A presentation conducted by Dr Shuaian Wang, School of Mathematics and Applied Statistics, University of Wollongong. Presented on Tuesday the 1st of October 2013 Sydney Harbour Bridge is a key transport infrastructure that connects North Sydney and Sydney Central Business District (CBD). To alleviate the congestion on Sydney Harbour Bridge, NSW Roads and Maritime Services imposes a time of day tolling between $2.5 and $4 on the southbound traffic to Sydney CBD. This study develops mathematical models for formulating the toll pricing problem on Sydney Harbour Bridge considering that different travellers may have different value-of-times (VOTs). The models examine quantitatively the effect of different toll levels on the efficiency (in terms of the total generalized travel time and generalized travel cost of all travellers) and equity (in terms of the ratio of generalized travel cost among different traveller classes). The proposed models can serve as a useful decision-support tool for NSW Roads and Maritime Services.

1. ENDORSING PARTNERS
Efficiency and equity
analysis of toll pricing on Sydney
Harbour Bridge with
heterogeneous travellers
www.isngi.org
The following are confirmed contributors to the business and policy dialogue in Sydney:
•
Rick Sawers (National Australia Bank)
•
Nick Greiner (Chairman (Infrastructure NSW)
Monday, 30th September 2013: Business & policy Dialogue
Tuesday 1 October to Thursday, 3rd October: Academic and Policy
Dialogue
Presented by: Dr Shuaian Wang, School of Mathematics and Applied
Statistics , University of Wollongong
www.isngi.org

2. Congestion Pricing:
Theory and Practice
Dr. Shuaian Wang
School of Mathematics and Applied Statistics
University of Wollongong
shuaian@uow.edu.au
Dr. Michelle Dunbar, Dr. Mark Harrison
SMART Infrastructure Facility, University of Wollongong

3. About my research
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Container liner shipping
Port operations
Intermodal freight transportation
Public transportation
Congestion pricing
Highway operations
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4. Outline
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Theory of transport network modeling
Theory of congestion pricing
Congestion pricing practice
Research problems with toll pricing at Sydney
Harbour Bridge
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7. How to alleviate congestion
• Aims to balance the travel demand and supply
• Approach 1: Increase supply (e.g. road
construction)
• Approach 2: Reduce demand (e.g. provide
public transport services)
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8. Advantage of public transport
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9. Approach 3: Manage demand:
Congestion Pricing
• Rationale of Using Congestion Pricing
– Demand managing: to adjust travel behaviors
– Public transport usage
– invest toll revenue into public transport
infrastructures
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10. Theory of transport
network modeling

11. A Two-Link Example
• How many people will travel on road a, and how
many travel on road b?
Road a, travel time = Number of travellers / 10
1
10 cars travel
from 1 to 2
2
Road b, travel time = 1
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12. User Equilibrium (UE) Traffic
Assignment
• UE: No traveler can improve her travel time by
unilaterally changing routes
– Travelers are “selfish”
– All the used routes have the same travel time. The
travel time of unused routes is not shorter than that
of the used routes.
– This is what happens in practice.
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13. User Equilibrium (UE) Traffic
Assignment
• All travelers travel on road a.
• The total travel time of all road users is 10
Road a, travel time = Number of travellers / 10
1
10 cars travel
from 1 to 2
2
Road b, travel time = 1
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14. System Optimal (SO) Traffic Assignment
• SO traffic assignment: Determine the flow of
road users in the transportation network, so as to
minimize total travel time of all road users.
– This is the target of transport authority
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15. System Optimal (SO) Traffic Assignment
• The transport authority hopes that 5 people
travel on road a, and 5 on road b.
• The total travel time would be 5*0.5+5*1=7.5
Road a, travel time = Number of travellers / 10
1
10 cars travel
from 1 to 2
2
Road b, travel time = 1
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16. UE v.s. SO
• The total travel time, 7.5 time units, under SO
traffic assignment, is 25% shorter than that (10
time units) under UE traffic assignment.
• The transportation network is not efficient
because road users are selfish.
• The transport authority needs to take measures
to improve the efficiency. One of the tools is
congestion pricing.
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17. Theory of congestion
pricing

