basic_demand_estimation

basic_demand_estimation - Demand in Air Transportation...

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Unformatted text preview: Demand in Air Transportation Systems Drs. A. Trani and D. Teodorovic Department of Civil and Environmental Engineering June 9-12, 2003 Virginia Tech 1 of 81 Basics Facts • Air transportation demand is related to the socio-economic characteristics of the region in question • Demand for air transportation services is greater in more developed regions of the world • The noted dependencies between the demand for air transportation services and the socio-economic characteristics of the region are used in the air transportation planning process • This process entails the planning of airports, needed transportation facilities, route networks, and planning the network of airways Virginia Tech 2 of 81 Basic Air Transportation Demand Models • As noted by Kanafani (1983), models of air transportation demand can be divided into: - Macroscopic models, and - Microscopic models • Macroscopic models are used to estimate the development of air transportation in a certain country or region. Typical indicators are flights, passengers, cargo, etc. • Microscopic models estimate air transportation demand between two cities. Typical indicators are the passenger traffic in a specific Origin-Destination (OD) route and the number of passengers in each class when there are various tariffs on a route. Virginia Tech 3 of 81 Basic Air Transportation Demand Models • Another classification of demand models used in air transportation relates to the number of modes modeled: - Multimode models, and - Unimode models • Multimode models attempt to estimate the mode split between air transportation submodes and other competing models of transportation. Suitable when more than one mode of transportation is present in the market to be studied • Unimode models consider a single model in the analysis of air transport demand. • Various classifications can be combined (i.e., a multimode, macroscopic model can be developed) Virginia Tech 4 of 81 Basic Air Transportation Demand Models • A final way to understand of demand models used in air transportation relates to the number of steps needed in the evaluation of the demand function: - Single step models (or direct demand models), and - Multi-step models • Single step models obtain the demand function using one or several explanatory variable in a single step procedure • Multi-step models develop air transportation demand function in multiple steps starting with a basic intercity demand function and then applying a suitable mode split analysis to derive air transport demand Virginia Tech 5 of 81 Where do People Live Around Airports? 1 3346 Airports 0.9 0.8 Towered Airports (474) Percent of Population 0.7 Hub Airports (135) 0.6 0.5 Large Hub Airports (30) 0.4 TextEnd 0.3 Census 1990 and 2000 Data with 61,224 tracts in NAS 0.2 0.1 0 0 10 20 30 40 50 60 Distance to Airport (statute miles) Virginia Tech 70 80 90 100 6 of 81 Basics on the American Travel Survey Find information about ATS at:http://transtats.bts.gov • Excellent source of information to understand travel patterns in the U.S. - 370,000 household trips - 540,000 person trips - 80,000 households interviewed • Each survey point has 300+ fields of information • ATS data is imperfect but some trends and calibration factors can be obtained from the data Virginia Tech 7 of 81 How do People Travel (American Travel Survey)? Percent Travelers by Air (%) 540,000 person trips 80,000 households 100 90 80 70 60 50 40 30 20 10 0 1.8 1.6 1.4 3500 3000 1.2 x 10 5 2500 1 2000 0.8 1500 0.6 5 $) Household Income (10 $) 1000 0.4 500 0.2 0 Virginia Tech One-Way Trip Distance (miles) 8 of 81 Observations from ATS 1995 Data: ATS 1995 100 Percent Travelers by Air (%) 90 80 70 60 50 High Income 40 30 Medium Income 20 Low Income 10 0 0 500 1000 1500 2000 2500 3000 3500 One-Way One-Way Trip Distance (miles) Virginia Tech 9 of 81 Resistance to Travel is a Function of Distance 90 Percent Travelers by Air (%) 80 1000 mile trip 70 60 750 mile trip 50 40 500 mile trip 30 20 10 0.2 0.4 0.6 0.8 1 1.2 1.4 Household Income level (105 $) $) Virginia Tech 1.6 1.8 5 x 10 10 of 81 Observations of Household Income in the U.S. Census 2000 Data Percent of Population 100 90 80 70 60 50 40 30 20 10 0 0 0.5 1 1.5 2 2.5 3 x 10 5 Household Income ($) Virginia Tech 11 of 81 Sample Results for Intercity Trips in the U.S. Virginia Tech 12 of 81 What we are Trying to Answer The main goal of the analysis is development of reliable models that can provide various information to decision makers related to some of the following questions: • How many passengers will use air transportation for business and/or leisure trips at the airport? • What is the expected number of operations (take-offs and landings) at the airport? • What is appropriate fleet size? • What is appropriate aircraft mix in the fleet? • What types of