1. Models of Network Growth
David Levinson

2. Acknowledgements Funding Sources Research Assistants Wei Chen
Minnesota Department of Transportation “If They Come, Will You Build It?”
Minnesota Department of Transportation “Beyond Business as Usual: Ensuring the Network We Want Is The Network We Get”
University of Minnesota Department of Civil Engineering Sommerfeld Fellowship Program
Hubert Humphrey Institute of Public Affairs Sustainable Transportation Applied Research Initiative/ University of Minnesota ITS Institute/ U.S. DOT
NSF CAREER Award
Digital Media Center: Technology Enhanced Learning Grant
Research Assistants
Wei Chen
Wenling Chen
Ramachandra Karamalaputi
Norah Montes de Oca
Pavithra Parthasarathi
Feng Xie
Bhanu Yerra
(Dr.) Lei Zhang
Shanjiang Zhu

3. Questions Why do networks expand and contract?
Do networks self-organize into hierarchies?
Are roads an emergent property?
Can investment rules predict location of network expansions and contractions?
How can this improved knowledge help in planning transportation networks?

4. Objectives Model the rise and fall of transportation networks
Study the interdependence of road supply and travel demand at the microscopic level
Demonstrate the model on the Twin Cities transportation network
Apply the model to evaluate alternative transportation investment and pricing policies
Use the model in the classroom

5. Macroscopic View

6. If They Come, Will You Build It?

7. Agent-Based Modeling Agents can be: Links, Nodes, Travelers, Land
“An agent is an encapsulated computer system that is situated in some environment and that is capable of flexible, autonomous action in that environment in order to meet its design objectives” - Nikolic
Agents can be: Links, Nodes, Travelers, Land
Agent properties
Rules of interaction that determine the state of agents in the next time step
Spatial pattern of interaction between agents
External forces and variables
Initial states

8. Layered Models System is split into two layers Network layer
Land use layer
Network is modeled as a directed graph
Land use layer has small land blocks as agents that represent the population and land use

9. Flowchart of the simulation model
Scope
Exogenous:
economic growth
land use dynamics
Endogenous:
travel behavior/ demand
link maintenance and expansion costs
network revenue (pricing)
investment
induced supply
induced demand

10. Network Ideal Chinese Plan Grid network Finite Planar Grid
Cylindrical network
Torus network
Modified (Interrupted) Grid
Realistic Networks (Twin Cities)
Initial speed distribution
Every link with same initial speed
Uniformly distributed speeds
Actual network speeds
Ideal Chinese Plan

11. Land Use & Demography Small land blocks
Population, business activity, and geographical features are attributes
Uniformly and bell-shaped distributed land use are modeled
Actual Twin Cities land use is also tested
Land use is assumed exogenous (future research aimed at testing endogenous land use)
MohenjoDaro background

12. Trip Generation
Using land use model trips produced and attracted are calculated for each cell
Cells are assigned to network nodes using voronoi diagram
Trips produced and attracted are calculated for a network node using voronoi diagram

13. Trip Distribution Calculates trips between network nodes Where:
Trs is trips from origin node r to destination node s,
pr is trips produced from node r,
qs is trips attracted to node s,
drs is cost of travel between nodes r and s along shortest path
w is “friction factor”
Calculates trips between network nodes
Gravity model
Working on agent-based trip distribution

14. Route Choice
Flow on a link is
Where
a,rs = 1 if a  Krs, 0 otherwise
Krs is a set of links along the shortest path from node r to node s,
Wardrop’s User Equilibrium Principle, travelers choose path with least generalized cost of traveling (s.t. all other travelers also choosing the least cost path)
Cases
No Congestion
Dijkstras Algorithm
With Congestion
Origin Based Assignment (Boyce & Bar-Gera)
Stochastic User Equilibrium (Dial)
Agent-based Assignment (Zhang and Levinson, Zhu and Levinson)

15. Link-Performance Function
Generalized link travel cost function
la is length of link
va is speed of link a
l is value of time
ta is “toll”
q1, q2 are coefficients
In No Congestion Case, q1 =0
VOT•BPR travel time + Toll

16. Revenue And Cost Models
Toll is the only source of revenue
Annual revenue generated by a link is total toll paid by the travelers
Initially assume only one type of cost, function of length, flow, link speed

