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Slide1: 

Challenges of road pricing CWI in bedrijf Amsterdam, 16 November 2006 Frank Kelly www.statslab.cam.ac.uk/~frank/TALKS

Slide2: 

History Background trends Technology - components, systems, privacy Network modelling issues

Delay and congestion: 

Delay and congestion Delay D(y) in terms of flow y along a link.

History : 

History Pigou, Knight 1920s Wardrop, Beckmann 1950s Vickrey, Walter 1960s Smeed Report, MoT 1964 Road Pricing: The Economic and Technical Possibilities

History : 

History Pigou, Knight 1920s Wardrop, Beckmann 1950s Vickrey, Walter 1960s Smeed Report, MoT 1964 Road Pricing: The Economic and Technical Possibilities Transport White Paper, 1966: “Road pricing – a metering system to charge directly for the use of congested roads – is from the economic point of view, the most obvious solution to this problem”

Vickrey: Washington (1959) and UK (1960s): 

Vickrey: Washington (1959) and UK (1960s) Vickrey not only argued the case for a system of differential prices for roads but provided the details of equipment needed to implement it. … He described the in-vehicle unit as a “a self-contained, passive response block which will provide a unique signal identifying any object moving on the ground to which it is attached”. The “response blocks” were to be identified by in-pavement equipment he called “electronic interrogators.” The data would be transmitted to a computer which would calculate the charges and make up bills to be sent to vehicle owners. The peak period charges envisioned by Vickrey were about $1 to $2 per trip. The total cost of the equipment for doing road pricing in the Washington metro area was estimated to be about $60 million. Reference: Congestion pricing originators www.tollroadsnews.com/cgi-bin/a.cgi/RoiIIAHLEdies9Gna6dvrA

Slide7: 

History Background trends Technology - components, systems, privacy Network modelling issues

TRAVEL TIME BUDGET: GLOBAL DATA: 

TRAVEL TIME BUDGET: GLOBAL DATA Reference: Schafer and Victor (2000) The future mobility of the world population, Transportation Research A34(3), 171-205.

TRAVEL MONEY BUDGET: 16 COUNTRIES: 

TRAVEL MONEY BUDGET: 16 COUNTRIES Reference: Schafer and Victor (2000) The future mobility of the world population, Transportation Research A34(3), 171-205.

Modes of transport: 

Modes of transport Reference: The evolution of transport J. H. Ausubel and C. Marchetti phe.rockefeller.edu/TIP_transport/transport.pdf

Slide11: 

Reference: Quality of Life Counts: Indicators for a strategy for sustainable development for the United Kingdom, 2004 Update, Indicator T4 www.sustainabledevelopment.gov.uk/sustainable/quality04/maind/pdf/qolc2004.pdf

Slide12: 

Reference: Commission for Integrated Transport Report: Paying for Road Use, page 20 www.cfit.gov.uk/reports/pfru/pdf/pfru.pdf

Slide13: 

Reference: Institute for Transport Studies, University of Leeds, “Surface Transport Costs and Charges: Great Britain 1998”, page 45 www.its.leeds.ac.uk/projects/STCC/downloads/SurfaceTransportCostsReport.pdf

Slide14: 

Reference: DfT Road Pricing Feasibility Study, Annex B - Modelling Results and Analysis; Figure B1 www.dft.gov.uk/stellent/groups/dft_roads/documents/page/dft_roads_029735.pdf

Feasibility study of road pricing: 

Feasibility study of road pricing “Forecasts using the National Transport Model suggest that a well-targeted national road pricing scheme has the potential to achieve £10 billion worth of time savings a year (at 2010 traffic levels) in Great Britain alone.” Reference: Feasibility study of road pricing in the UK, July 2004, DfT www.dft.gov.uk/stellent/groups/dft_roads/documents/divisionhomepage/029709.hcsp

Feasibility study of road pricing: 

Feasibility study of road pricing “Forecasts using the National Transport Model suggest that a well-targeted national road pricing scheme has the potential to achieve £10 billion worth of time savings a year (at 2010 traffic levels) in Great Britain alone.” “It would cost a lot to introduce a national road pricing scheme. As well as the costs of setting it up, there are the costs of enforcement and the back-office systems handling payments and enquiries, as well as compliance costs for industry.... The system could cost as much as £3 billion a year to run.” Reference: Feasibility study of road pricing in the UK, July 2004, DfT www.dft.gov.uk/stellent/groups/dft_roads/documents/divisionhomepage/029709.hcsp

Slide17: 

History Background trends Technology - components, systems, privacy Network modelling issues

London Congestion Charge: 

London Congestion Charge www.cclondon.com You can pay your congestion charge: Online At selected shops, petrol stations and car parks By post By telephone By SMS text message from your mobile phone At BT Internet kiosks Prices: self-declaration - by 10pm £8 10pm-midnight £10 camera,… - 14 days £50 14-28 days £100 later £150, ….