airport investments (new runways, air traffic control modernization, new aircraft types) will improve the regional, national system? Virginia Tech 13 of 81 Latitude (degrees) Sample OD Pairs (> 400,000 passengers/year) Longitude (degrees) Virginia Tech 14 of 81 Latitude (degrees) Sample OD Pairs (> 200,000 passengers/year) Longitude (degrees) Virginia Tech 15 of 81 Latitude (degrees) Sample OD Pairs (>100,000 passengers/year) Longitude (degrees) Virginia Tech 16 of 81 Demand Estimation Procedures There are several ways to estimate demand for air transportation services: • Expert opinion • Trend extrapolation techniques • Trip rate tables • Market share and market definition models • Econometric models Virginia Tech 17 of 81 Expert Opinion • Useful when no other information is available to make predictions • Relies on focus group analysis (a panel of experts) • Intuition is the basis for estimating demand • Relies on past trends but applies subjective evaluations Virginia Tech 18 of 81 Trend Extrapolation Techniques • Use of regression models (linear and nonlinear) to assess the demand in the future • Long-term trend behaviors are most frequently modeled using linear, quadratic or exponential functions We denote time by t, and the number of air passengers that changes over time by D(t). Trend models of the air transportation demand D(t) in a period t are described mathematically by: D(t ) = a+b⋅t D(t) = a ⋅ b D(t) = k ⋅ a t b Linear model Exponential Model t Gompertz Model Virginia Tech 19 of 81 Other Trend Extrapolation Models k D ( t ) = --------------------------- Logistic Model – at 1+b⋅e • These model can be calibrated using historical data about the airport facility or region. In most cases a transformation using logarithms is needed to simplify the analysis. • Once a logarithmic transformation has been done we can use standard regression techniques to the find coefficients of the model Virginia Tech 20 of 81 Example Transformation Suppose that we have data of demands and time and would like to use the exponential model: D(t) = a ⋅ b t Apply a logarithmic transformation to get, log D ( t ) = log ( a ) + t ⋅ log ( b ) The new equation is a linear model of the form, y = A + Bt This new model can be studied easily using standard linear regression techniques Virginia Tech 21 of 81 Example with Data Data on passenger traffic at the Belgrade Airport, Serbia, from 1962-1978 Year Number of Passengers Year Number of Passengers 1962 220,726 1971 1,036,311 1963 282,873 1972 1,155,166 1964 329,619 1973 1,434,454 1965 405,191 1974 1,688,247 1966 335,999 1975 2,020,291 1967 399,066 1976 2,047,016 1968 462,919 1977 2,280,972 1969 602,257 1978 2,660,670 1970 838,156 Virginia Tech 22 of 81 Graphical Analysis of Trend Models Demand (t) Exponential k Logistic Linear Time (yrs) Virginia Tech 23 of 81 Demand Function Example Given data representing demand at an airport (D(t)) we would like to derive the best nonlinear model to fit the data to a model of the form: D(t) = k ⋅ a b t Gompertz Model k D ( t ) = --------------------------- Logistic Model – at 1+b⋅e Virginia Tech 24 of 81 Data Given: data pairs for time and Demand (D(t)) Find: the best nonlinear regression equation that correlates with the data pairs (t, D(t)) Data File: airport2.xls Virginia Tech 25 of 81 Data Set Plot 8000000 7000000 6000000 5000000 Series1 4000000 3000000 2000000 1000000 0 1970 1975 1980 1985 1990 Virginia Tech 1995 2000 2005 26 of 81 Setup of Solver Procedure The idea is to minimize the Sum of Square Errors of the data and an assumed regressions equation • Create a column with values of the assumed regression equation • Leave parameters of the model as cells in the spreadsheet (Excel will iterate among any number of parameters) • Minimize the Sum of the Square Errors (SSE) of the data • You are done! Virginia Tech 27 of 81 Setup of Solver Virginia Tech 28 of 81 Setup of Solver Cells to Iterate Cell to Minimize Virginia Tech 29 of 81 Solution Set and Original Data 8000000 7000000 6000000 5000000 Series1 4000000 Series2 3000000 2000000 1000000 0 1970 1975 1980 1985 1990 Virginia Tech 1995 2000 2005 30 of 81 General Remarks • The logistic curve is perhaps the best representation of the capacity constraints that an airport gets to experience over time • The exponential model is good to approximate short-term behavior of the demand function • The linear model is the easiest to use, but the results in the long term are usually unacceptable Virginia Tech 31 of 81 Trip Rate Approach • The idea is to predict trips or demand using socio-economic variables of the region - Trips by air = f (income, population) • Socio-economic variables such as income, car ownership, education level, number of industries and other can represent the levels of activity for air transportation • This approach is difficult to implement over long periods of time unless an economic model exists for the region of interest • Watch out for the assumptions in