17. Network Investment Model (1)
A link based model
Speed of a link improves if revenue is more than cost of maintenance, drops otherwise
Where:
vat is speed of link a at time step t,
b is speed reduction coefficient.
No revenue sharing between links: Revenue from a link is used in its own investment

18. Initial Assumptions Base case Network - speed ~ U(1, 1)
Land use ~ U(10, 10)
Friction factor w=0.01
Travel cost, Revenue da {l = 1.0, o = 1.0, 1 = 1.0, 2 = 0.0}
Infrastructure Cost {m =365, 1 = 1.0, 2 = 0.75, 3 = 0.75}
Investment model {  = 1.0}
Speeds on links running in opposite direction between same nodes are averaged

19. Equilibrium network state after 9 iterations
Case 1: Base 15x15
Initial network
Equilibrium network state after 9 iterations
Slow
Fast
Figure 5 Equilibrium speed distribution for the base case on a 15x15 grid network

20. Case 2: Same as base case but initial speeds ~ U(1, 5)
Initial network
Equilibrium network state after 8 iterations
Slow
Fast
Figure 7 Equilibrium speed distribution for case 2 on a 15x15 grid network

21. Case 3: Base case with a downtown
Initial network
Equilibrium network state after 7 iterations
Slow
Fast
Figure 9 Equilibrium speed distribution for case 3 on a 15x15 grid network

22. Case 5: 50x50 Network

23. Case 6: A River Runs Through It

24. Case 7: Self-Fulfilling Investments
Invest in what is normally (base case) lowest volume links.
Results in that being highest volume link.
Decisions do matter: Can use investment to direct outcome.

25. Four Twin Cities Experiments
Value of time = $10/hr - MnDOT Value
Link performance function 1 = 0.15; 2 =4 - BPR Function
Friction factor =0.1 - Empirical
Revenue Model {1 = 1.0, 2 = 1.0, 3 = 0.75}
Infrastructure Cost { =365, 1 =20, 2 = 1, 3 = 1.25} -CRS in link length, DRS in speed
Coefficient in speed-capacity regression model (1 = -30.6, 2=9.8) - Empirical
Improvement model {  = 0.75} DRS in link expansion
CRS, DRS, IRS = Constant, Decreasing, Increasing Returns to Scale

26. Results Experiment 1: predicted 1998 network

27. Forecasting Investment Decisions
Build empirically-based network growth prediction models that address the questions:
Will “business as usual” network construction decision rules produce desirable networks?
Will new decision rules produce improved networks?
Should policies be changed to direct future network growth in a better direction?
Should policies be changed to produce networks that will generate the best performance measures?
Results would let decision makers see how current investment decision rules impact or limit future choices.

28. Processes * Structured process * Ranking system
through point allocation
* Task forces-committees
Formal
Processes
* Priorities
safety,preservation, capacity,
social and economic impacts,
community and agency involvement
Benefit/cost ratio, etc.
* No Ranking System
Informal

29. Informal Processes Jurisdictions priorities and decision making:
“ benefit/cost ratio > 1”
“ AADT > 15,000 on 3-lane roadways” (safety reasons)
“ Intersection volumes exceed 7,500 vehicles per day”
“Implementation of policy, strategy and investment level”
“Project development time”
“Most beneficial project for the system”
“Matching funds from local jurisdictions”

30. Formal Processes

31. Flowcharts-Informal processes
Roadways under
County’s jurisdiction
Scott County
Project
solicitation
Application
review
Average Daily
Traffic (ADT)
Safety
yes
ADT>15,000
3 lane-roads
Project in
top 200
high crash
location list no
yes
yes no
Reapplication?
Project approval no no
End
yes
Project
construction

32. Flowcharts - Formal Processes - City
Minneapolis streets
Project solicitation
Application review
Compute scores
Highest scored project selection
yes
Allocation of funding availability
Reapplication?
Project approval no no
End
yes
City of Minneapolis
Project
construction

33. Coded Decision Rules
1. Flowcharts that describe the decision-making process of jurisdictions with regard to road investment
2. Coded if-then rules of each jurisdiction
3. Rules of continuous scores that ensure a project gets a unique score from a jurisdiction
Example:
//ORIGINAL RULE:if(AADT>30000)juris_score[1][i]+=50;
//if(AADT >20000)juris_score[1][i]+=38;
//else if (AADT >10000)juris_score[1][i]+=25;
if(adt>30000)juris_score[1][i]+=Math.min(50,38+(50-38)*(AADT )/( ));
else if(adt>20000)juris_score[1][i]+=25+(38-25)*(AADT )/( );
else if (adt>10000)juris_score[1][i]+=0+(25-0)*(AADT )/( );

