models of network growth david levinson. acknowledgements research assistants wei chen wenling...
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Models of Network Growth
David Levinson
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Acknowledgements
Research Assistants
Wei Chen Wenling Chen Ramachandra Karamalaputi
Norah Montes de Oca Pavithra Parthasarathi
Feng Xie Bhanu Yerra (Dr.) Lei Zhang Shanjiang Zhu
• 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
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?
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
Macroscopic View
Miles of Road, Number of Vehicles in United States
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Year
Miles of Road (1,000)
0
50000
100000
150000
200000
Motor Vehicles(1,000)
Miles of Road Motor Vehicles (1,000)
Motor VehiclesRoad Miles
If They Come, Will You Build It?
If They Come, Will You Build It?
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
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
Land Use Layer
Network Layer
Figure 1: Splitting the system into network layer and land use layer
Flowchart of the simulation model
ScopeExogenous:
economic growth land use dynamics
Endogenous: travel behavior/ demand link maintenance and expansion costs network revenue (pricing)investmentinduced supply induced demand
TIME
Year t-1 Year t Year t+1
Exogenous land use, demographic, economic changes
Trip Generation
Trip Distribution
Zone production and attraction totals
UE Traffic Assignment
OD demand; k = 0
TIME
Revenue Model
Link flow k
OD cost table t + 1 OD cost table t
Cost Model
Revenue
Investment Model
Network t Network t + 1
Pricing Model
New capacity and free-flow speed
flow k = flow k–1 ?
Yes
No
k = k + 1 Link toll k
Flow, toll, travel time, OD cost
Maintenance cost Construction cost
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 speedsIdeal Chinese Plan
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)
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
Figure 3: An example representation of voronoi diagram
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Calculates trips between network nodes– Gravity model– Working on agent-based trip distribution
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115
Time (minutes)
Trip Distribution
€
Trs ∝prqs
ewd rs
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”
Route Choice• 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)
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,
€
fa = Trs
rs
∑ ⋅δa,rs
• Generalized link travel cost function
•
VOT•BPR travel time + Toll
tat
a
ta
ta
ata F
fv
lt τθλ
θ
+⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛+•=
2
11
Link-Performance Function
la is length of link
va is speed of link aλ is value of timeτa is “toll” θ1, θ2 are coefficients
In No Congestion Case, θ1 =0
Revenue And Cost Models
• Toll is the only source of revenue
• Annual revenue generated by a link is total toll paid by the travelers
€
τ a = ρ 0laρ1va
ρ 2
Ra = τ a (365 ⋅ fa )
• Initially assume only one type of cost, function of length, flow, link speed
€
Ca = μ ⋅ laα 1 ⋅ fa
α 2 ⋅vaα 3
Network Investment Model (1)
• A link based model• Speed of a link improves if revenue is more than cost of maintenance, drops otherwise
€
vat +1 = va
t Ra
Ca
⎛
⎝ ⎜
⎞
⎠ ⎟
β
Where:va
t is speed of link a at time step t,
is speed reduction coefficient.
No revenue sharing between links: Revenue from a link is used in its own investment
Initial Assumptions• Base case
– Network - speed ~ U(1, 1)– Land use ~ U(10, 10)– Friction factor w=0.01– Travel cost, Revenue da {λ = 1.0, o = 1.0, 1 = 1.0, 2 = 0.0}
– Infrastructure Cost { =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
Initial network
Equilibrium network state after 9 iterations
Slow
Fast
Figure 5 Equilibrium speed distribution for the base case on a
15x15 grid network
Case 1: Base 15x15
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
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
Case 5: 50x50
Network
Case 6: A River Runs Through It
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.
Four Twin Cities Experiments
Allow for link Initial contraction? condition
Yes
No
1978 Twin Cities network with real 1978 capacity
Experiment 1 Experiment 2
1978 network with uniform capacity (400veh/h)
Experiment 3 Experiment 4
• Value of time = $10/hr - MnDOT Value
• Link performance function θ1 = 0.15; θ2 =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
Results
Experiment 1: predicted 1998 network Experiment 2: predicted 1998 network
Experiment 3: predicted 1998 network Experiment 4: predicted 1998 network
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.
Processes
• Formal
* Structured process* Ranking system through point allocation* Task forces-committees
• Informal
* Priorities•safety,preservation, capacity, •social and economic impacts, •community and agency involvement•Benefit/cost ratio, etc.
