11.5: Chapter 11 Exercises
P11.1 (6 pts)
How would you design vehicle fees for different types of vehicles to account for different impacts on pavements? How does your suggested design compare to existing fees?
P 11.2 (6 pts)
The federal government collects diesel and gasoline taxes and puts them in the Highway Trust Fund. (a) How would you recommend that these funds be allocated among the different states? (b) Would you allocate any of the funds for public transit? (c) How might you tax (or should you tax) battery powered vehicles?
P 11.3 (14 pts)
Suppose I have a simple network as shown below. I have 300 vehicles going from A to B, and they can either take route A-B or route A-C-B. The travel time per vehicle on route A-B is 10 + 0.5 qAB min where qAB is the travel volume on route AB. The travel time per vehicle on route A-C-B is 15 + 0.2 qACB min.
a. Suppose vehicles chose routes such that any route that was used from A to B had equal travel times. This is called a ‘user equilibrium’ since no single user has an incentive to change routes as there is no opportunity to save time by doing so. What are the travel volumes on the two routes for a user equilibrium?
b. Suppose vehicles are assigned to particular routes to minimize the total travel time on the network. The resulting pattern is called a ‘system equilibrium’ since changing a route can only increase overall system travel times. What are the travel volumes on the two routes for a system equilibrium?
c. Why do the system and user equilibrium flow volumes differ?
d. Suppose travelers have a value of time of $ 1/6 per minute per vehicle. For example, if a toll p was imposed on route A-B, the effective travel time would be 10 + 0.5*qAB + 6*p. Is there a toll we could impose somewhere on the network that would be a user equilibrium but have the system equilibrium route volumes? What is it? What is the resulting revenue?
e. Using the value of time in part d, what is the dollar value of the difference between user equilibrium and system equilibrium?
f. Suppose we have to do roadway maintenance and shut down link A-B in the network, diverting all traffic to route A-C-B. What would be the travel time on this route? Comparing this to the base user equilibrium (in part a), what is the increase in travel time? Using the value of time in part d, what is the increase in user cost?
g. Roadway renovation contracts often use a system called ‘A+B’ in which contractors bid’s include a ‘rental fee’ for closing roadways (that is the +B, whereas A would be the estimated renovation costs themselves). In the case of our small network, this +B amount might be represented by your answer to part f. In practice, the +B amount would be calculated from a typical value of time, volume on a roadway, and an estimate of the travel time increase from using alternative routes. What might be the advantage of the A+B contract system versus a conventional system (call it A) for infrastructure management? Do you think renovation costs overall would go up or down with the A+B system? (Hint: the table below is an example from WSDOT, with C being the winning, low bidder).
| Contractor | A | B | C |
| A Bid Amount | $4,300 K | $4,900 K | $4,450 K |
| No. Days Bid | 130 | 110 | 115 |
| Road User Cost | $12 K | $12 K | $ 12 K |
| Combined A+B Bid | $5,860 K | $6,220 K | $5,830 K** |