34. State Expansion
2005
2010
2015

35. To Add: Constraints * Environmental restrictions (wetland areas)
* Right of way

36. To Add: Legacy Links
Road segments that were planned in the 1960s and have not been built.
Fundamental for the State Budget New Construction Plans

37. SONG 1.0: Simulator of Network Growth Interface
Visualized
Graphic
Parameter panel
Snapshot
Three parts
Output Panel

38. Simulator In The Classroom
Simulator in Education
SONG 1.0 as a learning tool
Soft simulation
Simplification of the reality: a conceptual tool
Natural tool for learning the network growth process
To learn judgment skills not facts
Softer skills instead of hard skills
Objectives
Stimulate new ways of thinking
Help students understand principles of network development
Help students develop judgment skills in investment decision making
Increasingly, simulation has been applied into classroom as an educational tool. “a simulation is a software package that re-creates or simulates, a complex phenomena, environment, or experience, providing the user with the opportunity for some new level of understanding.” --Kurt Schumaker
simulation let students make mistakes and learn directly from the outcomes of their own actions. (Billhardts, 2004)
Use the new conceptual tool to develop heuristics and qualitative tool to help student think about decentralized systems in new ways. The hope is to help people move beyond the centralized mindset. The best way to develop better intuitions about decentralized systems is to construct and play with such systems (Resnick, 1997)
It is worth to notice that SONG 1.0 shows a different kind of simulation, called “soft simulation”, which “provides qualitative understanding of a complex system by constructing a simple one that shares the same principle (Papert, 1992).” By developing the simulator, the focus is not on perfect reproductions of the real world, but rather to help people explore the “microworld” of transportation network and to stimulate new ways of thinking about the transportation network growth process.
SONG 1.0 makes a natural tool for learning network growth because (1) topics that are best taught through simulations areas where judgment skills, not facts are being taught in general, (2) the softer the skill being taught, the more open-ended and complex a simulation will need to be.
Also note:
effective in modeling complex financial or economic behavior, e.g., a simulation on how to invest one’s funds and observe the outcome of one’s investment over the course of a lifetime would be effective learning experience. (Billhardts, 2004)

39. Conclusions
Succeeded in growing transportation networks (Proof of concept)
Sufficiency of simple link based revenue and investment rules in mimicking a hierarchical network structure
Hierarchical structure of transportation networks is a property not entirely a design
Policy can drive shape of hierarchy
Model scales to metropolitan area (Application of concept)
Derivation of stated decision rules
Ability to use model in classroom

40. Yerra, Bhanu and Levinson, D
Yerra, Bhanu and Levinson, D. (2005) The Emergence of Hierarchy in Transportation Networks. Annals of Regional Science 39 (3)
Zhang , Lei and David Levinson (2005) Road Pricing on Autonomous Links Journal of the Transportation Research Board (in press).
Levinson, David and Bhanu Yerra (2005) Self Organization of Surface Transportation Networks Transportation Science (in press)
Chen, Wenling and David Levinson (2006) Effectiveness of Learning Transportation Network Growth Through Simulation. ASCE Journal of Professional Issues in Engineering Education and PracticeVol. 132, No. 1, January 1, 2006
Zhang , Lei and David Levinson. (2004a) An Agent-Based Approach to Travel Demand Modeling: An Exploratory Analysis Transportation Research Record: Journal of the Transportation Research Board #1898 pp
Levinson, D. and Karamalaputi, Ramachandra (2003) Predicting the Construction of New Highway Links. Journal of Transportation and Statistics Vol. 6(2/3) 81-89
Levinson, D and Karamalaputi, R (2003), Induced Supply: A Model of Highway Network Expansion at the Microscopic Level Journal of Transport Economics and Policy, Volume 37, Part 3, September 2003, pp
Parthasarathi, P, Levinson, D., and Karamalaputi, Ramachandra (2003) Induced Demand: A Microscopic Perspective Urban Studies Volume 40, Number 7 June 2003 pp
Zhang, Lei David M. Levinson (2005) Pricing, Investment, and Network Equilibrium ( ) presented at 84th Annual Meeting of Transportation Research Board in Washington, DC, January 9-13th 2005.
Zhang, Lei , David M. Levinson (2005) Investing for Robustness and Reliability in Transportation Networks ( ) presented at 84th Annual Meeting of Transportation Research Board in Washington, DC, January 9-13th 2005 and presented at 2nd International Conference on Transportation Network Reliability. Christchurch, New Zealand August 20-22, 2004.
Levinson, D, and Wei Chen (2004) Area Based Models of New Highway Route Growth presented at 2004 World Conference on Transport Research, Istanbul
Levinson, D. (2003) The Evolution of Transport Networks. Chapter 11 (pp ) ﾊin Handbook 6: Transport Strategy, Policy and Institutions (David Hensher, ed.) Elsevier, Oxford
Xie, Feng and David Levinson (2005) The Decline of Over-invested Transportation Networks
Research Papers
Xie, Feng and David Levinson (2005) Measuring the Topology of Road Networks
Xie, Feng and David Levinson (2005) The Topological Evolution of Road Networks
Montes de Oca, Norah and David Levinson (2005) Network Expansion Decision-making in the Twin Cities
Levinson, David and Bhanu Yerra (2005) How Land Use Shapes the Evolution of Road Networks
Levinson, David and Wei Chen (2005) Paving New Ground: A Markov Chain Model of the Change in Transportation Networks and Land Use
Zhang, Lei and David Levinson (2005) The Economics of Transportation Network Growth

