Fundamentals of Transportation/Modeling

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

Modeling is a means for representing reality in an abstracted way. Your mental models are your world view: your outlook on life, and the world. The world view is your internal model of how the world works; it is employed every time you make a prediction: what do you expect, what is a surprise. The expression “Where you stand depends on where you sit” epitomizes this idea. Your world view is shaped by your experience and your position.

When modeling, the issue of Point of View should be considered. It must be clear who (and what) the results are for. If you are modeling for personal pleasure, it will naturally reflect your own worldview, but if you are working for an employer or client, their point of view must also be considered, if the inputs or results deviate significantly from their worldview, they may adapt their worldview, but more likely will dismiss the model.

Modeling can be conducted both for subjective advocacy and for objective analysis. The same methods may be employed in either, and the ethical modeler will produce the same results in either case, but they may be used differently.

Why Model?

There are a variety of reasons to model. Modeling helps

gain insight into complex situations by understanding simpler situations resembling them
optimize the use of resources in building or maintaining systems
operate system, particularly by testing alternative operational scenarios
educate and provide experience for model-builders
provide a platform for testing contending ideas and use in negotiations.

Particular applications in transportation include:

Forecasting traffic
Testing scenarios (alternative land uses, networks, policies)
Planning projects/corridor studies
Regulating land use: Growth management/public facility adequacy
Managing complexity, when eyeballs are insufficient, (different people have different intuitions)
Understanding travel behavior
Influencing decisions
Estimating traffic in the absence of data

Developing Models

As an engineer, economist, or planner you may be given a model to use. But that model was not spontaneously generated, it came from other engineers, economists, or planners who undertook a series of steps to translate raw data into a tool that could be used to generate useful information.

The first step, specification, tells us what depends on what (the number of trips leaving a zone may depend on the number of households). The estimation step tells us how strong these relationships mathematically are, (each household generates two trips in the peak hour). Implementation takes those relationships and puts them into a computer program. Calibration looks at the output of the computer program and compares it to other data, if they don't match exactly, adjustments to the models may be made. Validation compares the results to data at another point in time. Finally the model is applied to look at a project (e.g. how much traffic will use Granary Road after Washington Avenue is closed to traffic).

Specification:
- $y=f(X)\,\!$
Estimation:
- $y=mX+b\,\!$ ; m=1, b=2
Implementation
- If Z > W, Then $y=mX+b\,\!$
Calibration
- $y_{predicted}+k=y_{observed}\,\!$
Validation
- $y_{predicted1990}+k=y_{observed1990}\,\!$
Application

Specification

When building a model system, numerous decisions must be made. These are discussed below:

Types of Models

There are numerous types of models, a short list is below. Each has different applicability, multiple methods may be used in pursuit of the same question, sometimes they are complementary, and sometimes competitive techniques.

Network analysis
Linear Programming
Nonlinear Programming
Simulation
Deterministic queuing
Probabilistic queuing
Regression
Neural Nets
Genetic Algorithm
Cost/ Benefit Analysis
Life-cycle costing
System Dynamics
Control Theory
Difference Equations
Differential Equations
Probabilistic Risk Assessment
Supply/Demand Equilibrium
Game Theory
Statistical Decision Theory
Markov Models
Cellular Automata
Etc.

Model Trade-offs

Building a model requires trading-off time and resource constraints. One could always be more detailed, more accurate, or more comprehensive if resources were not constrained. However, the following must also be considered.

Money,
Data,
Computation,
Labor,
Ease of Use,
Convincing (e.g. Graphic Displays),
Extendable,
Evidence of Model Benefits,
Measuring Model Success

Organization of Model System

Hierarchy of Models
Centralized vs. Decentralized (Optimization (Global) vs. Agent, Local Optimization)

Time

Time Frame
Static vs. Dynamic
Real Time vs. Offline
Short Term vs. Long Term (Partial vs. General Equilibrium)
Proactive vs. Reactive (Predictive vs. Responsive)

Space

Scale/Detail
Spatial Extent
Boundaries (Boundary Effects)
Macroscopic vs. Microscopic (Zones, Flows vs. Individuals, Vehicles)

Process

Stochastic vs. Deterministic
Linear vs. Nonlinear
Continuous vs. Discrete
Numerical Simulation vs. Closed Form Solution
Equilibrium vs. Disequilibrium

Type

Behavioral vs. Aggregate Model
Physical vs. Mathematical Models

Solution Techniques

When solving the model, the system as a whole must be understood. Several questions arise:

Does the solution exist?
Is the solution unique?
Is the solution feasible?

Solution techniques often trade-off accuracy vs. speed. Some solution techniques may only guarantee a local optima, while others (such as brute force techniques) can guarantee a global optimum, but may be much slower.

“Four-Step” Urban Transportation Planning Models

We want to answer a number of related questions (who, what, where, when, why, and how):

Who is traveling or what is being shipped?
Where are the origin and destination of those trips, shipments?
When do those trips begin and end (how long do they take, how far away are the trip ends)?
Why are the trips being made, what is their purpose?
How are the trips getting there, what routes or modes are they taking?

If we know the answers to those questions, we want to know what are the answers to those questions a function of?

Cost: Money, Time spent on the trip,
Cost: Money and Time of alternatives.
Benefit (utility) of trip (e.g. the activity at the destination)
Benefit of alternatives

The reason for this is to understand what will happen under various circumstances:

How much “induced demand” will be generated if a roadway is expanded?
How many passengers will be lost if bus services are cut back?
How many people will be “priced off” if tolls are implemented?
How much traffic will a new development generate?
How much demand will I lose if I raise shipping costs to my customers?

In short, for urban passenger travel, we are trying to predict the number of trips by:

Origin Activity,
Destination Activity,
Origin Zone,
Destination Zone,
Mode,
Time of Day, and
Route.

This is clearly a multidimensional problem.

In practice, the mechanism to do this is to employ a "four-step" urban transportation planning model, each step will be detailed in subsequent modules. These steps are executed in turn, though there may be feedback between steps:

Trip Generation - How many trips $T_{i}$ or $T_{j}$ are entering or leaving zone $i$ or $j$
Trip Distribution or Destination Choice - How many trips $T_{ij}$ are going from zone $i$ to zone $j$
Mode Choice - How many trips $T_{ijm}$ from $i$ to $j$ are using mode $m$
Route Choice - Which links are trips $T_{ijmr}$ from $i$ to $j$ by mode $m$ using route $r$