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CONGESTION PRICINGECONOMIC MODELS AND INTERNATIONAL EXPERIENCE

Aya Aboudina, PhD Student

Civil Engineering Dept, University of Toronto

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Outline

Introduction Motivation Microeconomic foundations

Congestion Pricing Models Static vs. dynamic pricing Profit-maximizing vs. social-welfare maximizing

pricing Social-welfare maximizing pricing Congestion pricing models: a conclusion

International Experience and Research Vision

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Motivation

Users/consumers should pay the full cost of whatever they consume

Otherwise, they are subsidized Therefore, they unnecessarily consume

more to the detriment of all i.e. “Tragedy of the Commons” Garrett Hardin, journal Science in 1968

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Tragedy of the Commons

A dilemma arising from the situation in which multiple individuals, acting independently and rationally consulting their own self-interest, will ultimately deplete a shared limited resource even when it is clear that it is not in anyone's long-term interest for this to happen.

Examples: Overgrazing Congestion

Criticized for promoting privatization Used here to encourage “control”

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Motivation (cont’d)

Recent research conducted at UofT eliminates

both capacity expansions and extensions to public

transit as policies to combat traffic congestion. On

the other hand, it indicates that vkt (vehicle

kilometres travelled) is quite responsive to price.

Together these findings strengthen the case for

congestion pricing as a policy response to traffic

congestion.

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Microeconomic Foundations I:Demand, Cost, Revenue, and Profit

Demand (aka Marginal Benefit) The change in the quantity purchased to the

price. Downward slopping curve

Demand

Output (Q)

$

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Microeconomic Foundations I:Demand, Cost, Revenue, and Profit (cont’d)

Costs Average Cost (AC) = Total Cost (TC)/Total

Production (Q) Marginal Cost (MC): the change in total cost

required to increase output by one unit = ΔTC/ ΔQ → d(TC)/d(Q)

MC

AC

Demand

Output (Q)

$

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Revenue Total Revenue (TR) = Price (p) * Total Production

(Q) Marginal Revenue (MR) = ΔTR/ ΔQ → d(TR)/d(Q)

Profit = TR – TC (maximized when MR = MC) MC

AC

DemandMR

Output (Q)

P

Q

$

Profit

Microeconomic Foundations I:Demand, Cost, Revenue, and Profit (cont’d)

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Microeconomic Foundations I:Demand, Cost, Revenue, and Profit (cont’d)

In Transportation AC = Monetary Expenses + VOT * Travel Time The AC increases with the level of road use. This

implies that the MC exceeds the AC. This is because the MC includes both the cost incurred by the traveler himself (AC) and the additional cost (s)he imposes on all other travelers. This additional cost is known as the marginal external congestion cost (mecc).

MC

AC

Flow

$

V

mecc

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Numerical Example When the flow entering some bridge is 10,999 veh/hr, it

takes 1.07 min to cross bridge. Whereas it takes 1.09 min when the flow is 11,000 veh/hr. Then we have the following cost values at flow = 11,000:

TC = 11,000 *(1.09 min * VOT) AC = TC/Flow = 1.09 min * VOT MC = TC (11,000) –TC (10,999)

= 11,000*(1.09 min*VOT) –10,999 *(1.07 min*VOT)

= (1*1.09min*VOT) +10,999 ((1.09-1.07)min*VOT)

= AC + externality cost

Microeconomic Foundations I:Demand, Cost, Revenue, and Profit (cont’d)

10,999 11,000

1.091.07

MCAC

Flow

Travel Time

externality = 10,999* 0.02 min

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Microeconomic Foundations II:Consumer ,Producer, and Social Surpluses

Consumer Surplus (CS) = Total Benefit – Amount Paid

Producer Surplus (PS) = Total Revenue – Total Cost = Profit

Social Surplus (SS) = CS + PS = Total Benefit – Total Cost

P

Q

Consumer Surplus

Producer Surplus Demand

$

Quantity

MC

Social Surplus

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Microeconomic Foundations III:Engineers vs. Economists Definition of Congestion

Economists: system is congested if the performance of the system (e.g. travel time) rises with the intensity of use (e.g. flow levels).

Traffic engineers: system is congested when traffic density exceeds the critical density, resulting in traffic breakdown.

AC

p

Cost(1/speed)

Flow(veh/hr)

Capacity (max flow)

Economists

TrafficEngineers

EconomistsTraffic

Engineers Capacity

Critical density

Density (veh/km)

Flow (veh/hr)

Breakdown

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“Congestion” for traffic engineers is termed “hyper-congestion” for economists.

Hyper-congestion causes a significant drop in capacity (at critical density).

Eliminating hyper-congestion allows the sustenance of the original capacity.

