Dr. A.A. Trani Virginia Tech November 2009

Dr. A.A. TraniVirginia Tech

November 2009

Transportation Systems Analysis Modeling

CEE 3604Introduction to Transportation

Engineering

Organization

• Discuss all four steps in transportation systems planning and modeling

• Discuss urban applications of the transportation systems modeling approach

• If you want to know more about this topic take a senior class called: Transportation Planning (CEE 4624)

Why do We Need a Transportation Systems Planning and Modeling?

• Because transportation engineers plan, design and construct facilities

• Because predicting how people travel is more difficult than predicting a “nuclear reaction at the molecular level” (true statement from Los Alamos Physicists)

• Keeping up with demand is difficult in constrained budget environments

The Basic Idea and Few Steps

Trip GenerationTrip Generation

Trip DistributionTrip Distribution

Mode Split/ChoiceMode Split/Choice

Traffic AssignmentTraffic Assignment

Predicts trips from Predicts trips from zone to zonezone to zone

Distributes trips Distributes trips between zonesbetween zones

Splits trips among Splits trips among various modes of various modes of traveltravel

Assigns trips among Assigns trips among various transport various transport networksnetworks

Transportation Planning Idea

RestonRestonPopulation = 60,000Population = 60,000Household Income = $55,000Household Income = $55,000Car Ownership = 2.1 (per house)Car Ownership = 2.1 (per house)

FairfaxFairfaxPopulation = 120,000Population = 120,000Household Income = $70,000Household Income = $70,000Car Ownership = 2.3 (per house)Car Ownership = 2.3 (per house)

Washington DCWashington DCPopulation = 230,000Population = 230,000Household Income = $45,000Household Income = $45,000Car Ownership = 1.3 (per house)Car Ownership = 1.3 (per house)

Road NetworkRoad Network

CentroidsCentroids

How Many Trips?RestonRestonInterzone trips = 230,000 person-tripsInterzone trips = 230,000 person-tripsIntrazone trips = 70,000 person-tripsIntrazone trips = 70,000 person-trips

FairfaxFairfaxInterzone trips = 360,000 person-tripsInterzone trips = 360,000 person-tripsIntrazone trips = 100,000 person-tripsIntrazone trips = 100,000 person-trips

Washington DCWashington DCInterzone trips = 400,000 person-tripsInterzone trips = 400,000 person-tripsIntrazone trips = 130,000 person-tripsIntrazone trips = 130,000 person-trips


Basic Definitions

• Intrazone trips – trips that stay within the zone where the person making the trips starts its journey

– A trip to a shopping center

– A trip to drop children to school

• Interzone trips – trips that extend beyond the zone where the person starts its journey

– Commuting trip to work

– Commuting trip to airport, train station to make a long-distance trip

• The definition of a zone in our context is a subarea of interest in our study with similar socio-economic characteristics or perhaps physical boundaries

What Drives the Number of Trips?

• Number of persons per household

• Number of cars per household

• Income levels

• Road infrastructure density (lane-km or road per square kilometer)

• Many others

Back to General Transportation Planning Method





Trip Generation

• Use of cross classification tables

• Provides a snapshot of potential trips per household

• Obtained through surveys

• Socio-economic parameters dictate trips

Trip Rate Table for Urban AreasTrip Rate Table for Urban Areas(units are trips per household per day)(units are trips per household per day)

Sample Surveys Done in the US

• National Household Travel Survey (NHTS)

• American Travel Survey (ATS)

http://www.bts.gov/publications/1995_american_travel_survey/

http://nhts.ornl.gov/

Trip Generation Output

• A trip matrix of trip Attractions (Aj) and trip Productions (Pi)

• The matrix predicts all trips produced and attracted to and from every zone

• Trip attractions depend on variables like employment, retail floor space, etc.

