International Forum on Shipping, Ports and Airports (IFSPA) 3-4 June 2013, Hong Kong, China

Tradable Travel Credit Schemes for Network Mobility Management

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Hai Yang Chair Professor

Department of Civil and Environmental Engineering

The Hong Kong University of Science and Technology, Hong Kong

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Outline of Presentation

Introduction to current network mobility management strategies

Introduction to tradable travel credit schemes

Model and properties of network traffic equilibria under tradable credit schemes

Recently published and ongoing studies

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Pricing and Quantity Instruments for Network Mobility Management

Pricing Instrument

Efficient utilization of limited network resources

Inequality problem etc. public opposition

Quantity Instrument Road space rationing Tradable travel credit scheme

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Road Space Rationing (e.g., Beijing)

Restrict private cars’ access to roads on a uniform fraction of days.

Effective (short-term).

More equitable (?)

Low efficiency (spatially and temporally).

Long-run policy may lead to a sharp increase of old, cheap and high-polluting second-car consumption (negative impact to the environment).

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Tradable Travel Credit Schemes Proposed by Yang and Wang (2011)

Yang, H., Wang, X.L., 2011. Managing network mobility with tradable credits. Transportation Research Part B 45 (3), 580-594.

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Introduction to Tradable Travel Credit Schemes for Managing Network Mobility

Each participating agent receives a proportion of credits (on a periodic basis such a month or a quarter)

Equity

Initial distribution for free

Revenue-neutral incentives for mobility and environmental quality

Credit charging scheme

Link-specific or cordon-based; distance or time-based; time-invariant or time-varying

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A policy target in terms of fix-quantity travel credits can be easily achieved.

Qualitative Properties of Tradable Travel Credit Schemes

Example: Distance-based credit charge for achieving control of total veh-km traveled on the network

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The equilibrium price of credits is determined by the market through free trading.

Market driven

Credit flow from the higher income groups to the lower; the flow of money from the wealthy to the less.

Enhance income distribution or financial transfer confined only to within the predefined group of travelers:

Qualitative Properties of Tradable Travel Credit Schemes

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Mathematical Model of Traffic Equilibrium under Tradable Travel Credit Schemes

Equivalent model formulation:

subject to:

, , , w

a r w a rw W r R

v f a A∈ ∈

= δ ∈∑ ∑

( )( )

0,min dav

av f at

∈Ωω ω∑∫

, , w

r w wr R

f d w W∈

= ∈∑

a aa A

v K∈

κ ≤∑

( )( )* *, , 0, ,a a a a r w r w w

a At v p f r R w W

∈

+ κ δ −µ = ∈ ∈ ∑

( )( )*, 0, ,a a a a r w w

a At v p r R w W

∈

+ κ δ −µ ≥ ∈ ∈∑

, 0, ,r w wf r R w W≥ ∈ ∈

* 0a aa

v K p κ − = ∑

*a a

av Kκ ≤∑

*, 0, ,r w wf r R w W≥ ∈ ∈

0p ≥

First-order optimality conditions:

Equivalent traffic equilibrium and credit market equilibrium conditions

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Theoretical Properties of Tradable Travel Credit Schemes

For a given credit scheme, a unique equilibrium flow pattern exists; the equilibrium credit price is unique subject only to very mild assumptions.

Proposition 1. Given a tradable credit scheme ( ),K κ ∈Ψ , the

credit price *p at equilibrium is unique if there exists at least one

O-D pair whose equilibrium path set always contains the same two (or more) paths with different credit charges.

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Theoretical Properties of Tradable Travel Credit Schemes

A properly designed tradable credit scheme can emulate a congestion pricing system and support various desirable traffic flow optima:

Social optimum

Capacity-constrained traffic flow pattern

Pareto-improving and revenue-neutral

Proposition 3. Given an SO credit charging scheme, soκ , and a total amount

of credits issued, so so soa aa A

K v∈

= κ∑ , if the credit price *p at market

equilibrium is unique and the total system travel time at SO is strictly less than that at UE without any policy intervention, then there exists an O-D based credit distribution scheme that can make every traveler strictly better off.

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Link travel time: ( )1 1 18 2t v v= + , ( )2 2 216t v v= +

O-D demand: 1 2 10d → = ,

Initial credit allocation: 30K = , 1 2 3k → =

Link credit charge: 1 4κ = , 2 2κ = .

2

1

1Link 1; 4κ =

Traffic Equilibrium and Market Equilibrium with Tradable Credits: An Example

2Link 2; 2κ =

User equilibrium and credit market equilibrium conditions:

1 2

1 2

1 2

8 2 4 16 2

10

4 2 30

v p v p

v v

v v

+ + = + +

+ =

+ =

A unique equilibrium solution:

Link flow: * *1 2 5v v= =

Link travel time: *1 18t = , *

2 21t =

Unit credit price; * 1.5p =

Subsequent Recent Studies after Yang and Wang (2011)

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Tradable Parking Permits for Improving Travel Efficiency

Morning commuters often choose their departure times not only to trade off bottleneck congestion and schedule delays, but also in order to secure a parking spot due to limited parking spaces.

Parking permit scheme to eliminate the external cost arising from the competition for parking spots.

Free trading of parking permits among commuters to better cater for commuters’ parking needs.

Zhang, X., Yang, H., Huang, H.J., 2011. Improving travel efficiency by parking permits distribution and trading. Transportation Research Part B 45 (7), 1018-1034.

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Implementation Issue under Limited Information

Analytical demand functions tailored for traffic demand control are difficult to establish in practice.

A fundamental question: how to design the optimal credit scheme in a simple yet practical manner ?

