Dr. A.A. Trani Virginia Tech November 2009 Transportation Systems Analysis Modeling CEE 3604 Introduction 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 Generation Trip Distribution Mode Split/Choice Traffic Assignment Predicts trips from zone to zone Distributes trips between zones Splits trips among various modes of travel Assigns trips among various transport networks

Transportation Planning Idea Reston Population = 60,000 Household Income = $55,000 Car Ownership = 2.1 (per house) Fairfax Population = 120,000 Household Income = $70,000 Car Ownership = 2.3 (per house) Washington DC Population = 230,000 Household Income = $45,000 Car Ownership = 1.3 (per house) Road Network Centroids

How Many Trips? Reston Interzone trips = 230,000 person-trips Intrazone trips = 70,000 person-trips Fairfax Interzone trips = 360,000 person-trips Intrazone trips = 100,000 person-trips Washington DC Interzone trips = 400,000 person-trips Intrazone trips = 130,000 person-trips Road Network

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 Trip Distribution Mode Split/Choice Traffic Assignment

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 Areas (units are trips per household per day)

Sample Surveys Done in the US National Household Travel Survey (NHTS) American Travel Survey (ATS)

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 Area (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

Back to General Transportation Planning Method Trip Generation Trip Distribution Mode Split/Choice Traffic Assignment

Trip Distribution Answers the question: Where do the trips generated go? Reston Fairfax Washington DC Distance = 10 km Distance = 20 km

Trip Distribution Methods Gravity Model (just like the attraction between planets!) Growth factor models (Fratar Models) Reston Productions = 230,000 Attractions = 200,000 Fairfax Productions = 360,000 Attractions = 200,000 Washington DC Productions = 400,000 Attractions = 590,000 Distance = 10 km Distance = 20 km

Gravity Model FormulationReston Productions = 230,000 Attractions = 200,000 Fairfax Productions = 360,000 Attractions = 200,000 Washington DC Productions = 400,000 Attractions = 590,000 Distance = 10 km Distance = 20 km Tij = Pi Aj Fij /  (Aj Fij) where Pi = Productions at zone I Aj = Attractions at zone j Fij = 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) Reston Washington DC Distance = 10 km Travel time = 30 minutes Distance = 20 km Travel time = 1 hour Fij = Cij exp(-alpha) or Cij = travel time

Output of Trip Distribution A trip interchange matrix (Tij) How many trips go from zone I to zone j

Back to General Transportation Planning Method Trip Generation Trip Distribution Mode Split/Choice Traffic Assignment

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 Reston Washington DC Travel time (transit) = 1 hour Travel cost (transit) = $1.50 Travel time (auto) = 45 minutes Travel cost (auto) = $5.00 (includes parking) How many trips by auto? How many by transit?

Mode Split Formulation Z mj = travel characteristics (time and cost)  m = Mode specific constant  j = Model parameter (from calibration)  = stochastic term with zero mean U 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 P m = probability that mode m is selected m is selected M = index over all modes included in the choice set included 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 = 0.30 Auto = 2.2

Back to the Original Problem Reston Washington DC Travel time (transit) = 1 hour Travel cost (transit) = $1.50 Travel time (auto) = 45 minutes Travel cost (auto) = $5.0 (includes parking) How many trips by auto? How many by transit?

Calculation of Utilities (U m )Reston Washington DC Travel time (transit) = 60 minutes Travel cost (transit) = $1.50 Travel time (auto) = 45 minutes Travel cost (auto) = $5.00 (includes parking) U auto = (5) (45) = 0.05 U transit = (1.5) (60) =

Estimate Probabilities of Travel by Mode m U auto = (5) (45) = 0.05 U transit = (1.5) (60) =

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

Back to General Transportation Planning Method Trip Generation Trip Distribution Mode Split/Choice Traffic Assignment

Traffic Assignment (Final Step in Transportation Systems Planning) Road Network Route 1 Route 2 Route 3 Reston Washington DC Fairfax What routes are selected by travelers? Link 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 Time Traffic Volume Route 1 Route 2 Total t V1V1V1V1 V2V2V2V2 VTVTVTVT Demand Route 1 Route 2

Calculation of Travel Times Use any of the known traffic flow models For example: Greenshield’s model Travel Time Flow Speed

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) Reston Washington DC Freeway (2 lanes per side) Arterial Road (3 lanes per side) 6000 person-trips/hr Find q a and q f (volumes on arterial and freeway, respectively) qaqaqaqa qfqfqfqf

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) –Freeway Travel Time (minutes) –Freeway Volume per lane (veh/hr) 1500 –Total Freeway Volume(veh/hr) 3000 –Freeway Capacity (veh/hr) 4125 – –Arterial Speed (km/hr) –Arterial Travel Time (minutes) –Arterial Volume per lane (veh/hr) –Total Arterial Volume(veh/hr) 2000 –Arterial Capacity (veh/hr) 5400 Note: travel times are not in equilibrium

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) –Freeway Travel Time (minutes) –Freeway Volume per lane (veh/hr) –Total Freeway Volume(veh/hr) 3535 –Freeway Capacity (veh/hr) 4125 – –Arterial Speed (km/hr) –Arterial Travel Time (minutes) –Arterial Volume per lane (veh/hr) –Total Arterial Volume(veh/hr) 1465 –Arterial Capacity (veh/hr) 5400 Note: travel times are in equilibrium System is In 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 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 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 n Include Airport Choice

Multi-route Mode Split/Choice Model Probability of selecting mode m Utility function = U m =  m +   j z mj + 

Auto Travel Time Estimation

Airport-to-Airport Travel Times 450 commercial airports 2001 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 trajectories Aircraft vs auto trajectories I-95 Route A1-A Route Airway Route

Market Share Screen

Market Share By Segment SATS Very Light Jet $1.50 per seat-mile

SATS Trip Demand in NE Corridor (Using 2000 Census Socio-Economic Data) SATS Very Light Jet $1.50 per seat-mile 3,416 airports

SATS Demand at Airports (Using 2000 Census Socio-Economic Data) SATS Very Light Jet $3.50 per seat-mile 3,416 airports

Fastest Travel Times by Mode (from Grafton Co., NH) SATS Single-Engine Aircraft 200 knots cruise speed 700 mile range

Model Output Distance (statute miles) Automobile Airline SATS $1.50/seat-mile Market Share (%) Low Income (<$25K) Medium Income ($25-50K) Medium Income ($50-100K) High Income (> $100K)

National-level Demand Statistics by Distance $1.50 per seat-mile) One-way Distance (statute miles) Person-trips SATS Mode Airline Mode Auto Mode

Market Share of SATS (Business Trips Only) Annual Intercity Business Trips in the U.S. (all modes) = 225 million 2.7% Market Share 1.0% Market Share 0.5% 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-mile 3091 counties in the US

Average Speed Gains (by Trip) Average Speed Gains per Trip (Miles per Hour) 0.0 to to to to to to 5.0 SATS Cost = $1.50 per seat-mile

Total Travel Time Savings SATS Very Light Jet $1.50 per seat-mile

Per Capita Travel Time Savings SATS Very Light Jet $1.50 per seat-mile