Load Balancing


Early

HBW 30min speeds kmh

Road pricing has been unsuccessful because it is framed wrong. I say it is unsuccessful because it is not widely adopted, despite being a policy proposal on the table for decades, despite its widespread support among transport economists. Unfortunately, it is perceived (by drivers) as punitive.

Pricing has two complementary objectives, raising funds and allocating resources. We already raise funds for roads, with gas taxes. Gas taxes are in the present (non-EV) world almost perfect as a fund raising mechanism, as they don't have much in the way of administrative costs, but they are poor at allocating resources. See Marty Wachs' paper on this.

We of course might want more funds, but I believe we cannot raise revenue and switch methods at the same time. If we want to switch methods (to better allocate roadspace) we need to be revenue neutral. If want to raise revenue, we should raise rates under whatever system is adopted. These two debates should not be conflated.

The primary objective of any new road pricing strategy should be to better balance loads, i.e. manage the use of a scarce resource, roadspace, during the peak hours. Basically we want to move some drivers from the peak to the shoulders of the peak or the off-peak to reduce congestion.

Because it is costlier to provide extra capacity to support travel in the peak, and because of congestion externalities, travelers in the peak should pay more than travelers in the off-peak to satisfy both equity and efficiency arguments. Currently most federal and state road funding is from a gas tax that is proportional to fuel consumed, more or less proportional to miles traveled, but almost entirely independent of when that travel takes place (more fuel may be consumed per mile in the peak than the off-peak because of additional braking events in stop-and-go traffic, but this is too small to affect people's behavior).

Temporal variations

The critical aspect of urban travel is its peak by time of day. We have morning and evening rush hours, corresponding to when most people go to and from work. However, there is a lot of non-work travel in these periods as well, people going shopping, to the gym, or eating out, which may have more sensitivity to price than work travel. We can see peaking in the attached figures. Demand for work travel peaks in the morning and evening (non-work trips are flatter, but not flat). Speeds drop in the morning and afternoon peaks. If we balanced the load more evenly, average speeds would rise in the peak and drop in the off-peak. But the net should be an overall gain, since there is excess off-peak capacity.

Figures from Parthasarathi, Pavithra, Anupam Srivastava, Nikolas Geroliminis, and David Levinson (2011) The Importance of Being Early. Transportation 38(2) pp. 227-247

Spatial variations

Just as we want to balance trips across time of day, we might want to balance trips across the network. While during the peak, some links are congested, others have spare capacity. Perhaps we can move travelers around?

Work in our labs with computer models of the Twin Cities road networks is that moving from a user equilibrium solution, where each driver selfishly chooses his or her own route, to a system optimal solution where each driver chooses a route that is best for society, reduces total Vehicle Hours Traveled by less than 5 percent. This suggests there is not much to gain for all of the complexity involved in getting travelers to switch routes, but keep their time of day.


A strategy that respects privacy.

A concern that arises with most road pricing proposals is government tracking. While I am personally of the belief we don't really have privacy anymore, I can understand the desire to at least make it more difficult to track you. Installing devices in vehicles as a government mandate is not reassuring to anyone, tin-foil hat wearing or not. To be adopted, policy has to respect that.

Suppose we increase the gas tax to the desired peak hour rate. [This is the politically difficult part.] We then offer a discount for off-peak travel. This discount requires voluntarily installing in your vehicle a device which tracks when your car is in operation, and the odometer reading. (Not where, just when). For each hour of travel during the peak, you have already paid the peak rate. For each hour of travel in the off-peak, you get an off-peak discount.

So for instance, let's assume you consume 500 gallons of fuel per year (@20 MPG, this would be 10000 miles). Let's assume half of your time is in the peak and half is in the off peak, as measured by the clock. Assume previously, the gas tax was 35 cents a gallon, all the time. You would have paid $175 a year.

Now the "peak" gas tax is 50 cents a gallon, so you paid $250. The off-peak gas tax is 20 cents a gallon. If you install the device, you would get an annual off-peak travel rebate of $250-$175 = $75 (500 gallons * 50% of time * $0.50/gallon peak + 500 gallons * 50% of time * $0.20/gallon off-peak = $175). If you wanted to keep your privacy, you would not install the device. Privacy is not costless.

The device of course makes the system somewhat more complicated than existing, but is hopefully inexpensive in large numbers (my insurance company issues one to me, it can't be that expensive), and the rates make the system slightly more complicated. Altogether, that is unavoidable if you want to add a time dimension to the prices charged to travelers.

As the saying goes YMMV (Your Mileage May Vary), so while this example was revenue neutral in a world of static demand, it might lose money if everyone installed the device and people respond to incentives and change behavior. Based on experience with changes in gas prices, we expect those changes are relatively small (the elasticity of demand with respect to gas price changes is pretty low). Further, not everyone will install the device. But changes don't have to be large to have an effect, and we don't want them to be too large (otherwise the peak is uncongested and the off-peak is congested). We could come up with schedules that would be appropriate, and might have different rates at different times (e.g. peak of the peak, shoulder, mid-day, and off-peak).

Another objection is out-of-state travel. Here, we are simply computing when you travel and assuming all fuel is purchased in the home state. If every state has such a system, this probably has very small boundary effects. If one small state adopts this, and its neighbors don't some residents might travel out of state to purchase fuel (leading them to not adopt this). Again, I suspect the losses will be small, though they may be measurable. There could either be a federal mandate for such a system (which I would not like), or agreement among the various states to coordinate the pricing mechanism. If the rates differences (peak vs. off-peak) are small, they will not distort behavior much, and that might be the best way to implement, and then the differences can be increased over time (peak prices increasing, off-peak decreasing, until the desired load balance was achieved).

David Levinson

Network Reliability in Practice

Evolving Transportation Networks

Place and Plexus

The Transportation Experience

Access to Destinations

Assessing the Benefits and Costs of Intelligent Transportation Systems

Financing Transportation Networks

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This page contains a single entry by David Levinson published on October 11, 2012 9:30 AM.

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