41. ¿Questions? ?

42. Future Work  Consider substitution effects in a hyper-network
 A systematic way to adjust cost and revenue functions based on
area-specific factors such as type of roads, land value, and public
acceptance should be considered
 Additional land use and socio-economic data must be collected to
calibrate and validate coefficients in the proposed model
 Evaluate alternative investment and pricing polices on a realistic network
 Consider substitution effects in a hyper-network
 Models for addition of new roads and nodes to an existing network
are currently under development
 Make the model available online for educational purposes

43. Future Work (cont.)
 An agent-based travel demand model is needed to make the model
inherently consistent and capable of evaluating a broader spectrum of policies, such as those related to travel behavior

44. Future Work (cont. 1)
An exploratory agent-based travel demand model has been developed
 Running time does not increase exponentially as the network size increases
 Travelers find their destinations and routes based on searching, information exchange with other agents, and learning
 No aggregate trip distribution or traffic assignment in the model and only one coefficient needs to be calibrated
 The model was successfully applied to the Chicago Sketch network with 933 nodes and 2950 links; travelers identify more than 98% of shortest routes based on decentralized learning

45. Future Work (cont. 2)
Chicago sketch network: trip length distribution
 However, the agent-based demand model does not consider congestion effects
 The model needs to be improved and incorporated to the broader network dynamics model

46. Empirical Models
Change in infrastructure supply in response to increasing demand has been largely unstudied
To what extent do changes in travel demand, population, income and demographic drive changes in supply?
Transportation supply varies in the long run but inelastic in the short run
Can we model and predict the spatially specific decisions on infrastructure improvements?

47. Growth of VKT Vs. Capacity
120
100 80 60
VKT 40
Lane-km 20
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
Year

48. Theory
Construction or expansion of a link is constrained by the decisions made in past.
Capacity increases often aim to decrease congestion on a link or to divert traffic from a competing route
Some cases in anticipation of economic development of an area.
Finite budget constrains the number of links developed
Supply curve more inelastic with time

49. Supply-Demand Curve Demand Supply Capacity Expenditure B C1 C2 E1 E2

50. Induced Demand & Consumers’ Surplus
Supply Before
Quantity of traffic
Price of Travel Q1 Q2 P1 P2
Supply After

51. Data 1. Network data from Twin Cities Metropolitan Council
2. Average Annual Daily Traffic (AADT) data from Minnesota Department of Transportation: Traffic Information Center
3. Investment data from:
Transportation Improvement Program for the Twin Cities
Hennepin County Capital Budget.
4. Population of MCD’s from Minnesota State Demography Center

52. Adjacent links in a Network
Divided into two categories: supplier links and consumer links
For link 2-5: 1-2, 3-2 are supplier links and 5-7, 5-8 are consumer links 1 2 3 4 5 6 7 8