the economic model Virginia Tech 32 of 81 Trip Rate Table Approach 8 Person-trips Per Year (per Household) 6 Given : Socio-economic characteristics for each county (for all states) 4 2 Predict : a) Number of trips produced per household/year for various income levels b) Trips attracted to a county 0 8 6 10 8 4 Years After High School Use: Trip rate tables Virginia Tech 6 2 4 0 2 x 10 4 Annual Household Income ($) 33 of 81 Example of Trip Rate Tables to Predict GA Demand Virginia Tech 34 of 81 Market Share Models • Start with a national-level picture of the share of an airport • Assume that over time, share of passengers can change or remain the same as before • For example: - Atlanta handles 5% of the enplanements of the US per year (695 million in 2000) - if the number of enplanements in the US is estimated, then ATL would continue capturing 5% of the total • These have to use stated preference surveys when studying multi-airport systems Virginia Tech 35 of 81 Econometric Models • Use of economic variables to predict demand • SE – set of socio-economic variables (population (current and forecasted), income, employment, volume of trade, average level of education,...) • LOS – set of level-of-service variables (service frequencies, total travel times, departure and arrival schedule, routing, waiting times, fares, travel costs, schedule reliability, perceived level of comfort, perceived level of safety, carrier reputation,...) Virginia Tech 36 of 81 General Model • A general model where demand is a function of socio-economic characteristics and the characteristics of the transportation system can be written in the following general form: m • D(t) = a ∏ b S it i i=1 m • D(t) = a ⋅ ∏ i=1 n bi S it ⋅ ∏ T jt cj j=1 • where: • m - the total number of socio-economic characteristics, • n- the total number of transportation system characteristics, • D(t) – the number of air passenger in year t Virginia Tech 37 of 81 • Sit - the value of the i-th socio-economic characteristics in year t • Tjt - the value of the j-th transportation system characteristics in year t • a, bi, cj, - parameters to be estimated Virginia Tech 38 of 81 Choice of Variables in the Model (Sit and Tjt) Socio-economic vector Sit (variables) • Income (most important) • Age and role in household • Car ownership • Household size • Residential location • Profession Virginia Tech 39 of 81 Choice of Variables in the Model (Sit and Tjt) Transportation-related variables (for vector Tjt) • In-vehicle travel time • Access, waiting and transfer times • Travel cost • Qualitative variables (comfort, reliability, safety) Virginia Tech 40 of 81 Case Study Integrated Transportation Systems Model for NASA Langley Research Center Virginia Tech 41 of 81 Application of the Model to Study SATS IMpacts Airspace and Airport ATM Procedures Environmental (noise and pollution) CNS Infrastructure Intercity Travel (Mobility Benefits) Airport Infrastructure NAS System Capacity Safety Energy Use Virginia Tech Picture source: NASA LaRC 42 of 81 Integrated Approach to Study Air Transportation Systems (Virginia Tech Model) Scenaro i Definition National and Re gional Economic Models National Airspace System Feedback Loop Trip Generation Analysis Trip Distribution Analysis Inventory Studies Travel Studies (all modes) Feedback Loop Transport ation Vehicle Intercity vehicle characteristics Performance Models Information Technology Intercity Modal Split Analysis Intercity Net work Analysis Intercity Model Scenario Analysis Virginia Tech Transport ation Cost Models Feedback Loop Metrics Travel time Economic benefits Noise Traffic densities Energy use 43 of 81 Model Implementation Policies (Op. Capability Deployment) Time = Base Year Inventory Scena rio Studies Definition Time = 1 Scenario Studies Inventory Trip Generation 2 National and Time = DefinitionTravelmodes) Studies (all Analysis Regio nal E conomic Models Inventory Scenario Transportation Studies Definition Travel Studies Intercity vehicle characteristics Trip G neration e National and (all Vehicle modes) Feedback Performance Models Re gional Trip Distr ibution Analysis Feedback Loop Analysis Travel Studies E conomic Models Loop Transportation Invent ory Scenario National Airspace Trip Generation National and (all modes)Definition Intercity vVehicle ehicle characteristics St udies Information System Analysis Regi nal o Feedback Performance Models Trip Distribution Technology Feedback Economic Models Loop Transportation Loop Intercity Modal Analysis National Airspace Trav el Studies Intercity vehicle characteristics Vehicle Trip Generation Split Analysis National and Feedbac System (all modes) Performance Models Trip Distribution Information k Transportation Feedback Analysis Loop Regi Cost Models Technology Analysis onal Loop Economic Models National Airspace Transportation Intercity Modal Information System Intercity Network Analysis Vehicle Intercity vehicle characteristics Split Feedback Transportation