* No Ranking System
Informal ProcessesJurisdictions 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”
Formal Processes
1. Reduction in SOV trips and/or VMT 0-75 0-100 2. Reduction of vehicle emissions 0-100 0-150 3. Measure of project effectiveness 0-300 0-300B. Congestion Mitigation 200 350 1. Congestion/increase hourly person reduction 0-100 0-175 2. Traffic congestion reduction 0-100 0-175C. Service Efficiency and productivity 250 - 1. Service efficiency 0-125 -
2. Productivity 0-125 -
D. Regional Transit Priorities 300 - 1. Corridor priority (as ranked in 2030 TPP) 0-100 - 2. Location Suitability & Market Area Demand 0-100 - 3. Integration with existing Infrastructure 0-100 -
E. Development Framework Implementation 200 200
1. Employment, housing and transportation integration 0-200 0-200
a) Intensity 60 75
b) Linkages 60 75
c) Brownfields & Natural Resources 40 50
d) Affordable/Life Cycle housing 40 -
F. Maturity of project concept 100 100
TOTAL 1,525 1,200
A. Reduction in carbon monoxide (CO), nitrogen oxide (Nox), and volatile organic compound (VOC) emissions
475 550
Transit expansion
Demand or System
Management
Project ID NumberPoints
Project PriorityLevel of NeedCritical 51-60Significant 41-50Important 21-40Desirable 0-20
In adopted Five Year Plan2006 302007-2009 202010 10New for 2006-2009 0
Integrated Project 10
Sub-Total Project Priority
Contributions to City Goals/Objs:Strong Contribution 46-70Moderate Contribution 16-45Little or No Contribution 0-15
Operating Costs: -25 to +25'
Sub-total Goals & Operating Costs
Qualitative Criteria:Neighborhood Livability & Safety 0-15Public benefit 0-15Capital Cost/Customer Service Delivery 0-15Environmental Quality 0-15Collaboration & Leveraging 0-15Effect on Tax Base & Job Creation 0-15Intellectual & Cultural Implications 0-15
Sub-Total Qualitative
Total Rating Points300
PossibleSource: Capital Long Range Improvement Committee. 2005 Capital Guidelines
CLIC Rating form
PERFORMANCE MEASUREPOINTSCapacity V/C ratio 100
Pavement 100
Safety 100
Municipal support 100
DETAILS
for example:
Pavement quality indexRatio of project crash rate to county average
=(ADDT X 0.10)/Capacity
City council resolution supports ISTEA application…………………………………….…………50City staff gives verbal support for project…..…………20
City approves preliminary design and commits to cost share greater than required by county policy………………………………………………..…..100
>5=100 points, >3=90, >20=80…<.50=0
Ratio of 10% AADT to current capacity
AADT=11900Current capacity/hr=1200Ratio=0.99Normalized score=651.52 = 100 points0.67 = 44 pointsPavement Condition IndexPresent Service-ability rating rideability
A. Relative Importance of the route 0-100 0-100 0-100 0-150 0-100B. Deficiencies and Solutions on category 425 425 425 375 425 1. Crash reduction - 0-150 0-150 0-100 0-150 On principal Arterial 0-50 - - - - On the reliever 0-50 - - - - 2. Access Management 0-125 0-175 0-125 0-125 0-175
3. Air Quality 0-100 0-50good
movement 0-75
0-100 0-50
4. Congestion Reduction - 0-50shoulder
improvement 0-75
0-50 0-50
On principal Arterial 0-50 - - - - On the reliever 0-50 - - - -C. Cost Effectiveness 275 275 275 275 275 1. Crash reduction 0-125 0-125 0-125 0-125 0-125
2. Congestion Reduction 0-75 0-75good
movement 0-75
0-75 0-75
3. Air Quality 0-75 0-75shoulder
improvement 0-75
0-75 0-75
D. Development Framework Implementation 300 300 300 300 300 1. Employment, housing and transportation integration0-200 0-200 0-200 0-200 0-200 a) Intensity 60 60 60 60 60 b) Linkages 60 60 60 60 60 c) Brownfields & Natural Resources 40 40 40 40 40 d) Affordable/Life Cycle housing 40 40 40 40 40 2. Integration of modes 0-100 0-100 0-100 0-100 0-100E. Maturity of project concept 0-100 0-100 0-100 0-100 0-100
TOTAL 1,200 1,200 1,200 1,200 1,200
Non-freeway Principal Arterial
Reliever ExpanderConnectorAugmenter
Flowcharts-Informal processesRoadways under
County’s jurisdiction
Project solicitation
ADT>15,000
3 lane-roads
Scott County
Application review
SafetyAverage Daily Traffic (ADT)
Project intop 200
high crash location list
Project approval
Reapplication?