Attraction and Production Table for Sample AreaAttraction and Production Table for Sample Area(units are trip-persons per day)(units are trip-persons per day)

Techniques to Perform Trip Generation Models

• Cross classification trip rate tables for trip productions

• Regression analysis for trip attractions

Trip attractions = A + B * (employment)

where: A and B are regressions constants to be obtained using statistical regression techniques such as the least-squares method

Trip Distribution

• Answers the question:

• Where do the trips generated go?

RestonReston

FairfaxFairfaxWashington DCWashington DC

Distance = 10 kmDistance = 10 km


Trip Distribution

• Methods

• Gravity Model (just like the attraction between planets!)

• Growth factor models (Fratar Models)

RestonRestonProductions = 230,000Productions = 230,000Attractions = 200,000Attractions = 200,000

FairfaxFairfaxProductions = 360,000Productions = 360,000Attractions = 200,000Attractions = 200,000

Washington DCWashington DCProductions = 400,000Productions = 400,000Attractions = 590,000Attractions = 590,000



Gravity Model Formulation

RestonRestonProductions = 230,000Productions = 230,000Attractions = 200,000Attractions = 200,000

FairfaxFairfaxProductions = 360,000Productions = 360,000Attractions = 200,000Attractions = 200,000

Washington DCWashington DCProductions = 400,000Productions = 400,000Attractions = 590,000Attractions = 590,000



Tij = Pi Aj Fij / Tij = Pi Aj Fij / (Aj Fij) (Aj Fij)wherewhere

Pi = Productions at zone IPi = Productions at zone I

Aj = Attractions at zone jAj = Attractions at zone j

Fij = Impedance of travel between I and jFij = Impedance of travel between I and j

What is the Impedance (Fij)?• A common term to state that there is resistance to

travel between two zones

• The resistance is proportional to the travel time between the zones (time ij)

RestonReston

Washington DCWashington DC

Distance = 10 kmDistance = 10 kmTravel time = 30 minutesTravel time = 30 minutes

Distance = 20 kmDistance = 20 kmTravel time = 1 hourTravel time = 1 hour

Fij = Cij exp(-alpha) orFij = Cij exp(-alpha) or

Cij = travel timeCij = travel time

Output of Trip Distribution

• A trip interchange matrix (Tij)

• How many trips go from zone I to zone j

Trip Mode Split

• Estimates the number of trips made taking a specific mode of transportation

• For the sample area, travelers will have choices of mode:

– Bus

– Auto

– Rapid transit

– Walk

– Bicycle

Mode Split or Mode Choice

• Out-of-pocket costs (Cost ij via mode k) is important

• Travel time (time ij via mode k) is important

RestonReston


Travel time (transit) = 1 hourTravel time (transit) = 1 hourTravel cost (transit) = $1.50Travel cost (transit) = $1.50

Travel time (auto) = 45 minutesTravel time (auto) = 45 minutesTravel cost (auto) = $5.00 (includes parking)Travel cost (auto) = $5.00 (includes parking)

How many trips by auto?How many trips by auto?How many by transit?How many by transit?

Mode Split Formulation

ZZmj mj = travel characteristics (time and cost)= travel characteristics (time and cost)

mm = Mode specific constant = Mode specific constant

jj = Model parameter (from calibration) = Model parameter (from calibration)

= stochastic term with zero mean= stochastic term with zero mean

UUm m = Utility of travel using mode m= Utility of travel using mode m

Calculating Probabilities of Travel by a given Mode (Logit Model)

• W. McFadden (Nobel Price winner 30 years ago) developed a fundamental model called Logit Model to predict people’s choice in economic terms

• Basis for today’s logit models used in transportation

PPmm = probability that mode = probability that mode

m is selectedm is selectedM = index over all modes M = index over all modes included in the choice setincluded in the choice set

Example of Mode Split Equation

• A mode split has been calibrated using the maximum likelihood technique (an advanced statistical method)

• The following equation has been obtained as follows:

where: C is the out-of-pocket cost ($), T is the travel time (minutes) and the values of the mode specific constants (betas) are:

Transit = 0.30Transit = 0.30

Auto = 2.2Auto = 2.2

Back to the Original Problem

RestonReston


Travel time (transit) = 1 hourTravel time (transit) = 1 hourTravel cost (transit) = $1.50Travel cost (transit) = $1.50


How many trips by auto?How many trips by auto?How many by transit?How many by transit?

