Congestive collapse and its avoidance in a dynamic dial-a-ride system with time windows

In a dynamic dial-a-ride problem (DARP) the task is to provide a transportation service in a given area by dynamically routing a set of vehicles in response to passengers' trip requests. Passengers share vehicles similarly as with buses, while the schedule and routes are chosen ad hoc. Each trip is defined by the origin-destination pair in plane augmented with a latest feasible delivery time. Optimal control of such a system is a complicated task in general and outside the scope of this paper. Instead, we consider a set of well-defined heuristic control policies that can be evaluated by means of simulations. The main contribution of this paper is two-fold: (i) to demonstrate that a phenomenon known as congestive collapse occurs as the rate of trip requests increases beyond a capacity threshold of the given control policy (the value of which itself is unknown a priori); (ii) to propose a robust and computationally lightweight countermeasure to avoid the congestive collapse in such a way that the system's performance still improves after the capacity threshold has been passed. Despite its appealing simplicity, the proposed method succeeds in rejecting customers detrimental for the common good.