Project construction
End
yesyes
yes
nono
yes
no
no
Flowcharts - Formal Processes - CityMinneapolis streets
Project solicitation
City of Minneapolis
Application review
Reapplication?
End
Compute scores
Highest scored project selection
Allocation of funding availability
Project approval
Project construction
yes
no no
yes
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 -30000)/(100000-30000));else if(adt>20000)juris_score[1][i]+=25+(38-25)*(AADT -20000)/(30000-20000);else if (adt>10000)juris_score[1][i]+=0+(25-0)*(AADT -10000)/(20000-10000);
State Expansion
2005
2010
2015
To Add: Constraints
* Right of way
* Environmental restrictions (wetland areas)
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Road segments that were planned in the 1960s and have not been built.
Fundamental for the State Budget New Construction Plans
To Add: Legacy Links
SONG 1.0: Simulator of Network Growth Interface
Parameter panel
Output Panel
Visualized Graphic
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
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
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) 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
•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
¿Questions?
?
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
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
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
Future Work (cont. 2)
0
100000
200000
300000
400000
500000
600000
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 >90Trip Length (min)
Num. Of Trips
Observed 1990 HTS
Beta = 0.02
Beta = 0.1
Beta = 0.42 Optimum
Beta = 1
Beta = 2
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
Chicago sketch network: trip length distribution
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?
0
20
40
60
80
100
120
1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000
Year
% Growth
VKT
Lane-km
Growth of VKT Vs. Capacity
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
Demand
Supply
Capacity
Expenditure
B
C1 C2
E1
E2
P
Supply-Demand Curve
Demand
Supply Before
Quantity of traffic
Price of Travel
Q1 Q2
P1P2
Supply After
Induced Demand & Consumers’ Surplus
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
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
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)
Cost Function
Eij = f (Lij*∆Cij, N, T, Y, D, X)
Eij = cost to construct or expand the linkLij*∆Cij = lane miles of construction
N = dummy variable to new construction T = type of roadY = year of completion – 1979D =duration of constructionX = distance from the nearest downtown
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
Results of Cost Model
Ln(Eij)Variable Coef. P>|t|
Lane-miles added 0.47 0.00*New construction 0.40 0.03*Interstate highways 1.43 0.00*State highways 0.52 0.03*Log (Year-1979) 0.76 0.00*Log (Duration) 0.36 0.01*Distance from nearestdowntown
-0.03 0.04*
_Constant 5.45 0.00** Significance at 95% confidence interval
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
Results: Link
Expansion
Variable Hypo. Interstate TH CSAH
Cij -S -2.06E+00* -8.15E+00*Lij -S -2.62E+00* -2.28E+01* -5.52E-01
Qij/Cij +S -2.50E-05* -9.30E-05* 1.97E-04*Qp/Cp +S 1.57E-05* 1.05E-05 -1.99E-05
∆02(Qij*Lij) +S 3.98E-04* 1.67E-03* 2.81E-03*∆24(Qij*Lij) +S 5.10E-04* 4.89E-04 2.72E-03*∆46(Qij*Lij) +S 5.10E-04* 4.89E-04 2.72E-03*∆68(Qij*Lij) +S -5.96E-04* 4.54E-03* 3.80E-03*
Eij -S -3.21E-09* -8.18E-10 6.84E-10B +S 4.38E-06* 7.32E-05* 1.07E-05*Y -S -1.09E+00* -1.17E+00* 8.37E-02X +S -6.23E-03 1.13E-01 5.19E-02
Qhi+Qjk +S 1.09E-05* 2.37E-05* -1.71E-05*Chi+Cjk- Cij -S -6.07E-01* -5.49E-01* 5.43E-02
P - 2.56E-06* 1.28E-05* -1.63E-05*∆P +S 2.54E-04* 1.17E-03* -1.40E-04*
No. of Obs:10986 No. of Obs:17926 No. of Obs:6531LL= -293.92 LL= -41.34 LL= -202.98
Psuedo R2 = 0.46 Psuedo R2 = 0.61 Psuedo R2 = 0.29* Significance at 90% level
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
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
New Construction Model
Where:
N = New construction
C = Capacity of the link
L = Length of the link
Q = Flow on the link
Y= Year
€
N ijt +1 = f(L ij,Cp,L p,Qp/Cp, A, E ij ,B,Y, X,D)
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
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
Results of New Construction Models
Variable Hypo. CoefficientLength of the link - -5.91E-01
Capacity of the parallel link +S -3.31E-01*Length of the parallel link +S 4.93E-01*Congestion on parallel link +S -1.96E-05
Access measure +S 4.24E-05*Year -S 7.31E-01*
Cost of construction -S -2.82E-01*Budget +S 5.68E-06*
Distance from downtown +S -1.21E-01*No. of nodes in the area -S -6.32E-04
Constant -6.09E+00*
Number of Observations: 89031Logit LL = -473.19
* Significant at 90% confidence interval
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
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.