Calculation of Utilities (Um)

RestonReston


Travel time (transit) = 60 minutesTravel time (transit) = 60 minutesTravel cost (transit) = $1.50Travel cost (transit) = $1.50


UUautoauto = 2.2 - 0.25 (5) - 0.02 (45) = 2.2 - 0.25 (5) - 0.02 (45) == 0.05 0.05

UUtransittransit = 0.3 - 0.25 (1.5) - 0.02 (60) = 0.3 - 0.25 (1.5) - 0.02 (60) == -1.275 -1.275

Estimate Probabilities of Travel by Mode m

UUautoauto = 2.2 - 0.25 (5) - 0.02 (45) = 2.2 - 0.25 (5) - 0.02 (45) == 0.05 0.05

UUtransittransit = 0.3 - 0.25 (1.5) - 0.02 (60) = 0.3 - 0.25 (1.5) - 0.02 (60) == -1.275 -1.275

Interpretation of Results

• The probability that a traveler from Reston to DC uses auto is 79%

• The probability that a traveler from Reston to DC uses transit is 21%

• Why is this important?– Because as a transportation engineer you have to

plan how many lanes of highway should you provide between Reston and DC

– You also need to figure out how many transit vehicles will be needed and how often they should be scheduled

Sensitivity of Logit Model Results

Interpretation of Results

• If the auto cost is $1.00 the model predicts a ridership of 9% for the bus (compared to 21%)

– This is a bargain in using the auto mode

– the bust still captures a small fraction of the riders

• If the auto cost is $20.00 the model predicts a ridership of 9% for the auto mode

– This provides incentives for riders to take the bus

– The cost of auto is quite high and forces many decision makers to “walk away” from auto mode

Traffic Assignment (Final Step in Transportation Systems Planning)


Route 1Route 1

Route 2Route 2Route 3Route 3

RestonReston


FairfaxFairfax

What routes are selectedWhat routes are selectedby travelers?by travelers?

Link ijLink ij

How do Travelers select Routes?

• Consideration of travel time and congestion in transportation links

• Travelers tend to take routes that minimize travel time

• After a long period of time traveling a network, a traveler selects routes that reach equilibrium for that traveler

– For example, if two routes are feasible to take me from an origin (say Reston) to a destination (say DC), I will select these routes in a way that gains in travel time are not possible once we load the network

Travel Time vs Demand

Travel TimeTravel Time

Traffic VolumeTraffic Volume

Route 1Route 1 Route 2Route 2 TotalTotal

tt

VV11 VV22 VVTT

DemandDemand

Route 1Route 1

Route 2Route 2

Calculation of Travel Times

• Use any of the known traffic flow models

• For example:

• Greenshield’s model

Travel TimeTravel Time

FlowFlow

SpeedSpeed

Other Ways to Find Travel Times on Highway Links

• Use of empirical data is useful in finding travel times if the model is suspected not follow Greenshield or Greenberg models

Other Ways to Find Travel Times

• Use of empirical data is useful in finding travel times if the model is suspected not to follow Greenshield or Greenberg models

Computational Example(Two-Zone Network)

RestonReston


FreewayFreeway(2 lanes per side)(2 lanes per side)

ArterialArterialRoad (3 lanes per side)Road (3 lanes per side)

6000 person-trips/hr6000 person-trips/hr

Find qFind qaa and q and qf f (volumes on arterial and freeway, (volumes on arterial and freeway,

respectively)respectively)

qqaa

qqff

Sample Problem (Traffic Assignment)

• Two zones are linked by a simple highway network with network characteristics as shown:

