  Capacity drop at active bottlenecks is one of the most puzzling traffic
phenomena, but a thorough understanding is practically important for designing
variable speed limit and ramp metering strategies. In this study, we attempt to
develop a simple model of capacity drop within the framework of kinematic wave
theory based on the observation that capacity drop occurs when an upstream
queue forms at an active bottleneck. In addition, we assume that the
fundamental diagrams are continuous in steady states. This assumption is
consistent with observations and can avoid unrealistic infinite characteristic
wave speeds in discontinuous fundamental diagrams. A core component of the new
model is an entropy condition defined by a discontinuous boundary flux
function. For a lane-drop area, we demonstrate that the model is well-defined,
and its Riemann problem can be uniquely solved. We theoretically discuss
traffic stability with this model subject to perturbations in density, upstream
demand, and downstream supply. We clarify that discontinuous flow-density
relations, or so-called "discontinuous" fundamental diagrams, are caused by
incomplete observations of traffic states. Theoretical results are consistent
with observations in the literature and are verified by numerical simulations
and empirical observations. We finally discuss potential applications and
future studies.