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.
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-maximizingAssumptions 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
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
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
An Example of Normative Applications
1010 Grid network 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)
32 km
MOEs By Pricing Policy
Pricing policies - Vehicle Hours Traveled
100000
1000000
1 11 21 31 41 51 61 71 81 91
Iterations
VHT Regulation(Distance&LOS)
Regulation(Distance)
MC
Profit-Max
MOEs - 1
Pricing policies – Vehicle Kilometers Traveled
5.00E+06
1.00E+07
1.50E+07
2.00E+07
2.50E+07
3.00E+07
1 11 21 31 41 51 61 71 81 91
Iteration
VKT
Regulation(Distance&LOS)Regulation(Distance)
MC
Profit-Max
MOEs - 2
Pricing policies – Average Network Travel Speed
0
10
20
30
40
50
60
70
80
90
100
1 11 21 31 41 51 61 71 81 91
Iteration
Speed(kph)
Regulation(Distance&LOS)
Regulation(Distance)
MC
Profit-Max
MOEs - 3
Pricing policies – Total Revenue
0
5000000
10000000
15000000
20000000
25000000
30000000
1 11 21 31 41 51 61 71 81 91
Iteration
Revenue($)
Regulation(Distance&LOS)
Regulation(Distance)
MC
Profit-Max
MOEs - 4
Pricing policies – Consumers’ Surplus + Revenue
-50000000
-40000000
-30000000
-20000000
-10000000
0
1 11 21 31 41 51 61 71 81 91
IterationsCS+Revenue $
Regulation(Distance&LOS)
Regulation(Distance)
MC
Profit-Max
Toll evolution under π-max behavior
Pricing policies – Toll Evolution
Profit-Max: Toll Evolution
0
50
100
150
200
250
300
350
400
0 0.0625 0.125 0.25 0.5 1 2 4 8 16 32 >32Toll
#Links Series1Series2Series3Series4Series5Series6Series7Series8Series9
Demand and profit functions
Demand curve Profit versus toll
Regulation
Profit-Max
MOEs By Investment Policies
Investment policies: Speed
0
10
20
30
40
50
60
70
1 6 11 16 21 26 31 36 41 46 51 56Iteration
Speed (kph)
Decentralized-Continuous
Decentralized-Discrete
Centralized-Continuous-VC
Centralized-Discrete-VC
Centralized-Discrete-BC
MOEs - a
Speed (Decent-Continuous = 100)
75
85
95
105
115
125
1 6 11 16 21 26 31 36 41 46 51 56Iteration
Decentralized-Continuous
Decentralized-Discrete
Centralized-Continuous-VC
Centralized-Discrete-VC
Centralized-Discrete-BC
Investment policies: Speed after transformation
MOEs - b
Investment policies: Consumers’ Surplus + Revenue
90
100
110
1 6 11 16 21 26 31 36 41 46 51 56
Iteration
CS+Revenue Decentralized-Continuous
Decentralized-Discrete
Centralized-Continuous-VC
Centralized-Discrete-VC
Centralized-Discrete-BC
A model of the rise and fall of roads is developed and successfullyapplied 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
Conclusions
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
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
Acknowledgements
Additional slides
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
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?
