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Congestion Pricing
An Introduction


Prof. David Bernstein
James Madison University

Computer Science Department
bernstdh@jmu.edu

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Motivation
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  • Review:
    • We've considered an equilibrium model of route choice behavior
  • What We Didn't Consider:
    • Whether the equilibrium is "good" from a societal perspective (i.e., total travel costs)
An Example Revisited
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  • Travel Times (in Minutes) on the Two Routes:
    • \(t_1(n_1) = 5 + n_1\)
    • \(t_2(n_2) = 10 + 1.5 \cdot n_2\)
  • Value of Time:
    • $15.00 per hour (i.e., 25 cents per minute)
  • Demand:
    • 20
An Example Revisited (cont.)
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  • Total Travel Cost:
    • \(S(n_1,n_2) = c_1(n_1) \cdot n_1 + c_2(n_2) \cdot n_2\)
  • Total Travel Cost in Equilibrium:
    • \(S(n_1,n_2) = c_1(14) \cdot 14 + c_2(6) \cdot 6 = 19 \cdot 0.25 \cdot 14 + 19 \cdot 0.25 \cdot 6 = 95\)
  • The Question:
    • Is this the minimum?
An Example Revisited (cont.)
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Total Travel Costs

images/route-choice-equilibrium_total-costs.png
An Example Revisited (cont.)
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  • An Important Observation:
    • Total travel costs are minimized when \(n_1 = 13\) and \(n_2 = 7\), not at the equilibrium
  • The Answer to the "Motivating" Question:
    • The equilibrium solution is not optimal from a societal perspective
An Explanation
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  • Negative Externalities:
    • A cost incurred by a party who had no control over how it was created
  • In This Case:
    • The private cost (i.e., the travel cost incurred by the traveler) does not reflect the social cost (i.e., the cost incurred by other travelers)
An Explanation (cont.)
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  • Getting Started:
    • Suppose there are 10 vehicles and there is only one route (route 1)
    • The cost incurred by each vehicle is \(t_1(10) \cdot 0.25 = 15 \cdot 0.25 = 3.75\) and the total cost incurred is \(37.50\)
  • Consider a Change:
    • Suppose one more person decides to travel
  • Continuing the Example:
    • That person incurs a cost of \(t_1(11) \cdot 0.25 = 16 \cdot 0.25 = 4.00\) but the increase in the total cost is \(44.00 - 37.50 = 6.50\)
    • So, the private cost to the additional person does not reflect the societal cost
    • As a result "too many" vehicles will use the route
Changing Behavior
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  • What Do We Want To Change?
    • Too many vehicles are using route 1 (i.e., 14 rather than the socially optimal 13)
  • Can We Order People/Vehicles Around?
    • In the two route example, what would happen if we ordered one vehicle on route 1 to use route 2?
  • Can We Provide An Incentive?
    • In the two route example, we could charge a toll on route 1 to make it more expensive and provide an incentive for people/vehicles to voluntarily change routes
Changing Behavior (cont.)
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  • The Route Costs at the Optimal Solution in the Example:
    • \(c_2(7) = (10 + 1.5 \cdot 7) \cdot 0.25 = 5.125\)
    • \(c_1(13) = (5 + 13) \cdot 0.25 = 4.500\)
  • The Implication:
    • We want to make route 1 \(5.125 - 4.500 = 0.625\) more expensive
Overcoming Opposition
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  • Electronic Toll Collection:
    • Without it, collecting the toll itself can impose costs
  • Revenue Redistribution:
    • Return the toll revenues (e.g., tantamount to some people paying others to change their behvaior)
  • Disguises:
    • For example, HOT lanes charge for the "good" choice
  • Negative Tolls:
    • Make the "bad" choice more attractive rather then the "good" choice less attractive (e.g., reduce tolls during the off-peak rather than raise them during the peak)
Going Beyond Route Choice
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  • Travel Choices:
    • The decision to travel
    • The origin of the trip (short run vs. long run)
    • The destination of the trip (short run vs. long run)
    • The mode
    • The route
    • The departure time
  • Incentives:
    • Different incentive mechanisms (e.g., gasoline taxes, vehicle registration fees, usage fees) may need to be used to influence differen vehaviors
Actual Implementations
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  • Different Spatial Structures:
    • Facility-Based
    • Zone-Based
    • Cordon-Based
  • Different Temporal Structures:
    • Static
    • Dynamic Interday
    • Dynamic Intraday
There's Always More to Learn
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