Architecture

David Levinson

East Asian Grids

Ideal Chinese Plan Chang-an Nara Kyoto

1785 and 1787 Northwest Ordinance

Other Grids

Mohenjo-Dara above, Delos below Teotihuacan below

Miles of Road (1,000)

4,000

Macroscopic View

Miles of Road, Number of Vehicles in United States

Motor Vehicles (1,000)

200000 3,500 3,000 2,500 2,000 1,500 Road Miles Motor Vehicles 150000 100000 1,000 500 50000 0 1900 1910 1920 1930 1940 Miles of Road 1950

Year

1960 1970 Motor Vehicles (1,000) 1980 1990 0 2000

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

High

Movement

Arterials

FLOW

Low Slow Collectors

Access SPEED

Fast Locals

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

Min or arterial Freeway Major arterial Neighbo rhood distrib utor Lo cal web (acces s-on ly fun ctio n) Lo cal tree Traffic ligh t Interch ang e

Root

A City Is Not A Tree

Link A Link E Link B Link C Link H Link F Branches Link G

A City Is A Web

Origin Link A Link B Link C Link E Link D Destination

Types of Goods

Rivalry Ye s No Excludability Ye s Private Club No ‘Congesting’ Public

H

Service Areas

L Link service area for web Web link Tree link Link service area for tree

Roadway Classification

Property Topology Excludable to abutters Excludable traffic Congesting to non-local Competitive Contestable Localit y of Traffic Capacity Free-flow Speed Flow Scale economi es Service Area Locals Tree, Local web No Ye s No No No High Low Low Low Sma ll Sma ll Collectors Web No No Arterials Web Ye s No Ye s Ye s Maybe Medium Medium Medium Medium Medium Medium Ye s Maybe Maybe Low High High High Large Large

Hypothesized Effects

Local governme nt State governme nt Short-distance road Fair and efficient Overinvest or underprice Long-distance road Underinvest or overprice 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

Network Layer Land Use Layer Figure 1: Splitting the system into network layer and land use layer

Models Required

User Defi ned Events Travel Demand Model • Land use and population model • Travel demand model • Revenue model • Cost model • Network investment model Network Structure Land Use and Demographic s Data Storage Model Coordinator Revenu e Model Cost Model Investment Model ASCII Output Fil es Visualization Data Export Model

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 Q uickTim e™ and a TI FF ( Uncom pr essed) decom pr essor ar e needed t o see t his pict ur e.

Figure 3: An example representation of voronoi diagram



Trip Distribution

Calculates trips between network nodes – Gravity model

t rs



p r q s f

(

d rs

) Where: t rs is trips from origin node r to destination node s , p r is trips produced from node r , q s is trips attracted to node s, d rs 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

d a

 

l a



v a

• Flow on a link is 

o l a

 1

v a

 2 Where l a is length of link v a  is speed of link is value of time a  o is tax/toll rate  1 ,  2 are coefficients K rs is a set of links along the shortest path from node r to  a,rs node s, = 1 if a  K rs , 0 otherwise

f a

 

t rs

 

a

,

rs rs



Revenue Model

• Toll is the only source of revenue • Annual revenue generated by a link is total toll paid by the travelers

R a

 

o l a

 1

v a

 2 (365 

f a

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

Cost Model

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

C a



c



l a

 1 

f a

 2 

v a

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

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



Network Investment Model

• A link based model • Speed of a link improves if revenue is more than cost of maintenance, drops otherwise

v a t

 1 

v a t

 

R a C a

   Where: v a t is speed of link time step t, a  is speed reduction coefficient.

at 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 d a {  = 1.0,  o = 1.0,  1 – Cost model { c = 365,  1 = 1.0,  2 = 1.0, = 0.75,  2  3 = 0.0} = 0.75} – Improvement model {  = 1.0} – Speeds on links running in opposite direction between same nodes are averaged – Symmetric route assignment

Base Case

Initial network Slow Fast Equilibrium network state after 9 iterations Figure 5 Equilibrium speed distribution for the base case on a 15x15 grid network

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

Initial network Slow Fast Equilibrium network state after 8 iterations Figure 7 Equilibrium speed distribution for case 2 a 15x15 grid network on

Case 3: Base case with a downtown

Initial network Slow Fast Equilibrium network state after 7 iterations Figure 9 Equilibrium speed distribution for case 3 a 15x15 grid network on

Case A - Results

Probability Distribution of Flows 1 0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 0 1 2 3 4 Rank 5 6 7 8 9 10X10 15X15 20X20 30X30 Twin Cities 1998

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

Initial network Slow Fast Equilibrium network state after 7 iterations Figure 9 Equilibrium speed distribution on a 10x10 grid network

Results - Cases B1 & B2

Probability Distribution of Volumes 1 0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 0 1 2 3 4 Rank 5 6 7 8 9 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

Q uickTim e™ and a TI FF ( Uncom pr essed) decom pr essor ar e needed t o see t his pict ur e.

Q uickTim e™ and a TI FF ( Uncom pr essed) decom pr essor ar e needed t o see t his pict ur e.

• 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.

• Policy Brief

Beltways

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.