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 studyFew studies considering network growth at microscopic level
Induced Supply and Induced Demand
Demand
Supply
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
Results – Convergence Properties
10
100
1000
10000
100000
1978 1983 1988 1993 1998 Year
Num. of link expansions
Experiment 1Experiment 2Experiment 3Experiment 4
10
100
1000
10000
100000
1978 1983 1988 1993 1998 Year
Num. of link Contraction
Experiment 1Experiment 3
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
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
• 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
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)
€
.....exp(α ij + βijxij )
exp(α ij + βijxij )∑∫∫∫ f (β1 /Ω1).... f (βn /Ωn )dβ1.....dβn
€
Pij =exp(α ij + β ij x ij )
exp(α ij + β ij x ij )∑
ExperimentsExperiment
No.Description/ Variables Range of variables
1 Grid search for 2 an d3 (2, 3) – (0.75, 1.25) with0.05 steps
2 γ - Coefficien t in Gravi tyModel 0 t 0o .1 wit 0h .01 step s& 0.1t o1.0 wit h0.1 steps
3 Randoml y distribute dinitia l speed - s v0a v0a ~ Un(1, 5)4a Downtow n lan duse gz, hz (10, 15) (min, max)4b 4 a wi th randoml y distribute dinitia l speeds v0a ~ Un(1, 5)
5 3 - Coefficien t in Revenu eMode l andGeneralized cos t of travel
Fro m0 t o1.0 wit 0h .1 steps
6 Rando mnetworks (realisti cnetwork )s -7 Realist ic lan dus epattern -8 Cylindric al topology – random lydistributed
initi al speeds v0av0a ~ Un(1, 5)
9 Toru s topology - randoml y distribute d initialspeeds v0a
v0a ~ Un(1, 5)
10a Bas e cas ewit hrandoml ydistribute d land use gz, hz ~ Un(10, 15)10b 10 awit hrandom lydistribut ed init ialspeeds v0a ~ Un(1, 5)
Start
Set no. of simulations,N
Determine number of Random parameters and their distributions, M
n = n + 1
n > N?
EndYES
NO
Set n=1
Generate 2M Halton sequence numbers based on M prime numbers
Convert them into appropriate distributions
Calculate simulated probability and add to previous probability
Mixed Logit Algorithm
Variable Hypo. ∆Cijt+1=1 ∆Cijt+1=2Capacity -S -1.92E+00* -2.22E+00*Length -S -2.20E+00* -3.54E+00*
Congestion +S -1.82E-05* -3.84E-05*Congestion on parallel link +S 1.82E-05* 1.79E-06Change in VKT (t to t-2) +S 4.58E-04* 3.63E-04*
Change in VKT (t-2 to t-4) +S 5.34E-04* 5.33E-04*Change in VKT (t-4 to t-6) +S 5.34E-04* 5.33E-04*Change in VKT (t-6 to t-8) +S -8.04E-04* -3.53E-04*
Cost of Exapnsion -S -6.54E-09* -3.19E-09*Budget +S 4.16E-06* 7.83E-06*
Year- 1979 -S -1.12E+00* -1.72E+00*Distance from downtown +S 2.09E-01* -1.54E-01*
Inflow+outflow +S 1.17E-05* 1.13E-05*Capacity of adjacent links -S -7.18E-01* -5.27E-01*
Population - 7.78E-06* -3.09E-06Change in Population (t to t-2) +S 1.63E-04* 4.97E-04*
_cons 3.02E+00* 7.59E+00*Number of Observations: 10986
Log Likelihood = -277.65Psuedo R2: 0.51
* Significant at 90 % Confidence Interval
Multinomial Logit for Interstate Highways
Variable Hypo. ∆Cijt+1=1 ∆Cijt+1=2Capacity -S -2.15E+00* -2.27E+00*Length -S -2.21E+00* -3.69E+00*
Congestion +S -1.12E-05* -2.94E-05*Congestion on parallel link +S 2.12E-05* 8.62E-06Change in VKT (t to t-2) +S 5.41E-04* 2.29E-04*
Change in VKT (t-2 to t-4) +S 6.51E-04* 5.10E-04*Change in VKT (t-4 to t-6) +S 6.51E-04* 5.10E-04*Change in VKT (t-6 to t-8) +S -1.24E-03* -2.13E-04
Cost of Exapnsion -S -7.39E-09* -3.35E-09*Budget +S 4.73E-06* 8.59E-06*
Year- 1979 -S -1.20E+00* -1.82E+00*Distance from downtown +S 2.44E-01* -1.46E-01*
Inflow+outflow +S 1.17E-05* 1.15E-05*Capacity of adjacent links -S -7.35E-01* -6.46E-01*
Population - 7.65E-06* -3.50E-06Change in Population (t to t-2) +S 1.34E-04* 5.27E-04*
_cons 3.47E+00* 8.79E+00*Triangular Dev.
