Architecture David Levinson

East Asian Grids Kyoto Nara Chang-an Ideal Chinese Plan

1785 and 1787 Northwest Ordinance

Other Grids Teotihuacan below Mohenjo-Dara above, Delos below

Macroscopic View

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

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

A City Is Not A Tree

A City Is A Web

Types of Goods

Service Areas

Roadway Classification

Hypothesized Effects

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

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

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

Trip Distribution Calculates trips between network nodes –Gravity model 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 Dijkstras Algorithm Flow on a link is Where l a is length of link v a is speed of link a  is value of time  o is tax/toll rate  1,  2 are coefficients K rs is a set of links along the shortest path from node r to node s,  a,rs = 1 if a  K rs, 0 otherwise

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

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

Network Investment Model A link based model Speed of a link improves if revenue is more than cost of maintenance, drops otherwise Where: v a 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 d a {  = 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 networkEquilibrium network state after 9 iterations Slow 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 networkEquilibrium 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 networkEquilibrium network state after 7 iterations SlowFast Figure 9 Equilibrium speed distribution for case 3 on a 15x15 grid network

Case A - Results

Case B2: Base case with initial speeds ~ U(1,5) and land use ~ U(10, 15) Initial networkEquilibrium network state after 7 iterations SlowFast Figure 9 Equilibrium speed distribution on a 10x10 grid network

Results - Cases B1 & B2

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 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.