Pricing with and without Reservations

The Twin Cities freeway system, like many places, is designed so everyone who wants to use a freeway can do so on-demand by showing up and getting on the road (or queueing at a ramp meter waiting for the opportunity). The Twin Cities also has a MnPass system on some of its freeways, which it plans to expand.

MnPass System of Dynamic Pricing
MnPass System of Dynamic Pricing

The MnPass High Occupancy/Toll (HOT) lanes guarantee free-flow travel times, but have tolls which vary systematically over time-of-day (rising during the peak period), or in modern installations, dynamically. In the case of dynamic tolls (like MnPass), they are intended to ensure the toll is high enough to prevent congestion (ensure the level of traffic is far enough below capacity that bottlenecks are not activated, and if temporary queues are formed they are quickly discharged.) However with the dynamic toll,  travelers don’t know what it is until they are about to decide between using the priced lane or not. (It is capped at $8.00, but the price has variability).

Almost everywhere else, we guarantee the price on a road ($0) with variable travel time.

We thus have either uncertainty on price with certainty on time, or certainty on price and uncertainty on time. We should be able to have certainty about both of these, assuming we allow the price to be non-zero.

First-come, first-serve is not the only way to allocate space. We don’t allocate table space that way during prime time at nice restaurants. We don’t generally allocate airline seats that way. We don’t have to allocate roads that way.

We could, for instance, have reservation pricing (which has been proposed for intersections in a real-time way). At its most basic level, for instance, every day the commuter pre-purchases a ticket to use a particular road segment (e.g. between exit 400 and exit 401) during a particular time slot (say between 7:45 and 8:00). The ticket cost is known in advance before departure, like a plane ticket. The road agency would only sell as many tickets as the road would accommodate (without congestion) at that period. The ticket would be validated electronically through some form of Electronic Toll Collection.

But, roads are not like airplanes, the traveler might arrive at 7:44 or 8:01, does the road agency force the car onto the shoulders? More likely they just charge a penalty which increases with deviation from the purchased window. So if the charge were $2, there might be a $0.10/minute surcharge added for each minute early or late the traveler was.

If the system were deployed universally, congestion would be a rarer occurrence (seeing only non-recurring congestion, due to crashes and other incidents, not the daily recurring congestion because of excess demand for the available capacity). Further the system would know whether the traveler or the agency was the caused the earliness or lateness. If there were non-recurring congestion, it might waive the penalty. If on the other hand the traveler left too early or too late to reasonably make their slot under planned for circumstances, the surcharge would stand.

But travelers don’t want to map out their route every day. OK, the agency can probably just sell a ticket allowing travelers to be “on the roads” (as opposed to being on a specific road), and let individual travelers sort out the best path. The losses from not micro-managing spatially are relatively small, compared to the gains from spreading traffic out by time of day. See the literature on Macroscopic Fundamental Diagrams about this.

In this case, the traveler pre-purchases a ticket to use any metropolitan area road between 7:00 and 7:30 am, but the number of passes is limited by system capacity. If purchase is made far enough in advance there is a lower price then if the ticket is bought real time. But no-one wants to plan their schedule that far in advance, or log-in daily spending even 5 minutes to buy tickets for a 20 minute trip.

Here the road agency managing the system can be a little bit more clever. They could sell various types of season passes (just like transit agencies). A traveler might buy an unlimited use pass for a premium, but there would be a limited number sold to residents of each zip code (if spatially fixed, passes would not be transferrable, the electronic transponder would be linked to a license plate) (or any other local geography that makes sense, the key is there is still finite space on the roads, and too many pass-holders from a wealthy suburb won’t save time just because there is excess capacity elsewhere). Or they could buy a more limited use pass at a lower price. And of course, travelers would buy these as recurring subscriptions, billed to a credit or debit card.

People without passes could take their chances with same-day tickets which might be more expensive if traffic is on the edge of congestion, or cheap if traffic is low that day.

If set up properly, these passes replace existing revenue sources for the agency.

How should the agency allocate these passes? Clearly it should not just give them away. But setting a fixed  price and selling them does not real allow discovery of demand patterns. Here Dutch or Vickrey auctions might be appropriate. For instance, the passes would be available at a posted price (‘buy-it-now’), but the agency would also accept lower bids. Suppose there were 100 passes, there would be a bidding period, and at the end of the period, the top 100 bids would win and the price would be set at the willingness to pay of the 100th bidder. There are many variations on auctions, which each have advantages for buyers or sellers in terms of maximizing revenue or price discovery or fairness.