53. Parallel link in a Network
Bears brunt of traffic if the link were closed
Fuzzy logic using the modified sum composition method
Four attributes defined by:
Para = 1 – (angular difference) / 45
Perp = 1 – a*(perpendicular distance) / length of link
Shift = 1– b*(sum of node distances) / length of link
Comp = 1 – c*(lratio-1)
(a=0.4, b=0.25, c=0.5)

54. Cost Function Eij = f (Lij*∆Cij, N, T, Y, D, X)
Eij = cost to construct or expand the link
Lij*∆Cij = lane miles of construction
N = dummy variable to new construction
T = type of road
Y = year of completion – 1979
D =duration of construction
X = distance from the nearest downtown

55. Hypothesis Cost increases with lane miles added
New construction projects cost more
Cost is proportional to the hierarchy of the road
Cost increases with time
Longer duration projects cost more
Cost is inversely proportional to the distance from the nearest downtown

56. Results of Cost Model

57. Expansion Model: Hypothesis
The following factors favor link expansion:
Congestion on a link
Increase in Vehicle Kilometers Traveled (VKT)
Higher budget for a year
Increase in capacity of downstream or upstream links
Increase in population
The following factors deter link expansion:
High capacity
Length of the link
Parallel link expansion
Cost of expansion

58. Results: Link Expansion

59. Results: Expansion Model
Most of the hypotheses are corroborated
Change in demand favors expansion, consistently
Higher cost decreases probability of expansion while higher budget increases the same
Probability of a two-lane expansion over one-lane expansion declines with time
Lower hierarchy roads depend on budget but not on cost
Interstate links showed significant variation in response to variables length and change in VKT over two years

60. New Construction Assumptions:
Follow different criteria than expanding existing links
Choice made in a network of possible construction sites
Road type of the new link unknown
Modeled in 5-year intervals due to few construction projects
Assumptions:
Interchange is a single node
New construction does not cross any existing higher class road
Can cross lower level roads without intersecting
Links of length between 200m and 3.2 Km only considered

61. New Construction Model
A = Access measure
E= Cost of construction
X = Dist. from downtown
D = number of nodes in the area
ij = link in consideration
p = parallel link
Where:
N = New construction
C = Capacity of the link
L = Length of the link
Q = Flow on the link
Y= Year

62. Hypothesis: New Link Construction
The following factors favor new link construction:
High capacity of parallel link
Congestion on parallel link
Length of parallel link
Higher budget
Higher access score
The following factors deter new link construction:
Cost of expansion
Number of nodes in the area

63. Results of New Construction Models

64. Results: New Construction
Significantly depends on surrounding and alternate route conditions
High capacity parallel link reduces need for a new link
High dependence on the accessibility measure
Highly connected areas require fewer new links
Policy shift from expansion to construction

65. Conclusions
We have illustrated and modeled using both agent based and econometric methods “How Networks Grow”
We can replicate the emergence of hierarchy on road networks without any initial differentiation in land use or network flows.
We can statistically estimate likely links which will be expanded.

66. Implications
Just as we could forecast travel demand, demographics, and land use, we can now forecast network growth.
We can now understand the implications of existing policies (bureaucratic behaviors) on the shape of future networks.
By forecasting future network expansion, we can decide whether or not this is desireable or sustainable outcome, and then act to intervene.

67. On-going And Future Work
Develop agent based travel demand models
Enable revenue sharing between links (account for jurisdictions)
Consider alternative pricing and investment policies
Modeling construction of new links
Modeling network topology as an emergent property in agent models,
Estimating better econometric models using full 80 year database
Obtaining MOE’s from these networks, comparison with “optimal” networks.
Link with land use models such as urbansim
Use of Network Dynamics Model as learning tool in class

68. Normative Applications
Evaluating transportation-related policies
 Investment policies
 Decentralized
 Centralized – VC ratio
 Centralized – BC analysis
 Pricing policies
 Regulated price – f (distance, LOS)
 Regulated price – f (distance)
 Short-run marginal cost pricing
 Marginal cost w/ maintenance cost recovery
 Profit-maximizing
Assumptions
 Closed system: All profits are spent on maintenance or new investment
 Centralized-VC ratio: The most congested link will be expanded such that its VC ratio is reduced to the average of the whole system
 Centralized-BC analysis: Links can be expanded by one or two additional lanes Planning horizon 25 years, annual traffic growth 3%, interest rate 2%
 Profit-maximizing: Links seek for local maximum through quadratic line fitting

