Abstract

20 pages; International audience; This paper studies the pattern of departure times at a single bottleneck, under general heterogeneous preferred arrival times. It delivers three main outputs. Firstly, the existence of equilibrium is proven without the classical "S-shape" assumption on the distribution of preferred arrival time i.e. that demand, represented by the flow rate of preferred arrival times, may only exceed bottleneck capacity on one peak interval. Secondly, a generic algorithm is given to solve the departure time choice equilibrium problem. Lastly, the graphical approach that pervades the algorithm provides insight in the structure of the queued periods, especially so by characterizing the critical instants at which the entry flow switches from a loading rate (over capacity) to an unloading one (under capacity) and vice versa. Numerical illustration is given.

Abstract

This discussion paper led to a publication in 'Transportation Research Part B: Methodological' . The traditional bottleneck model for road congestion promotes the implementation of a triangular, fully time varying, charge as the optimal solution for the road congestion externality. However, cognitive and technological barriers put a practical limit to the degree of differentiation real world implementations can handle. The traditional approach to accommodate for this concern has been a step toll, with the single step coarse charge as its simplest case. In this paper we study how efficiency of the coarse charge can be improved by differentiating its level and timing across groups of travellers. We use the traditional bottleneck model to analyse how the coarse charge can be differentiated over two groups of travellers assuming inelastic peak-hour demand. The results of our analysis indicate that differentiating the coarse charge across two groups of travellers considerably improves its efficiency without increasing cognitive effort and decision making costs for the individual traveller. A numeric illustration reveals a welfare gain of 69% of the first best charge, up from 53% for the generic coarse charge. This increase is similar to what is obtained by moving from the coarse charge to a generic two step toll. Once different groups have been defined, one could in fact achieve the same gains by temporal separation of drivers, for example by use of licence plate numbers. The presented charging regime has a considerable degree of flexibility with respect to share of travellers to attribute to each scheme, which further adds to its merits in practical applicability.