Stockholm Congestion Tax: 

Stockholm Congestion Tax 18 control points located at Stockholm city entrances and exits. Vehicles registered automatically by cameras that photograph the number plates. Those vehicles equipped with an electronic onboard unit for direct debit payment are also identified through this means. Vehicles are registered when driving both into and out of the inner city zone. Payment must be made within 14 days of passage. Paying the tax is the responsibility of the vehicle owner, and not the driver. No invoice or payment slip is sent out. www.stockholmsforsoket.se

Slide20: 

Pay as you drive insurance Norwich Union’s personalised tariffs Example: night time (11pm to 5.59am) - £1 per mile day time (6am to 10.59pm) -4p per mile www.payasyoudriveinsurance.co.uk/benefits.htm

Privacy: 

Privacy Our attitudes are evolving rapidly GPS Locator FOR CHILDREN Comes in two colors: Galactic Blue and Cosmic Purple

Slide22: 

History Background trends Technology - components, systems, privacy Network modelling issues

Parallel roads: 

Parallel roads The toll on one road is T; a parallel road is untolled. The total traffic on both roads is 1 (and is unaffected by the toll T ). The delay on each road is a function D(x) of the traffic x on that road, the same function for each road. Each user has a value of time, v, chosen at random from a distribution with density f(v), v > 0, and distribution function F(v). A user will choose the toll road if her value for time is greater than a critical value v*, the solution to the equation T = [D(F(v*)) - D(1-F(v*))] v* tolled untolled

Parallel and series roads: 

Parallel and series roads Would a revenue maximizing operator of the tolled road charge too much, or too little, in comparison with the system optimum charge? The answer can go either way. (Possibility of hierarchical mechanism design.) tolled untolled untolled

Partial tolling in a network: 

Partial tolling in a network If all values for time are identical, and if all roads can be tolled, then charging the marginal social cost will maximize welfare. The toll on a road is then a local calculation, unaffected by network topology or traffic patterns. But we need more! In presence of heterogeneity of time values and partial tolling, both network topology and traffic patterns matter.

Who travels where?: 

Who travels where? Known row and column totals Known trip length distributions ? Origin-Destination matrix

How do people choose modes?: 

How do people choose modes? Known time and money costs Known demands BUT un-measurable preferences for comfort, security, and privacy

Land use and transport interaction : 

Land use and transport interaction Map of Cambridge and surrounds showing times of departure to reach the West Cambridge site by 9 o'clock on a weekday morning www.dft.gov.uk/stellent/groups/dft_science/documents/page/dft_science_611659.hcsp

Land use and transport interaction : 

Land use and transport interaction Highly path dependent and non-convex. Land values, Disneyland etc www.mysociety.org/2006/travel-time-maps

Discussion : 

Discussion

Network structure: 

Network structure

Notation: 

Notation - set of links - set of routes - link j is on route r - set of source-destination pairs route r serves s-d pair s flow rate on route r - flow through link j delay on link j flow between s-d pair s

Wardrop equilibrium : 

Wardrop equilibrium x is a Wardrop equilibrium if for every pair of routes, r, r’, serving the same s-d pair If a route r is actively used, then it achieves the minimum delay over all routes serving its s-d pair s(r). Wardrop, 1952.

Optimization formulation : 

subject to minimize Optimization formulation A Wardrop equilibrium solves the problem: over Beckmann, McGuire and Winsten, 1956

Slide35: 

Let Then Thus L minimized when

Slide36: 

Let Then Thus L minimized when minimum delay over routes serving s(r)

Preferred optimization formulation : 

subject to minimize Preferred optimization formulation over Minimum occurs when

Preferred optimization formulation : 

subject to minimize Preferred optimization formulation over Minimum occurs when traffic dependent toll on link j

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