69. Measures of Effectiveness
 Vehicle hours traveled
 Vehicle kilometers traveled
 Average network travel speed
 Accessibility
 Consumer surplus
 Total revenue/profit
 Productivity
 Equity
 Network reliability w.r.t. random failure or targeted attack
 Decision flexibility

70. Existing Procedures
Existing methods for evaluating transportation investment and pricing policies
 Equilibrium analysis dominates theoretical studies
 Benefit cost analysis is the most popular practical tool
Problems with existing methods
 Description of transportation network dynamics is incomplete
 Non-local and non-immediate effects are usually ignored
 The equilibration process (if the system is moving to a new equilibrium at all) is not considered
 Theories are hard to be apply to large-scale networks
The simulation model addresses those issues

71. An Example of Normative Applications
1010 Grid network
32 km
 Uniform land use with 1 million total trips
 All links are one-lane with capacity 735 veh/hr
 A very congested network (speed 10 km/h)
 All pricing policies are compared under the same investment rule. (decentralized immediate investment)
 All investment policies are compared under the same pricing rule (regulated price)

72. MOEs By Pricing Policy
Pricing policies - Vehicle Hours Traveled

73. MOEs - 1
Pricing policies – Vehicle Kilometers Traveled

74. MOEs - 2
Pricing policies – Average Network Travel Speed

75. MOEs - 3
Pricing policies – Total Revenue

76. MOEs - 4
Pricing policies – Consumers’ Surplus + Revenue

77. Toll evolution under π-max behavior
Pricing policies – Toll Evolution

78. Demand and profit functions
Demand curve Profit versus toll
Regulation
Profit-Max

79. MOEs By Investment Policies
Investment policies: Speed

80. MOEs - a
Investment policies: Speed after transformation

81. MOEs - b
Investment policies: Consumers’ Surplus + Revenue

82. Conclusions
 A model of the rise and fall of roads is developed and successfully
applied to a large-scale real congesting network
 The process of road development and degeneration at the
microscopic level is analyzed and an agent-based simulation structure
seems to be appropriate for modeling that process
 The simulation model is capable of replicating and predicting transportation network growth
 Hierarchical structure of transportation networks is a property
not entirely a design

83. Conclusions (cont.)
 The simulation model can also evaluate the benefits and costs of transportation investment and pricing policies over time, not just at the equilibrium
 A travel demand model that describe travelers’ behavioral adjustments to new policies in detail is desirable for the proposed simulation approach
 The performance of a transportation infrastructure system in a privatized profit-maximizing environment is explored

84. Acknowledgements
 Sustainable Technologies Applied Research (STAR) TEA-21 Project
 Intelligent Transportation Systems Institute at the
University of Minnesota
 Professor David Boyce and Professor Hillel Bar-Gera for providing
the Origin-Based Traffic Assignment program

85. Additional slides

86. Motivation
 240 km of paved road in the United States in 1900 (Peat 2002)
6,400,000 km by 2000 (BTS 2002)
 How transportation networks grow is one of the least understood areas
in transportation, geography, and regional science
 Network investment decisions are myopic; non-immediate and non-
local effects are ignored in planning practices
 Is network growth simply designed by our planners or it can be indeed
explained by underlying natural and market forces?
 It is important to understand how markets and policies translate into
facilities in transportation systems

87. Key Research Questions
 Why do links expand and contract?
 Do networks self-organize into hierarchies and how?
 Are roads (routes) an emergent property of networks?
 What are the parameters to be calibrated in a microscopic network dynamics model?
 Is the model computationally feasible on a realistic transportation network?
 Is the model capable of replicating real-world network dynamics?

88. Review of Related Research
 Taaffe et al. 1963: initial roads connect activity centers; lateral road surrounds
initial roads; positive feedback between infrastructure supply and population
 Miyao 1981: macroscopic model taking transportation investments as either an
endogenous effects of economy or as an exogenous effects on economy
 Aghion and Howitt 1998: endogenous growth theory; transportation growth
 Grübler 1981: macroscopically, the growth of infrastructure flows a logistic curve
 Miyagi 1998: Spatial Computable General Equilibrium model to study interaction
 Yamins et al. 2003: a highly simplified model of growing urban roads
 Carruthers and Ulfarsson 2001: Demographics and politics affect public service
 Aschauer 1989, Gramlich 1994, Nadiri and Mamuneas 1996, Boarnet 1997
Button 1998: how transportation investment affects the economy at large
 Christaller 1966, Batty and Longley 1985, Krugman 1996, Waddell 2001:
consider land use dynamics allowing central places to emerge but taking network as given
A need for research that makes the network the object of study
Few studies considering network growth at microscopic level

