A Pareto improving strategy for the time-dependent morning commute problem

This research shows that certain time-dependent congestion reduction schemes involving tolls have the potential for benefiting every driver even if the collected revenues are not returned to the payers. The paper considers a population of commuters who use a single bottleneck during the morning rush hour and try to arrive at work on time. It is assumed that the number of commuters is fixed (independent of the control strategy) and that each commuter wishes to pass through the bottleneck at a given time, which may differ across commuters. Commuters are otherwise identical. Each of them chooses his/her arrival time at the bottleneck so as to minimize a linear combination of monetary cost (tolls) queuing time, and deviation from the desired passage time. A time-dependent toll is applied during a time window, but some commuters are exempted from paying it. Every day, each commuter is classified as either ‘free’ or ‘paying’. The classification method is such that, in the long run, the fraction of days, f, that a commuter is free is the same for all commuters, and the fraction of free commuters is f every day. Free commuters are allowed to use the bottleneck without paying the toll, whereas paying commuters can avoid the toll only if they pass through the bottleneck outside the time window. It is shown that, if commuters wish to pass through the bottleneck close together, then the toll, the window, and the fraction of free commuters can be chosen in a way that will benefit everyone by inducing an equilibrium where the ‘peak is smoothed out’ in a particular way. Up to 25% of the total user cost can be eliminated in this way.