18. Value of Time (VOT)
• Untolled urban roads: Travel time is 30 min
• Tolled highway: Travel time is 25 min, but $5
must be paid to access the roads.
• VOT transfers time unit to monetary unit. For
higher income population groups, the VOT is
generally higher.
• Unit of VOT: $/min
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19. Road Pricing/Congestion Pricing
• Suppose that the VOT of road users is $1/min. A
toll of $0.5 is imposed on road a.
• How would users choose their paths?
Road a, travel time = Number of travellers / 10, toll = $0.5
1
10 cars travel
from 1 to 2
2
Road b, travel time = 1
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20. Road Pricing/Congestion Pricing
• Users still choose their paths in the selfish manner (UE).
• Both roads a and b have 5 users (0.5 min + $0.5, or 1
min).
• The total travel time is reduced from 10 to 7.5
Road a, travel time = Number of travellers / 10, toll = $0.5
1
10 cars travel
from 1 to 2
Road b, travel time = 1
2
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21. Practice of congestion
pricing

22. 1st Best Pricing
• All links (roads) are tolled.
• It has been proven that the SO state can be achieved.
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23. 1st Best Pricing
• Resistance from commonwealth.
• Expensive to setup: one toll gantry may cost A$1 million.
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24. 2nd Best Pricing
• A subset of links (roads) are tolled
• Minimize the total travel time.
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25. 2nd Best Pricing-toll roads in NSW
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26. 2nd Best Pricing (Cordon-based pricing)
London
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27. Electronic Road Pricing in Singapore
(1998-)
1. Gantry
2. In-vehicle Unit
3. Central Computer System
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28. Congestion Pricing Schemes
in North Europe
Trondheim, Norway
Stockholm, Sweden
A trial in 2006
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29. Congestion pricing at
Sydney Harbour Bridge

30. Congestion pricing at Sydney
Harbour Bridge
• Traffic relocation effect
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31. Congestion pricing at Sydney
Harbour Bridge
• Demand management
– When the travel time/cost is too high, some people cancel their
trips
Trip to ISNGI
Travel time = 20 × Number of travellers
Value of time = $1/min
$100
Trip to have a hair cut
$45
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32. Congestion pricing at Sydney
Harbour Bridge
Total social benefit: $65
Trip to ISNGI
Benefit
$60
Travel time = 20 × Number of travellers
Value of time = $1/min
No toll,
Two persons
travel and
travel time = 40
Benefit $5
Trip to have a hair cut
$40
$40
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33. Congestion pricing at Sydney
Harbour Bridge
Total social benefit: $80
Trip to ISNGI
$30
Benefit
Toll collected by the
government, which can
be invested to public
transport infrastructure
$50
Travel time = 20 × Number of travellers
Value of time = $1/min
Toll = $30,
One person
travels and
travel time = 20
$50
$45
Cancel the
trip; Benefit
$0
Trip to have a hair cut
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34. Congestion pricing at Sydney
Harbour Bridge
• Heterogeneous travelers in terms of value of time
Source: Australian Bureau of Statistics
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35. Congestion pricing at Sydney
Harbour Bridge
• Other factors
– Rush issue
– Mood
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36. References
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Wang, S., Harrison, M., Dunbar, M., 2013. Toll pricing with elastic demand and
heterogeneous users, working paper.
Wang, S., Meng, Q., Yang, H., 2013. Global optimization methods for the discrete
network design problem. Transportation Research Part B, Vol. 50, pp. 42–60.
Liu, Z., Meng, Q., Wang, S., 2013. Speed-based toll design for cordon-based congestion
pricing scheme. Transportation Research Part C, Vol. 31, pp. 83–98.
Meng, Q., Liu, Z., Wang, S., 2012. Optimal distance tolls under congestion pricing and
continuously distributed value of time. Transportation Research Part E, Vol. 48, No. 5, pp.
937–957.
Liu, Z., Wang, S., Meng, Q., 2013. Toll pricing framework under logit-based stochastic
user equilibrium constraints. Journal of Advanced Transportation, accepted on 16
September 2013.
Liu, Z., Meng, Q., Wang, S., 2013. Variational inequality model for cordon-based
congestion pricing under side constrained stochastic user equilibrium conditions.
Transportmetrica A, doi: 10.1080/23249935.2013.821228.
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