• Freeway– vf_freeway = 110; % free flow speed in kilometers per hour

– kj_freeway = 75; % jamming density in vehicles per km-lane

– d_freeway = 30; % length of freeway (km)

– N_freeway = 2; % number of lanes per side

• Arterial road– vf_arterial = 90; % free flow speed in kilometers per hour

– kj_arterial = 80; % jamminf density in vehicles per km-lane

– d_arterial = 33; % length of arterial (km)

– N_arterial = 3; % number of lanes on arterial road

Problem

• Assign traffic so that volumes on the freeway and the arterial road reach equilibrium assignment

• Equilibrium means: if a travelers switches from a link to another one, there is no gain in travel time

• In other words, assign volumes so that travel times on the freeway and the arterial are the same

Solution: Use Traffic Assignment Simulator (traffic_assignment.m)

• Simple Matlab script to ease computations

• Uses Greenshield’s traffic flow model to estimate travel time

• Inputs:– Trips between zones (person trips)

– Vehicle occupancy (passengers per vehicle)

• Outputs: – Freeway Speed (km/hr)

– Freeway Travel Time (minutes)

– Freeway Volume per lane (veh/hr)

– Total Freeway Volume(veh/hr)

– Freeway Capacity (veh/hr)

– Freeway Number of Lanes (lanes)

Running traffic_assignment.m• The program requires that you enter the percent of the trips to be

assigned to each link

• Try the following parameters: 6000 person-trips, vehicle occupancy = 1.2 persons/veh and 60% of trips assigned to the freeway

– Freeway Speed (km/hr) 83.7228

– Freeway Travel Time (minutes) 21.4995

– Freeway Volume per lane (veh/hr) 1500

– Total Freeway Volume(veh/hr) 3000

– Freeway Capacity (veh/hr) 4125

–

– Arterial Speed (km/hr) 80.7071

– Arterial Travel Time (minutes) 24.5331

– Arterial Volume per lane (veh/hr) 666.6667

– Total Arterial Volume(veh/hr) 2000

– Arterial Capacity (veh/hr) 5400

Note:Note:travel timestravel timesare not in are not in equilibriumequilibrium

Running traffic_assignment.m• Assign more traffic to the freeway to balance the travel times

• Try the following parameters: 6000 person-trips, vehicle occupancy = 1.2 persons/veh and 70.7% of trips assigned to the freeway

– Freeway Speed (km/hr) 75.8006

– Freeway Travel Time (minutes) 23.7465

– Freeway Volume per lane (veh/hr) 1767.5

– Total Freeway Volume(veh/hr) 3535

– Freeway Capacity (veh/hr) 4125

–

– Arterial Speed (km/hr) 83.4139

– Arterial Travel Time (minutes) 23.7371

– Arterial Volume per lane (veh/hr) 488.3333

– Total Arterial Volume(veh/hr) 1465

– Arterial Capacity (veh/hr) 5400

Note:Note:travel timestravel timesare in are in equilibriumequilibrium

System isSystem isIn user-equilibriumIn user-equilibrium

Applications to Intercity Travel

• Intercity travelers are faced with similar decisions as urban travelers

• Mode choices are based on attributes of the mode:

– Travel time

– Travel cost

– Route convenience

– Trip purpose, etc.

• Describe the study done for NASA in the period 2001-2006

• Small Aircraft Transportation System (SATS)

On-demand (Air Taxi) Air Transportation Assumptions

• Assumptions:

– SATS aircraft is very light jet vehicle• High mission reliability

• High perceived level of safety

• 350 knots cruise speed

• All-weather (pressurized)

– SATS aircraft cost (VT Eclipse 500 PW610F model)• Baseline cost $1.50 per seat-mile

• 60% load factor

• 2 professional pilots

– SATS airport set (3,364 public airports, paved runways > 3kft, all weather equipped)

– SATS access and egress times driven by airport set selected

Assumptions (continuation)

– Commercial airline service network (year 2000 - 419 airports in the continental U.S.)