89. Induced Supply and Induced Demand
Capacity
Expenditure C1 C2 E1 E2
 The network growth path may not start from an equilibrium
 An equilibrium may never been achieve when constant economic, land use and population growths are considered
 A simulation model of the network evolution process is appropriate

90. Results – Convergence Properties
 Running time: 20 minutes to
simulate the dynamics of link
expansions and contractions
in a year on P4 1.7Ghz PC
 The network approaches an
equilibrium smoothly
 The Most significant changes
take place during the first
twenty years of the evolution
 A goal of strict equilibrium,
i.e. no expansions/contractions,
is not practical
 The remaining presentation of
simulation results focuses on the
dynamics between 1978 and 1998

91. Proposed Calibration Procedure
A two-stage calibration framework
 Component functions are estimated empirically, which forms a starting solution in the search space
 An improving search algorithm then adjusts the starting solution to minimize the different between the observed data and the predicted link expansions and contractions
 Data requirements: Transportation network, land use, demographical and economical data in an urban area during a long period of time
 Transportation network data in the Twin Cities since 1978 has been collected while the land use data collection work is still on-going

92. Methodology developed to predict both expansion and construction
A model based on measurable attributes
Consistent behavior of fundamental variables on different highways
Significant effect of surrounding conditions
Lower hierarchies of roads depend on budget constraint but not on cost
Consistency of response among links of lower hierarchies
New links construction follow different criteria and has a high taste variance

93. Multinomial Logit Vs. Mixed Logit
According to multinomial logit, the probability that a decision-maker i chooses alternative j is:
Mixed logit allows variation of a coefficient across population
Disentangles Independent and Identically Distributed (IID) from Independence of Irrelevant Alternatives (IIA)

94. Experiments

96. Mixed Logit Algorithm Start Set no. of simulations,N
Determine number of Random parameters and their distributions, M
n = n + 1
n > N?
End
YES NO
Set n=1
Generate 2M Halton sequence numbers based on M prime numbers
Algorithm to Simulate Mixed Logit Model
Convert them into appropriate distributions
Calculate simulated probability and add to previous probability

99. Check Investment Data for lane additions in year T
Start
Set year, T=1978
Check Investment Data for lane additions in year T
Are there any lane additions for year T?
YES NO
T<=1995?
Subtract lanes for years < T
Add lanes for years >=T
T = T + 1
T > 1998?
End
Building the Network

100. Expansion Model C = Capacity L = Length ij = link in consideration
p = parallel link
Q = AADT on the link
E = Cost of expansion
Y = year
X = Distance from downtown
B = Budget Constraint
P = population of MCD

102. Demo

103. Models Required Land use and population model Travel demand model
Revenue model
Cost model
Network investment model

104. Case A - Results

105. Results - Cases B1 & B2

106. Introduction Elements of transportation network dynamics
 Previous research focuses on traffic assignment and management
 How do the existing roads develop and degenerate?
 How are new roads added to the existing network?
 How are new nodes added to the existing network?
Research objectives
 Model the rise and fall of existing roads
 Study the interdependence of road supply and travel demand at
the microscopic level
 Demonstrate the model on the Twin Cities transportation network
 Apply the model to evaluate alternative transportation investment
and pricing policies

107. Equilibrium network state after 8 iterations
Base Case: 10x10
Initial network
Equilibrium network state after 8 iterations
Slow
Fast
Figure 4 Equilibrium speed distribution for the base case on a 10x10 grid network

108. Case 2: Same as base case but initial speeds ~ U(1, 5)
Initial network
Equilibrium network state after 8 iterations
Slow
Fast
Figure 6 Equilibrium speed distribution for case 2 on a 10x10 grid network

109. Case 3: Base case with a downtown
Initial network
Equilibrium network state after 7 iterations
Slow
Fast
Figure 8 Equilibrium speed distribution for case 3 on a 10x10 grid network

110. Case 4: Base case with land use ~ U(10, 15)
Initial network
Equilibrium network
Slow
Fast
Figure 8 Equilibrium speed distribution on a 10x10 grid network