Traffic Demand0

(unknown benefit orinverse demand function)

Gen

eral

ized

Cos

t

(1)d (1)d

optu

( )1u

uedsod

( )AC d

( )MC d

( )B d

Trial-and error implementation of marginal cost pricing and

tradable credit scheme

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Implementation Issue under Limited Information

Wang, X., Yang, H., 2012. Bisection-based trial-and error implementation of marginal cost pricing and tradable credit scheme. Transportation Research Part B 46 (9), 1085-1096.

Wang, X., Yang, H., Han, D., Liu, W., 2013. Trial-and-error method for optimal tradable credit schemes: The network case. Journal of Advanced Transportation (in press).

Available information: observed flow; revealed credit price.

The revealed credit price signalizes the necessity for an upward or downward adjustment of the total amount of credits to be issued in a subsequent implementation period.

The observed road flow can be utilized to adjust cred charge.

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Impacts of Transaction costs

Nie, Y., 2012. Transaction costs and tradable mobility credits. Transportation Research Part B 46 (1), 189-203.

In the absence of transaction cost, traffic equilibrium and market equilibrium are independent of initial credit allocations.

Nie (2012) incorporated transaction costs into the tradable credit scheme and model set up by Yang and Wang (2011)

Looked into the impacts of transaction costs on traffic and market equilibrium and the system efficiency.

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Income Effects

Wu, D., Yin, Y., Lawphongpanich, S., Yang, H., 2012. Design of more equitable congestion pricing and tradable credit schemes for multimodal transportation networks. Transportation Research Part B 46 (9), 1273-1287.

The initial endowment of travel credits as part of traveler’s income (measured by the market value of the credits or the number of credits allocated to each traveler multiplied by their market price).

Incorporated income effects into the analysis, modeling and evaluation of the tradable credit scheme within the framework of multimodal transportation networks.

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Impacts of User Heterogeneity

Wang, X., Yang, H., Zhu, D., Li, C., 2012. Tradable travel credits for congestion management with heterogeneous users. Transportation Research Part E 48 (2), 426-437.

Zhu, D., Yang, H., Li, C., Wang, X., 2013. Properties of the multiclass traffic network equilibria under a tradable credit scheme. Transportation Science (revised version under review).

Heterogeneous users with discrete or continuous value of travel time distribution.

Credits freely traded not only among travelers on different paths and origin-destination pairs, but also among travelers with different incomes or values of travel time.

PDF f τbg

VOT τ0

Value of travel time distribution

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Managing Bottleneck Congestion with a new Tradable Credit Scheme

Nie, Y., Yin, Y., 2013. Managing rush hour travel choices with tradable credit scheme. Transportation Research Part B 50, 1-19.

No commuter is entitled to receive credits through an allocation process; rather they have to earn the credits by traveling outside of a peak time window specified by the government agency.

Commuters can also earn credits by switching to an alternative uncongested route/mode.

Time-dependent credit charge during the peak time window.

0

1r

2r

AN

s

1t 2t 3t

ANδ β

Cumulative

*t Time

CumulativeArrival

CumulativeDeparture

Origin Destination

Vickrey’s bottleneck model

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Managing Bottleneck Congestion and Mode Choice

Tian. L.J., Yang, H., Huang H.J., 2013. Tradable credit schemes for managing bottleneck congestion and modal split with heterogeneous users. Transportation Research Part E 54, 1–13.

Xiao, F., Qian, Z., Zhang, H.M., 2013. Managing bottleneck congestion with tradable credits. Transportation Research Part B (revised version submitted).

Tradable travel credit scheme for managing bottleneck congestion and modal split in a competitive highway/transit network.

Pareto-improving system optimum can be achieved to make all commuters better off.

Origin Destination

Transit mode

Highway

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Day-to-Day Evolution of Credit Price and Traffic Flows

Ye, H., Yang, H., 2013. Day-to-day price and flow dynamics of tradable mobility credits. Transportation Research Part B (in press).

How the traffic flow and credit price will impact each other and evolve together.

Travelers’ learning behavior of route choice based on their perceived path travel cost and credit price and cost.

Price adjustment rule according to the fluctuation of credit demand and supply.

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Mixed Equilibrium Behaviors

He, F., Yin, Y., Shirmohammadi, N., Nie, Y., 2013. Tradable credit schemes on networks with mixed equilibrium behaviors. Transportation Research Part B (submitted).

Deal with not only individual travelers (Wardrop-equilibrium players) but also transportation firms, such as logistic companies and transit agencies Cournot-Nash players.

In the absence of transaction costs, anonymous credit schemes can be designed to decentralize the system optimum flow link pattern.

Transaction costs affect the trading and route-choice behaviors of both Cournot-Nash and Wardrop-equilibrium players.

Transaction costs may reduce the efficiency of those optimal credit schemes.

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Design Issue

Wang, G., Gao, Z., Xu, M., Sun, H., 2013. Models and a relaxation algorithm for continuous network design problem with a tradable credit scheme and equity constraints. Computers and Operations Research (in press)

Incorporate a tradable credit scheme into network design problems

Incorporate equity constraints for travelers travelling from different origins to different destinations.

Bi-level programing model and solution algorithm.

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Summary

Tradable credit scheme plays essentially the same role as road pricing in the regulation of congestion and environmental externalities, but addresses the social and political concerns of congestion charges:

Guarantee a predefined quantitative target to be attained;

Avoid unfairness and thus enhance political acceptability;

Make everyone better off and make less uneven income distribution through free credit allocation and trading;

Revenue-neutral. Tradable credit scheme thus offers the best

combination of cost-effectiveness, administrative flexibility and distributional fairness !