Length 6.13E-02* 7.45E-01*Change in VKT (t to t-2) 2.92E-04* 4.41E-05*
No. of Obs:10986LL= -232.99
*Significance at 90% confidence interval
Mixed Logit Model for Interstate and State Highways
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?
YES NO
Subtract lanes for years < T
Add lanes for years >=T
T = T + 1
T > 1998?
End
YES
NO
Building the Network
Expansion Model
€
Cijt +1 = f(Cij,L ij,Q ij/Cij,Qp/Cp,Δ(Q ij * L ij),.B,E ij,Y, X,
Qhi +Q jk ,Chi +C jk ,Δ(Chi +C jk ),Δ(Qhi + Q jk ),P,ΔP)
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
Variable Hypo. ∆Cijt+1=1 ∆Cijt+1=2Capacity -S -2.15E+00* -2.27E+00*Length -S -2.21E+00* -3.69E+00*
Congestion +S -1.12E-05* -2.94E-05*Congestion on parallel link +S 2.12E-05* 8.62E-06Change in VKT (t to t-2) +S 5.41E-04* 2.29E-04*
Change in VKT (t-2 to t-4) +S 6.51E-04* 5.10E-04*Change in VKT (t-4 to t-6) +S 6.51E-04* 5.10E-04*Change in VKT (t-6 to t-8) +S -1.24E-03* -2.13E-04
Cost of Exapnsion -S -7.39E-09* -3.35E-09*Budget +S 4.73E-06* 8.59E-06*
Year- 1979 -S -1.20E+00* -1.82E+00*Distance from downtown +S 2.44E-01* -1.46E-01*
Inflow+outflow +S 1.17E-05* 1.15E-05*Capacity of adjacent links -S -7.35E-01* -6.46E-01*
Population - 7.65E-06* -3.50E-06Change in Population (t to t-2) +S 1.34E-04* 5.27E-04*
_cons 3.47E+00* 8.79E+00*Triangular Dev.
Length 6.13E-02* 7.45E-01*Change in VKT (t to t-2) 2.92E-04* 4.41E-05*
No. of Obs:10986LL= -232.99
*Significance at 90% confidence interval
Mixed Logit Model for Interstate and State Highways
Demo
Models Required
• Land use and population model
• Travel demand model
• Revenue model• Cost model• Network investment model
Cos t
Mod el
A S C II
Ou t pu t
F il e s
Mod el
Coo r d i na t o r
Tr av el
D em and
Mod el
N et wo r k
S tr u c tu re
L and U s e
a nd
D em og r aph ic
s
U s e r-
D efi ned
E ven t s
D at a
S t o ra geI nv e s t m e n t
Mod el
R e venu e
Mod el
V i su al i za t i onD at a
E xpo r t
Mod el
Figure 2: Overview of modeling process
Probability Distribution of Flows
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9
Rank
Probability
10X1015X1520X2030X30Twin Cities 1998
Case A - Results
Results - Cases B1 & B2Probability Distribution of Volumes
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9
Rank
Probability
10X10 - B1
15X15 - B1
10X10 - B2
15X15 - B2
Twin Cities 1998
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
Initial network
Equilibrium network state after 8 iterations
Slow
Fast
Figure 4 Equilibrium speed distribution for the base case on a
10x10 grid network
Base Case: 10x10
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
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
Case 4: Base case with land use ~ U(10, 15)
Initial network
Equilibrium networkSlow
Fast
Figure 8 Equilibrium speed distribution on a 10x10 grid network
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
€
z =x − μ
σ
N1−
N
365
• Capacity = g (number of lanes)
• Free flow Speed = f (Capacity)
Two empirical functions
Twin Cities Applications
• Replicate previous network growth patterns
• Predict future network growth
• Explore emergent properties of network dynamics e.g. road hierarchy, congestion
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: observed 1998 - base Capacity change: Experiment 1 1998-base Capacity change: Experiment 2 1998-base
Real growth
Predicted growth
Emergence of Road Hierarchy
10
100
1000
10000
500 1500 2500 3500 4500 5500 6500 7500 More
Link Capacity (veh/hr)
Number of Links
Experiment 1Experiment 21998-observed
10
100
1000
10000
500 1500 2500 3500 4500 5500 6500 7500 MoreLink Capacity (veh/hr)
Number of Links
Experiment 3Experiment 41998-observed
10
100
1000
10000
0 1000 2000 3000 4000 5000 6000 7000 8000
Link flow (veh/hr)
Number of Links
