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Dr. A.A. Trani Virginia Tech November 2009

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

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Dr. A.A. Trani Virginia Tech November 2009

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  1. Dr. A.A. TraniVirginia TechNovember 2009 Transportation Systems Analysis Modeling CEE 3604 Introduction to Transportation Engineering

  2. 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)

  3. 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

  4. The Basic Idea and Few Steps Predicts trips from zone to zone Trip Generation Distributes trips between zones Trip Distribution Splits trips among various modes of travel Mode Split/Choice Assigns trips among various transport networks Traffic Assignment

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

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

  7. 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

  8. 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

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

  10. 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)

  11. Sample Surveys Done in the US • National Household Travel Survey (NHTS) • American Travel Survey (ATS) http://nhts.ornl.gov/ http://www.bts.gov/publications/1995_american_travel_survey/

  12. 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)

  13. 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

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

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

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

  17. Gravity Model Formulation Tij = Pi Aj Fij / S (Aj Fij) where Pi = Productions at zone I Aj = Attractions at zone j Fij = Impedance of travel between I and j Reston Productions = 230,000 Attractions = 200,000 Distance = 20 km Distance = 10 km Washington DC Productions = 400,000 Attractions = 590,000 Fairfax Productions = 360,000 Attractions = 200,000

  18. 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) Fij = Cij exp(-alpha) or Cij = travel time Reston Distance = 20 km Travel time = 1 hour Distance = 10 km Travel time = 30 minutes Washington DC

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

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

  21. 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

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

  23. Mode Split Formulation Um = Utility of travel using mode m Zmj = travel characteristics (time and cost) Bm = Mode specific constant aj = Model parameter (from calibration) e = stochastic term with zero mean

  24. 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 Pm = probability that mode m is selected M = index over all modes included in the choice set

  25. 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

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

  27. Calculation of Utilities (Um) Uauto = 2.2 - 0.25 (5) - 0.02 (45) = 0.05 Utransit = 0.3 - 0.25 (1.5) - 0.02 (60) = -1.275 Reston Travel time (transit) = 60 minutes Travel cost (transit) = $1.50 Travel time (auto) = 45 minutes Travel cost (auto) = $5.00 (includes parking) Washington DC

  28. Estimate Probabilities of Travel by Mode m Uauto = 2.2 - 0.25 (5) - 0.02 (45) = 0.05 Utransit = 0.3 - 0.25 (1.5) - 0.02 (60) = -1.275

  29. 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

  30. Sensitivity of Logit Model Results

  31. 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

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

  33. Traffic Assignment (Final Step in Transportation Systems Planning) What routes are selected by travelers? Reston Route 1 Washington DC Route 3 Route 2 Link ij Road Network Fairfax

  34. 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

  35. Travel Time vs Demand Route 1 Route 2 Travel Time Total Route 1 Route 2 t Demand V1 V2 VT Traffic Volume

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

  37. 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

  38. 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

  39. Computational Example(Two-Zone Network) qf Freeway (2 lanes per side) Reston 6000 person-trips/hr qa Arterial Road (3 lanes per side) Washington DC Find qa and qf (volumes on arterial and freeway, respectively)

  40. 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

  41. 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

  42. 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)

  43. 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: travel times are not in equilibrium

  44. 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: travel times are in equilibrium System is In user-equilibrium

  45. 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)

  46. 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

  47. 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

  48. Mode Choice (Modal Split) Auto Air Taxi (SATS) Commercial Aviation Route1 Route2... Route n Include Airport Choice

  49. Multi-route Mode Split/Choice Model Utility function = Um = Bm + Saj zmj + e Probability of selecting mode m

  50. Auto Travel Time Estimation

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