111. Data Merging and Accuracy
AADT on a different network; merged using linear and rotational transformation
MCD population superimposed using GIS
AADT checked using detector data, consistent

112. Two empirical functions
Capacity = g (number of lanes)
Free flow Speed = f (Capacity)

113. Twin Cities Applications
Replicate previous network growth patterns
Predict future network growth
Explore emergent properties of network dynamics e.g. road hierarchy, congestion

114. Observed vs. Predicted Growth
The model successfully predicts construction on several freeways (I-394, 10, I-494, I-35W, 36)
However, it forecasts more expansions on roads already having high capacities (freeways) while fewer expansions on arterials than reality
Either costs of arterial roads are overestimated or costs of freeways are underestimated
Base: observed 1978 network with real capacity
Real growth
Predicted growth
Capacity change: observed base
Capacity change: Experiment base
Capacity change: Experiment base

115. Emergence of Road Hierarchy

116. How Road Hierarchy Emerges
Base: 1978 network with uniform capacity (400veh/h)
Experiment 4 capacity change: predicted base
Real growth
Predicted growth
River
The three downtowns
 Three identifiable reasons
 Natural barriers  Existing Activity centers  Unbalanced demand pattern
Experiment 4 capacity change: predicted base

117. Network Congestion  If link contraction is allowed
(Exp. 1 and 3 ), the level of road
congestion is more evenly distributed in the network
 The link contraction prohibition
(Exp. 2 and 4) makes the prediction more realistic
 Link cost function should be
adjusted to local conditions

118. Methods Observation Agent Based Modeling Econometric Modeling of
(1) Link Expansion and
(2) New Construction

119. How networks change with time
Nodes: Added, Deleted, Expanded, Contracted
Links: Added, Deleted, Expanded, Contracted
Flows: Increase, Decrease

120. Research Objectives
Investigate efficacy of SONG 1.0 as a learning tool
Test the hypothesis that simulator enhances learning on the grounds that:
It provides learners with hands-on experiences
Importance of experiences in learning
Overcome budget and time constraints in getting network growth experiences
“Learning through doing” (Forsyth and McMillan, 1991)
“Do and understand”- a constructionism approach (Johnson et al., 1991, 1998)
Providing interactive learning environment – quick feedback
Diversifying teaching strategies
Accommodate different learning styles and preferences (Cross, 1976; Matthews, 1991; Chism et al., 1989)
Promote intellectual development (Perry, 1970; Kurfiss, 1988; Kolb,1984; Bonham, 1989)
Engaging motivation (Erickson, 1978; Forsyth and McMillan, 1991)

121. Costs
Initially assume only one type of cost, function of length, flow, link speed
A global link maintenance cost (MC) function for all links
MC Length Capacity
Link construction cost (CC) function (continuous or discrete)
CC Length Capacity Δ Capacity

122. Flowchart
The simulation model can be used as a normative or a descriptive tool depending on how investment and pricing rules are specified.

123. East Asian Grids Ideal Chinese Plan Chang-an Nara Kyoto
Nara
Kyoto

124. Other Grids Teotihuacan below Mohenjo-Dara above, Delos below
Plan of Excavated Housing Area Of Lower City, Mohenjo-Daro (Pakistan)  Drawing from "History of Urban Form" by A.E.J. Morris  (Published by George Godwin LTD, London, 1972)
(Nara Japan)
Urbanization at Teotihuacan, Mexico , Vol 1, The Teotihuacan Map, Rene Millon,

125. S-Curves

126. 1785 and 1787 Northwest Ordinance

127. Networks in Motion UK Turnpikes 1720-1790 UK Canals 1750-1950
Twin Cities
Twin Cities

128. Case 4: Base case with initial speeds ~ U(1,5) and land use ~ U(10, 15)
Initial network
Equilibrium network state after 7 iterations
Slow
Fast
Figure 9 Equilibrium speed distribution on a 10x10 grid network

129. Preliminary Results

130. Predicted Expansions Lane.Miles added Year 1990 1995 2000 2005 2010
2015

131. Hennepin Expansion
2005
2010
2015

132. Analysis and Evaluation
Priorities between every level of government vary
Main criteria:
1)Safety
2)Pavement conditions/maintenance
3)Capacity-ADT
Benefit/Cost Analysis - not a common criteria
Jurisdictions believe there are non-monetizable factors
- Trade off between safety and capacity projects
Jurisdictions expressed concern for air/environmental quality as a factor.