Experiment 1Experiment 21998-observed
10
100
1000
10000
0 1000 2000 3000 4000 5000 6000 7000 8000Link flow (veh/hr)
Number of Links
Experiment 3Experiment 41998-observed
How Road Hierarchy Emerges
Base: 1978 network with uniform capacity (400veh/h) Experiment 4 capacity change: predicted 1982 - base
Experiment 4 capacity change: predicted 1998 - base
Real growth
Predicted growth
River
The three downtowns
Three identifiable reasons Natural barriers Existing Activity centers Unbalanced demand pattern
Network Congestion
0
2000
4000
6000
8000
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6Volume/Capacity ratio
Number of Links
Experiment 1Experiment 21998-observed
0
2000
4000
6000
8000
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6Volume/Capacity ratio
Number of Links
Experiment 3Experiment 41998-observed
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
Methods
• Observation• Agent Based Modeling• Econometric Modeling of
– (1) Link Expansion and – (2) New Construction
How networks change with time
• Nodes: Added, Deleted, Expanded, Contracted
• Links: Added, Deleted, Expanded, Contracted
• Flows: Increase, Decrease
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)
MC Length Capacity
21 )()( taa
ta FlC ⋅=
321 )()()( 1 σσσφ ta
ta
taa
ta FFFlK −⋅⋅⋅= +
CC Length Capacity Δ Capacity
Costs• A global link maintenance
cost (MC) function for all links
€
Ca = μ ⋅ laα 1 ⋅ fa
α 2 ⋅vaα 3
• Initially assume only one type of cost, function of length, flow, link speed
Link construction cost (CC) function (continuous or discrete)
Flowchart
TIME
Year t-1 Year t Year t+1
Exogenous land use, demographic, economic changes
Trip Generation
Trip Distribution
Zone production and attraction totals
UE Traffic Assignment
OD demand
TIME
Revenue Model
Link flow
OD cost table t + 1 OD cost table t
Cost Model
Revenue and cost estimates for all links
Investment Model
Network t Network t + 1
Pricing Model
New capacity and free-flow speed
Travel Time
New toll
Toll t + 1 Toll t
The simulation model can be used as a normative or a descriptive tool depending on how investment and pricing rules are specified.
East Asian Grids
Kyoto
Nara
Chang-an
Ideal Chinese Plan
Other Grids
Teotihuacan below
Mohenjo-Dara above, Delos below
S-Curves
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000
Year
Proportion of Maximum Extent
Canals
Rail
Telegraph
Oil Pipelines
Surfaced Roads
Gas Pipelines
1785 and 1787 Northwest Ordinance
Networks in Motion
• UK Turnpikes 1720-1790• UK Canals 1750-1950• Twin Cities 1920-2000• Twin Cities 1962-2000
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
Preliminary ResultsYear 1990 1995 2000 2005 2010 2015
Total trips produced & attracted (thousands)
693.56 744.72 796.27 846.88 897.58 938.47
Total households (thousands)
875.5 948 1020.49 1110.49 1200.49 1283.01
vht 5.42E+08 6.06E+08 7.47E+08 8.61E+08 1.01E+09 1.28E+09
vkt 1.31E+10 1.45E+10 1.81E+10 2.08E+10 2.46E+10 2.95E+10
State expansion budget (million $)
246.42 271.55 331.01 370.21 429.2 524.43
Anoka expansion budget (million $)
7.75 14.04 19.43 27.69 31.94 42.34
Carver expansion budget (million $)
1.06 6.45 10.43 23.7 40.74 60.15
Dakota expansion budget (million $)
12.2 20.63 30.1 39.06 45.83 56.57
Hennepin expansion budget (million $)
42.37 52.6 73.56 84.56 100.59 115.43
Ramsey expansion budget (million $)
21.62 28.84 40.34 47.53 55.63 66.83
Scott expansion budget (million $)
0.98 8.31 19.52 36.06 54.85 77.23
Washington expansion budget (million $)
5.37 10.95 15.9 22.59 24.63 30.46
Predicted Expansions
0
5
10
15
20
25
StateAnokaCarverDakotaHennepinRamseyScottWashington
Lane.Miles added
Year1990 1995 2000 2005 2010 2015
Hennepin Expansion200520102015
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.