– Commercial air fares based on 2000 Department of Transportation data (12 million fares)

– No constraints in pilot production and aircraft production

– No constraints in ATC/ATM capacity

Mode Choice (Modal Split)

Commercial Aviation

Route1

Air Taxi (SATS) Auto

Route2... Route nInclude Airport ChoiceInclude Airport Choice

Multi-route Mode Split/Choice Model

Probability of selecting Probability of selecting mode mode mm

Utility functionUtility function = = UUmm = = mm + + jj z zmjmj + +

Auto Travel Time Estimation

Airport-to-Airport Travel Times

450 commercial airports450 commercial airports2001 Official Airline Guide2001 Official Airline Guide

Airline Network Structure

Detailed Trip Analysis

Air Taxi (SATS) Travel Time Map

Cost of Service (Air Modes)

• Airline fares from 12 million fares (DB1B DOT data)Airline fares from 12 million fares (DB1B DOT data)• SATS cost (Virginia Tech projections)SATS cost (Virginia Tech projections)

Traffic Assignment (Which Route?)

• Aircraft vs auto trajectoriesAircraft vs auto trajectories

I-95 RouteI-95 RouteA1-A RouteA1-A Route

Airway RouteAirway Route

Market Share Screen

Market Share By Segment

SATS Very Light JetSATS Very Light Jet$1.50 per seat-mile$1.50 per seat-mile

SATS Trip Demand in NE Corridor (Using 2000 Census Socio-Economic Data)

SATS Very Light JetSATS Very Light Jet$1.50 per seat-mile$1.50 per seat-mile3,416 airports3,416 airports

SATS Demand at Airports(Using 2000 Census Socio-Economic Data)

SATS Very Light JetSATS Very Light Jet$3.50 per seat-mile$3.50 per seat-mile3,416 airports3,416 airports

Fastest Travel Times by Mode (from Grafton Co., NH)

SATS Single-Engine AircraftSATS Single-Engine Aircraft200 knots cruise speed200 knots cruise speed700 mile range700 mile range

Model Output

Distance (statute miles)

Automobile

Airline

SATS

$1.50/seat-mile

Mar

ket

Sh

are

(%)

Low Income (<$25K)

Medium Income ($25-50K)

Medium Income ($50-100K)

High Income (> $100K)

National-level Demand Statistics by Distance (SATS @ $1.50 per seat-mile)

One-way Distance (statute miles)One-way Distance (statute miles)

Per

son

-tri

ps

Per

son

-tri

ps

SATS ModeSATS Mode

Airline ModeAirline Mode

Auto ModeAuto Mode

Market Share of SATS(Business Trips Only)

Annual Intercity Business Trips in the U.S. (all modes) = 225 millionAnnual Intercity Business Trips in the U.S. (all modes) = 225 million

2.7% Market Share2.7% Market Share



Nation-wide Mobility (Hours Saved)

(Total Hours Traveled Without SATS – Total Hours Traveled With SATS)

Fuel Used by SATS

Fuel Used by Airlines = 44,000,000,000 kg.

Increased Adoption of SATS With Increased Household Income

Frequency Plot of Total Travel Time Savings

SATS Cost = $1.50 per seat-mileSATS Cost = $1.50 per seat-mile3091 counties in the US3091 counties in the US

Average Speed Gains (by Trip)

Average Speed Gains per Trip (Miles per Hour)Average Speed Gains per Trip (Miles per Hour)

0.0 to 0.10.0 to 0.1

0.5 to 0.60.5 to 0.6

0.9 to 1.00.9 to 1.0

1.5 to 1.71.5 to 1.7

2.0 to 3.02.0 to 3.0

4.0 to 5.04.0 to 5.0

SATS Cost = $1.50 per seat-mileSATS Cost = $1.50 per seat-mile

Total Travel Time Savings


Per Capita Travel Time Savings


Dr. A.A. Trani Virginia Tech November 2009

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