Critical density

Density (veh/km)

Flow (veh/hr)

Uncongested capacity

Congested capacity

Breakdown

Normal- Congestion

Hyper- Congestion

Microeconomic Foundations III:Engineers vs. Economists Definition of Congestion

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Outline

Introduction Motivation Microeconomic foundations

Congestion Pricing Models Static vs. dynamic pricing Profit-maximizing vs. social-welfare maximizing

pricing Social-welfare maximizing pricing Congestion pricing models: a conclusion

International Experience and Research Vision

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Static vs. Dynamic Pricing

Dynamic

Open LoopVary according to fixed schedule (based on typical

conditions per time of day)

Closed Loopvary depending on

time of day and level of congestion (based on real-time system

state)

Reactive

Static

Congestion Pricing

Predictive

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Profit-Maximizing vs. Social-welfare Maximizing Pricing

Dead weight loss

But total social welfare declines by yellow area-

“dead weight loss”Producer Surplus

maximized

P*

Q*

Consumer Surplus

Producer Surplus

Demand

$

Output

MC

Social Welfare maximized

Social-Welfare Maximizing Price

Pm

Qm

Consumer Surplus shrinks

Monopolist maximizes its Producer Surplus

DemandMR

$

Output

MC

Profit Maximizing (Monopoly) Price

• Set to maximize the social welfare.

•Achieved when the “Demand” equals the MC.

• Set to maximize profits (PS).• It is the price consistent with

the output where the MR equals the MC.

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Social-Welfare Maximizing Pricing

First-best pricing

Second-best pricing

Static congesti

on

Dynamic

congestion

• Set to maximize the social welfare.

• No constraints on congestion prices.

• It is often impossible!

• It optimizes welfare given some constraints

on policies (e.g. the inability to price all

links on a network and the inability to

distinguish between classes of users).• Rules are more

complex.• Relative efficiency

less than one.

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This is the conventional diagram of optimal congestion pricing.

The un-priced equilibrium occurs at the intersection of demand and AC curves; it involves traffic flow V0 and cost c0.

The optimal flow V1 occurs at the intersection of demand and MC; it can be achieved by imposing a toll τ (marginal-cost pricing).

The gain in the social surplus is depicted by the shaded triangle, which gives the difference between social cost saved (under MC curve) and benefit forgone

(under demand curve) when

reducing traffic flow from

V0 to V1.Flow (V)

$

ACToll

Revenue

MC

Social Subsidy

MC1

AC1τ = mecc

V1 V0

Demand

First-Best Pricing with Static Congestion

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Static models limitations: Assumes static demand and cost curves for

each congested link and time period. Appropriate when traffic conditions do not

change too quickly or when it is sufficient to focus attention on average traffic levels over extended periods.

Cannot explain whether or not hyper-congestion will occur in equilibrium (i.e., whenever demand intersects the AC curve in its hyper-congested segment).

First-Best Pricing with Static Congestion

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First-Best Pricing from a Dynamic Perspective

The basic bottleneck model

Alternative dynamic congestion

technologies

Chu 1995

Verhoef 2003

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The Basic Bottleneck Model

The most widely used conceptual model of dynamic congestion pricing

Assumptions: No delay if inflow is below capacity Queue exit rate equals capacity

(when a queue exists) Single desired queue exit time t*

(for all users) Total demand for passages Q is inelastic

Two costs in un-priced equilibrium: Travel delay cost cT(t)

Schedule delay cost cs(t) (early and late arrival costs)

Queue forms

Time

Cumulative queue exits (slope: Vk)

Cumulative queue

entries

Queue disperses

Number of

vehicles

tqtq’t*

tq tq’ Exit time (t)

t*

cs(t)

cT(t)

cs(t) cs(t)c(t)Average cost

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The Basic Bottleneck Model (cont’d)

The optimum toll τ(t): Replicates travel delay costs (it has a triangular shape). Affects the patterns of entries (queue entry rate will

equal capacity) (flattening the peak). Results in the same pattern of schedule-delay cost. Produces zero travel delay costs.

The main source of efficiency gains from optimal dynamic pricing is the rescheduling of departure times from the trip origin

tq tq’ Exit time (t)

t*

cs(t)

τ(t)

cs(t) cs(t)c(t)Average

cost

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Alternative Dynamic Congestion Technologies: Chu 1995

Chu extends the same basic logic of (marginal-cost) toll to a dynamic setting in which traffic flow varies with time.

The optimal time-varying toll is a dynamic generalization of the standard toll for static congestion.

Hyper-congestion is absent in this model and both inflow and outflow from the road are assumed to have equal sub-critical value.

Flow

$

ACToll

Revenue

MC

MC1

AC1τ = mecc

V1 V0

Demand

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Alternative Dynamic Congestion Technologies: Verhoef 2003

It uses the car-following model to investigate optimal time-varying tolls on a road with a sudden reduction in the number of lanes by half (which produces hyper-congestion in the un-priced equilibrium).

