The Riemann problem with delta initial data for the homogeneous pressureless hydrodynamic model Available to Purchase

During road transportation, particularly during peak hours or under specific circumstances, severe traffic congestion often occurs, significantly reducing traffic flow. Therefore, it is essential to investigate the development of severe traffic congestion. The delta shock wave is commonly employed in traffic flow models to explain severe traffic congestion. In this paper, we primarily study the development of severe traffic congestion occurring at the initial moment by investigating the initial value problem with delta initial data for the homogeneous pressureless hydrodynamic model. Depending on the local mean headway variations, the problem is categorized into four distinct cases, and the structural solutions for each case are derived. Each solution incorporates a delta shock wave that persists indefinitely, indicating that the severe traffic congestion will continue. Thus, the Transportation Management Authority must take appropriate measures to prevent severe traffic congestion, such as proactively deploying real-time traffic monitoring and adaptive signal control systems. Otherwise, mitigating severe traffic congestion will be challenging once it occurs. Moreover, we present some typical numerical results consistent with our theoretical analysis.