Architecture

David Levinson

East Asian Grids

Kyoto

Nara

Chang-an

Ideal Chinese Plan

1785 and 1787 Northwest Ordinance

Other Grids

Teotihuacan belowMohenjo-Dara above, Delos below

Macroscopic ViewMiles of Road, Number of Vehicles in United States

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500

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1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

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Miles of Road (1,000)

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Motor Vehicles(1,000)

Miles of Road Motor Vehicles (1,000)

Motor VehiclesRoad Miles

Questions

• Should local, state, or federal agencies be responsible for a particular section of road?

• When we say “responsible”, do we mean financing it, paying for its capital costs, or paying for its operating costs?

• Is the hierarchy of roads due to “nature” or “nurture”?

• What does the hierarchy of roads imply for land use patterns?

Rationales For Network Hierarchy

• Aggregation of Traffic - Economies of Scale

• Separating Access and Movement Functions Reduces Conflict, Makes Both Safer

• Keeps Residential Neighborhoods Quiet• Less Redundant• Excludability of higher levels and

separability of layers makes financing by different agencies easier

Hierarchy of Roads

Access

Movement Arterials

Locals

SPEED

FLOW

Slow Fast

High

Low

Collectors

Downsides to Network Hierarchy

• Increased travel distance (backtrack costs)

• Increases criticality of specific points (less redundancy means greater vulnerability)

• Navigation more difficult than flat networks

• Others []

Governmental Hierarchies

• Homeowners Associations• Town, Cities• Counties• Metropolis• State• National

Typical Urban Network Elements

Traffic light

Interchange

Freeway

Major arterial

Minorarterial

Neighborhooddistributor

Local web(access-onlyfunction)

Local tree

A City Is Not A Tree

RootLink A

Link B

Link C

Link E

Link F

Link G

Link H

Branches

A City Is A Web

Link E

Link A

Link B

Origin Destination

Link C

Link D

Types of Goods

ExcludabilityYes No

Rivalry Yes Private ‘Congesting’No Club Public

Service Areas

L

H

Link service area for tree

Link service area for web

Web link

Tree link

Roadway Classification

Property Locals Collectors ArterialsTopology Tree, Local web Web WebExcludable to abutters No No YesExcludable to non-localtraffic

Yes No No

Congesting No Yes YesCompetitive No Yes MaybeContestable No Maybe MaybeLocality of Traffic High Medium LowCapacity Low Medium HighFree-flow Speed Low Medium HighFlow Low Medium HighScale economies Small Medium LargeService Area Small Medium Large

Hypothesized Effects

Short-distance road Long-distance roadLocalgovernment

Fair and efficient Underinvest or overprice

Stategovernment

Overinvest or underprice Fair and efficient

Network Growth, Not Design?

• Maybe we can think of networks as growing, rather than being designed top-down.

Movie

Methods

• Observation• Agent Based Modeling• Econometric Modeling (Logit and

Mixed Logit models) of – (1) Link Expansion and – (2) New Construction

How networks change with time

• State of a network node changes

• Travel time of a link changes• Capacity of a link changes• Flow on a link changes• New links and nodes are added• Existing links are removed• System properties, like

congestion, change over time

Agent-Based Modeling

• Links and nodes are agents• 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 determine the populations and land use

Land Use Layer

Network Layer

Figure 1: Splitting the system into network layer and land use layer

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

Network• Grid network

– Cylindrical network– Torus network

• Modified (Interrupted Grid)• Realistic Networks (Twin Cities)• Initial speed distribution

– Every link with same initial speed– Uniformly distributed speeds

Land Use and Demography

• Small land blocks are agents• Population, business activity, and

geographical features are attributes• Uniformly and bell-shaped

distributed land use are modeled• Land use is assumed fixed

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

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

Trip Distribution

Calculates trips between network nodes– Gravity model

€

trs ∝prqsf (drs)

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

Route Choice

• Path with least cost of traveling

• Cost of traveling a link is

• Dijkstras Algorithm• Flow on a link is

€

da =ηlava

+ ρ olaρ1va

ρ 2

Where la is length of link

va is speed of link a is value of timeo is tax/toll rate

1, 2 are coefficients

Krs is a set of links along the shortest path from node r to node s,

a,rs = 1 if a Krs, 0 otherwise

€

fa = trsrs

∑ ⋅δa,rs

Revenue Model• Toll is the only source of revenue• Annual revenue generated by a link is

total toll paid by the travelers

Where, coefficients are same as coefficients used in traveling cost function

• A central revenue handling agent can be modeled

€

Ra = ρ olaρ1va

ρ 2 (365 ⋅ fa )

Cost Model• Assuming only one type of cost• Cost of a link is

Where, c is cost rate,1, 2, 3 are coefficients.

• Introducing more cost functions makes the model more complicated and probably more realistic

€

Ca = c ⋅ laα 1 ⋅ fa

α 2 ⋅vaα 3

Network Investment Model

• A link based model• Speed of a link improves

if revenue is more than cost of maintenance, drops otherwise

€

vat+1 = va

t RaCa

⎛

⎝ ⎜

⎞

⎠ ⎟

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

Examples• Base case

– Network - speed ~ U(1, 1)– Land use ~ U(10, 10)

– Travel cost da { = 1.0, o = 1.0, 1 = 1.0, 2 = 0.0}

– Cost model {c =365, 1 = 1.0, 2 = 0.75, 3 = 0.75}

– Improvement model { = 1.0}– Speeds on links running in opposite direction

between same nodes are averaged– Symmetric route assignment

Initial network Equilibrium network state after 9 iterationsSlow Fast

Figure 5 Equilibrium speed distribution for the base case on a 15x15 grid network

Base Case

Case 2: Same as base case but initial speeds ~ U(1, 5)

Initial network Equilibrium network state after 8 iterationsSlow 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 iterationsSlow Fast

Figure 9 Equilibrium speed distribution for case 3 on a 15x15 grid network

Case A - ResultsProbability Distribution of Flows

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Rank

Probability

10X1015X1520X2030X30Twin Cities 1998

Case B2: Base case with initial speeds ~ U(1,5) and land use ~ U(10, 15)

Initial network Equilibrium network state after 7 iterationsSlow Fast

Figure 9 Equilibrium speed distribution on a 10x10 grid network

Results - Cases B1 & B2Probability Distribution of Volumes

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Rank

Probability

10X10 - B1

15X15 - B1

10X10 - B2

15X15 - B2

Twin Cities 1998

Base Case 50x50

Network

Self-Fulfilling Investments

• Invest in what is normally (base case) lowest volume links.

• Results in that being highest volume link.• Can use investment to direct outcome.

A River Runs Through It

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture. QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

• Break grid. Random initial distribution of speeds.

• As expected, bridges emerge as most important/highest speed links.

Summary of Agent Based Model

• Succeeded in growing transportation networks

• 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

Implications

• Just as we could forecast travel demand, demographics, and land use, we can now forecast network growth.

• We 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.

Beltways

• Policy Brief

Conclusions

• Network architecture is a complicated set of issues

• Design involves trade-offs, there are both advantages and disadvantages to steeper hierarchies.

• Designs “nurture” are highly constrained by “nature”, or the underlying structure of the problem that leads networks to be hierarchical with very simple, myopic decision rules.