The study provides a time- and location-specific version of Chu's toll; it extends the basic “marginal-cost" toll to more realistic cases where congestion varies both temporally and spatially in a continuous manner.

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Congestion Pricing: a Conclusion

Two types of models may be considered to set socially optimal prices, namely, static and dynamic methods.

Static pricing models: Assume static demand and cost curves and hence come out with

static (time-independent) tolls. The main benefit from static pricing is to force vehicles to pay

their full congestion externalities to the road (spatial distribution). Dynamic pricing models

Take into account the variations of demand (arrival rates) with time (how peak demand evolves then subsides); accordingly they produce dynamic (time-varying) tolls.

A main source of efficiency gains from optimal pricing would be the rescheduling of departure times (temporal distribution) from the trip origin, which can produce significant benefits going beyond those produced by static tolls.

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Outline

Introduction Motivation Microeconomic foundations

Congestion Pricing Models Static vs. dynamic pricing Profit-maximizing vs. social-welfare maximizing

pricing Social-welfare maximizing pricing Congestion pricing models: a conclusion

International Experience and Research Vision

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International Experience

USA, UK, France, Norway, Sweden,

Germany, Switzerland, Singapore, and

Australia have implemented major

road pricing projects.

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London Congestion Pricing

In service since 2003. The first congestion pricing program in a major

European city. £10 daily cordon fee (flat price) for driving in “Central

London Congestion Pricing Zone” during weekdays (from 7am to 6pm) (one time per chargeable day).

Bus and taxi service improved. Accidents and air pollution declined in city center. After 1 year of cordon tolls and during charging:

Traffic circulating within the zone decreased by 15%. Traffic entering the zone decreased by 18%. Congestion (measured as the actual minus the free-flow

travel time per km) decreased by 30% within the zone.

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London Congestion Pricing (cont’d)

The Central London Congestion

Pricing Zone

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I-15 HOT Lanes, San Diego, CA

First significant value pricing project. Implemented in 1996 along the 13-km

HOV section of I-15 in San Diego. Convert HOV to HOT; solo drivers pay

a monthly pass ($50 to $70) to use HOV during peak periods.

In 1998, automated and dynamic pricing scheme.

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I-15 HOT Lanes, San Diego (cont’d)

Toll levels determined from congestion level to maintain “free-flow” conditions in the HOV lane.

Tolls updated every 6 minutes ($0.5 to $4) (closed-loop regulator).

Toll level displayed on real-time sign. 48% increase in HOV volumes. Success in congestion minimization.

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407 ETR (Express Toll Route)

Multi-lane, electronic HYWY running 69 km across the top of the GTA from HYWY 403 (in Oakville) to HYWY 48 (in Markham).

Constructed in a partnership between “Canadian Highways International Corporation” and the Province of Ontario.

Currently owned by 407-ETR International Inc.

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407 ETR (Express Toll Route) (cont’d) Fees at the regular zone (open-loop

regulator): Monday-Friday:

Peak period (6-7:30am, 8:30-10am, 3-4pm, 6-7pm): 22.75¢/km

Peak hours (7:30-8:30am, 4-6pm ): 22.95¢/km Off-peak rates: 22.95¢/km

Weekends and holidays: 19.35¢/km

Speeds on HYWY 407 ~ double free HYWYs. High level of user satisfaction. Monopoly price!

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Research Vision

The purpose is to develop a comprehensive predictive real-time dynamic congestion pricing model for the GTHA.

The tolls will be set dynamically and adaptively according to location, time-of-day, distance driven (, and if possible, the level of pollution emitted from the vehicle).

The tolling system will target full cost pricing in the case of sub-critical traffic conditions and eliminating hyper-congestion and maintaining flow at the maximum capacity in case of super-critical traffic conditions.

Additionally, this research will attempt an extra step of basing the toll on the predicted (anticipated), rather than the prevailing, traffic conditions. This is to prevent traffic breakdown before it occurs.

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Research Vision (cont’d)

To consider how our envisioned systems will be applied to: Freeway only with HOT lanes. Freeway corridor (e.g. Gardiner-lakeshore, where

Gardiner would be tolled).  Cordoned network, e.g. downtown Toronto.  

Thank You

Questions, suggestions and comments are always welcome!

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References

The Fundamental Law of Road Congestion, Evidence from US Cities (UofT Economists)2009

CIV 1310 Infrastructure Economics lecture notes Kenneth A. Small and Erik T. Vehoef.The Economics of

Urban Transportation.

Jing Dong, Hani S. Mahmassani, Sevgi Erdoğan, and Chung-Cheng Lu. “State-Dependent Pricing for Real-Time Freeway Management: Anticipatory versus Reactive Strategies”. TRB Annual Meeting 2007 Paper #07-2109.

Price Elasticity of Demand

Price elasticity of demand: