource for road safety analysis over the past decades. Although such reliance seems quite straightforward, the rare nature of these events has made safety difficult to assess, especially for new and…
We present an analysis of risk levels on multi-lane roads. The aim is to use the crash metrics to understand which direction of the flow mainly influences the safety in traffic flow. In fact, on multi-lane highways interactions among…
Extreme events occur across the natural, engineering, and socioeconomic sciences, where rare but high-impact episodes can lead to disproportionate consequences that pose major challenges for prediction and risk management. Existing studies…
Uncovering the mechanism leading to the scaling law in human trajectories is of fundamental importance in understanding many spatiotemporal phenomena. We propose a hierarchical geographical model to mimic the real traffic system, upon which…
With the emergence of high-frequency connected and automated vehicle data, analysts have become able to extract useful information from them. To this end, the concept of "driving volatility" is defined and explored as deviation from the…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
Autonomous agents must be able to safely interact with other vehicles to integrate into urban environments. The safety of these agents is dependent on their ability to predict collisions with other vehicles' future trajectories for…
Scheduling control problems for a family of unitary networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control…
Ensuring the safety of road vehicles at an acceptable level requires the absence of any unreasonable risk arising from all potential hazards linked to the intended au-tomated driving function and its implementation. The assurance that there…
Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known…
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…
This paper deals with the modeling and numerical simulations of multilane vehicular traffic according to the discrete kinetic theory approach. The nonlinear additive interactions and external actions such as tollgates as well traffic signs…
Traffic signal control is an important and challenging real-world problem, which aims to minimize the travel time of vehicles by coordinating their movements at the road intersections. Current traffic signal control systems in use still…