Fundamentals of Transportation/Planning

Transportation Planning and Forecasting

All forecasts are wrong, some forecasts are more wrong than others. - anonymous

Hierarchy of Roads

Why aren’t all roads the same? []

Transportation facilities have two distinct functions: through movement and land access. permits the aggregation of traffic to achieve economies of scale in construction and operation (high speeds); reduces the number of conflicts; helps maintain the desired quiet character of residential neighborhoods by keeping through traffic away from homes; contains less redundancy, and so may be less costly to build.

Functional Classification	Types of Connections	Relation to Abutting Property	Examples
Limited Access (highway)	Through traffic movement between cities and across cities	Limited or controlled access highways with ramps and/or curb cut controls.	I-94, Mn280
Linking (arterial:principal and minor)	Traffic movement between limited access and local streets.	Direct access to abutting property.	University Avenue, Washington Avenue
Local (collector and distributor roads)	Traffic movement in and between residential areas	Direct access to abutting property.	Pillsbury Drive, 17th Avenue

Decision Making

How does one (rationally) decide what to do?

1. Identify Needs
2. Set Objectives
3. Develop Options
4. Evaluate Options
5. Select Best Option
6. Implement Best Option
7. Evaluate Outcome

We need a tool to "Identify Needs" and "Evaluate Options". This is the transportation forecasting model.

Why Model ?

• Forecasting
• Scenario testing (alternative land uses, networks, policies)
• Project planning/corridor studies
• Growth management/development regulation/public facility adequacy
• Manage complexity, when eyeballs are insufficient, (different people have different intuitions)
• Understanding travel behavior
• Influence decisions
• Estimation in the absence of data

Developing Models

• Specification y=f(X)
• Estimation y=mX+b; m=1, b=2
• Implementation if Z > W, then y=mX+b
• Calibration ypredicted+k=yobserved
• Validation ypredicted1990+k=yobserved1900
• Application PICTURE OF ADAM

“Four-Step” Urban Transportation Planning Models

Trip generation how many trips are entering or leaving zone i or j Trip distribution how many trips are going from zone i to zone j Mode choice how many trips from i to j are using mode m Route choice which links are trips from i to j by mode m using route r

Model Elements

Recall the hierarchy of roads, what can we simplify? It is typical for a regional forecasting model to eliminate local streets, and replace them with a centroid and centroid connector. Keep in mind that Models are abstractions

Network

zone centroid special node whose number identifies a zone, located by x y coordinate node (vertices) intersection of links, located by x y coordinate links (arcs) indexed by from and to nodes (including centroid connnectors), attributes include lanes, capacity per lane, allowable modes turns indexed by at, from, and to nodes routes, (paths) indexed by a series of nodes from origin to destination. (e.g. a bus route) modes car, bus, HOV, truck, bike, walk etc.

Matrices

• scalar, - a single value, e.g. the price of gas
• vector (origin), - a column of numbers indexed by traffic zones, describing attributes at the origin of the trip (e.g. the number of households in a zone)
• vector (destination) - a row of numbers indexed by traffic zones, describing attributes at the destination
• full matrix (interaction) - a table of numbers, describing attributes of the origin-destination pair

Jargon

• SOV - single occupant vehicle
• HOV - high occupancy vehicle (2+, 3+, etc.)
• TAZ - transportation analysis zone or traffic analysis zone

Key Terms

• Rational Planning
• Transportation planning model
• Matrix, Full Matrix, Vector Matrix, Scalar Matrix
• Trip table
• Travel time matrix
• Origin, Destination
• Purpose
• Network
• Zone (Traffic Analysis Zone or Transportation Analysis Zone, or TAZ)
• External station or external zone
• Centroid
• Node
• Link
• Turn
• Route
• Path
• Mode

Variables

msXX - scalar matrix moXX - origin vector matrix mdXX - destination vector matrix mfXX - full vector matrix

Equations

$T{\text{'}}_j=T_j\frac{\sum _{i=1}^I{T}_i}{\sum _{j=1}^J{T}_j}$

$T_i=\sum _j{T}_{ij}$

$T_j=\sum _i{T}_{ij}$

$T_{ij}=K_i{K}_j{T}_i{T}_{j}f(C_{ij})$

$K_i=\frac{1}{\sum K_j{T}_{j}f(C_{ij})}$

$K_j=\frac{1}{\sum K_i{T}_{i}f\left(C_{ij}\right)}$

$P_m=\frac{e^{U_{mij}}}{\sum _{n=1}^m{e}^{U_{nij}}}\Rightarrow \sum _{n=1}^m{P}_n=1$

$U_m=f(C_{ijm,...})$

$AverageCost=\frac{TC}{Q}$

$MarginalCost=\frac{\partial TC}{\partial Q}$