Models of Network Growth

1
Models of Network Growth

• David Levinson

2
Acknowledgements

• Funding Sources
• 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?
If They Come, Will You Build It?
7
Agent-Based Modeling

• 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

• 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)

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

• 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,

• Wardrops 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

• VOTBPR 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 w0.01
• 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
Case 1 Base 15x15
20
Case 2 Same as base case but initial speeds
U(1, 5)
21
Case 3 Base case with a downtown
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, ?29.8) - Empirical
• Improvement model ? 0.75 DRS in link
  expansion
• CRS, DRS, IRS Constant, Decreasing, Increasing
  Returns to Scale

26
Results
Experiment 2 predicted 1998 network
Experiment 1 predicted 1998 network
Experiment 3 predicted 1998 network
Experiment 4 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

• 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 gt 1
• AADT gt 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 Countys jurisdiction
Scott County
Project solicitation
Application review
Safety
Average Daily Traffic (ADT)
yes
ADTgt15,000 3 lane-roads
Project in top 200 high crash location list
no
yes
yes
Reapplication?
no
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
End
no
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 RULEif(AADTgt30000)juris_score1i
  50
• //if(AADT gt20000)juris_score1i38
• //else if (AADT gt10000)juris_score1i25
• if(adtgt30000)juris_score1iMath.min(50,38(5
  0-38)(AADT -30000)/(100000-30000))
• else if(adtgt20000)juris_score1i25(38-25)(
  AADT -20000)/(30000-20000)
• else if (adtgt10000)juris_score1i0(25-0)(A
  ADT -10000)/(20000-10000)

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
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

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
Research Papers

• Yerra, Bhanu and Levinson, D. (2005) The
  Emergence of Hierarchy in Transportation
  Networks. Annals of Regional Science 39 (3)
  541-553
• 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. 28-38
• 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. 297-318
• Parthasarathi, P, Levinson, D., and Karamalaputi,
  Ramachandra (2003) Induced Demand A Microscopic
  Perspective Urban Studies Volume 40, Number 7
  June 2003 pp. 1335-1353

• Zhang, Lei David M. Levinson (2005) Pricing,
  Investment, and Network Equilibrium (05-0943)
  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 (05-0897) 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 175-188) ?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

• 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

• ? 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
Growth
120
100
80
60
VKT
40
Lane-km
20
0
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
50
Induced Demand Consumers Surplus
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 MCDs 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

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)
• (a0.4, b0.25, c0.5)

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

• 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 MOEs 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 p-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
? 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)

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Experiments
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Mixed Logit Algorithm
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Expansion Model
C Capacity L Length ij link in
consideration p parallel link Q AADT on the
link E Cost of expansion Y year - 1979 X
Distance from downtown B Budget Constraint P
population of MCD
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Demo
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Models Required

• Land use and population model
• Travel demand model
• Revenue model
• Cost model
• Network investment model

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Case A - Results
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Results - Cases B1 B2
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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
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Base Case 10x10
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Case 2 Same as base case but initial speeds
U(1, 5)
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Case 3 Base case with a downtown
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Case 4 Base case with land use U(10, 15)
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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

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Two empirical functions

• Capacity g (number of lanes)

• Free flow Speed f (Capacity)

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Twin Cities Applications

• Replicate previous network growth patterns
• Predict future network growth
• Explore emergent properties of network dynamics
  e.g. road hierarchy, congestion

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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
Capacity change Experiment 1 1998-base
Capacity change observed 1998 - base
Capacity change Experiment 2 1998-base
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Emergence of Road Hierarchy
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How Road Hierarchy Emerges
Base 1978 network with uniform capacity
(400veh/h)
Experiment 4 capacity change predicted 1982 -
base
? Three identifiable reasons ? Natural
barriers ? Existing Activity centers ?
Unbalanced demand pattern
Experiment 4 capacity change predicted 1998 -
base
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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
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Methods

• Observation
• Agent Based Modeling
• Econometric Modeling of
• (1) Link Expansion and
• (2) New Construction

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How networks change with time

• Nodes Added, Deleted, Expanded, Contracted
• Links Added, Deleted, Expanded, Contracted
• Flows Increase, Decrease

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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)

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Costs

• A global link maintenance cost (MC) function for
  all links

• Initially assume only one type of cost, function
  of length, flow, link speed

• Link construction cost (CC) function (continuous
  or discrete)

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Flowchart
The simulation model can be used as a normative
or a descriptive tool depending on how investment
and pricing rules are specified.
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East Asian Grids
Ideal Chinese Plan
Chang-an
Nara
Kyoto
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Other Grids
Teotihuacan below
Mohenjo-Dara above, Delos below
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S-Curves
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1785 and 1787 Northwest Ordinance
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Networks in Motion

• UK Turnpikes 1720-1790
• UK Canals 1750-1950
• Twin Cities 1920-2000
• Twin Cities 1962-2000

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Case 4 Base case with initial speeds U(1,5)
and land use U(10, 15)
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Preliminary Results
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Predicted Expansions
Lane.Miles added
Year
1990
1995
2000
2005
2010
2015
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Hennepin Expansion
2005
2010
2015
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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.