Onset of Congestion from Low-Speed Merging Maneuvers Within Free-Flow Traffic Stream Analytical Solution

Low-speed merging maneuvers performed within a free-flow stream are believed to trigger congestion. These accelerating moving bottlenecks introduce local constraints that can disturb the flow at a local or global scale. Low-speed merging maneuvers are also suspected to cause capacity drop. Using the kinematic wave theory, this paper explores the analytical solution of a simple first-order model when moving boundary conditions are introduced. The paper shows that shock waves initiated by low-speed merging maneuvers are a linear transformation of the moving boundary conditions, no matter the shape of the moving boundary condition. These results are then applied to typical situations to show that the interaction of two moving boundaries can modify the analytical solution of the problem. The results are then extended to multiple merging maneuvers to show that they can interact. Every possible interaction between two identical merging maneuvers is explored to identify the conditions that lead to global congestion. Finally, these results are used to propose an analytical formulation of the capacity drop for multiple merging maneuvers at a single location. It is shown that capacity drop is related to the demands on the minor and major streams and to the speed of the merging vehicle.