Technology Analysis Feedback Performance Models Loop Trip Distribution Feedback Loop Intercity Modal Cost Models Analysis Loop National A irspace Split Analysis Intercity Network Transportat ion Information Feedback Sy stem Analysis Cost Models Loop Technology Intercity Model Scenario Analysis Intercity Modal Intercity Netw ork Feedback Split Analysis An alysis Transportation Loop Inter city Model Cost Models Scenario Analysis Intercity Ne twork Feedback Intercity Model An alysis Loop Scenario Analysis Time = Horizon Year Intercity Model Scenario Analysis Virginia Tech National Mobility Metrics 44 of 81 Scenario Definition 3346 Airports Virginia Tech 45 of 81 Inventory Studies 3346 Airports Runway Length > 3,000 Serves 95% of Aircraft Population < 12,500 lb. Per FAA AC 5325-5 Virginia Tech 46 of 81 Data Analysis of Intermodal Transportation Systems Source: NPTS Business trips (11.86% of total) Virginia Tech 47 of 81 Core Transportation Modules Some Details of the Methods Employed All methods have been coded in MATLAB at the county level Virginia Tech 48 of 81 Trip Generation Analysis 8 Person-trips Per Year (per Household) 6 Given: Socio-economic characteristics for each county (for all states) 4 2 Predict: a) Number of trips produced per household/year for various income levels b) Trips attracted to a county 0 8 6 10 8 4 Years After High School Use: Trip rate tables Virginia Tech 6 2 x 10 4 4 0 2 Annual Household Income ($) 49 of 81 Trip Generation Analysis Virginia Tech 50 of 81 Trip Distribution Analysis Given: Trips produced from and attracted to each county Predict: a) Number of person-trips from each origin to every destination (county to county) Use: Gravity Model PAF K j -- T = - --i-------ij --------- -- -- ij-ij n ∑ A jF ijK ij j1= Virginia Tech 51 of 81 Trip Distribution Analysis Use of a gravity model to distribute trips across NAS Tij: trips from zone i to zone j Pi: trip productions at zone i, Ai: trip attraction to zone j, Fij: friction factor between zone i and j, and Kij: trip production between zone i and j. Virginia Tech 52 of 81 Mode Split Analysis Given : Trips from each origin to each destination Predict : a) Number of person-trips for every mode of transportation available Use: Nested Multinomial Logit Model and Diversion Curves Traveler Aviation General Aviation Bus Commercial Aviation Automobile Key variables: travel cost, access time, travel time, safety Virginia Tech 53 of 81 Mode Split Analysis Temporal Decisions 8:00 am Virginia Tech 54 of 81 Mode Split Analysis Which Mode? Virginia Tech 55 of 81 Mode Split Analysis BWI DCA HEF JYO BCB Destination airport choice modeling Virginia Tech 56 of 81 Details of the Mode Split Model Virginia Tech 57 of 81 Presentation of a General Logit Model V ijk P ijk = e------------------ ∑e V ijr r Pijk - the proportion of traffic between origin I and destination j that uses k-th mode Vijk - the travel disutility (or utility) traveling from i to j via the k-th mode (a function of travel cost, travel time, waiting time, and access time) Virginia Tech 58 of 81 Disutility Function (Vijk) V ijk = a 1 x 1 + a 2 x 2 + … + a n x n where: V ijk is the disutlity to travel from city i to j via mode k a 1 , a 2 , ..., a n are model coefficients (to be determined from a stated preference survey) x 1 , x 2 , ..., and x n are attributes associated with mode of transportation k Potential attributes of the model are travel cost, travel time, comfort, frequency of service, etc. Any variable that helps discriminate two or more modes of transportation Virginia Tech 59 of 81 Mode Choices are Complex Travel patterns are heavily influenced by cost economics Virginia Tech 60 of 81 Calibration of a Mode Split Model 556,000 records ATS record ATS record ATS record ATS record Nested Multinomial Logit Model Specification 18,000 records ATS random ATS random record record Auto Cost DB1B UCB and VT SAS MDC Method Synthetic Trip Simulator Outputs: travel cost and travel time Airline Cost Sabre Virginia Tech Calibrated Nested MNLM GA/SATS Cost Prediction of Mode Choice (Pijkm) 61 of 81 Types of Travelers Modeled Consider two trip purposes: - business - non-business Consider two types of air transportation travelers: - Limited choice auto/commercial airline travelers - Choice travelers (can select auto, commercial air and GA/corporate) The end result of the analysis yields 4 distinct models to address mode choice Virginia Tech 62 of 81 Types of Trips Makers and Their Trip Purpose Trip Maker Trip Purpose Business Non-Business Limited Captive Choice Z Z Choice Z Z Virginia Tech 63 of 81 Modeling Technique • Use Random Utility Maximization (RUM) technique • We used a multinomial logit formulation with - Travel time - Relative travel cost (= trip cost / income) - *Level of GA use (for choice riders) as the explanatory variables in the disutility expressions Virginia Tech 64 of 81 Virginia Tech 65 of 81 Idea Behind a Logit Model • • Models how people make decisions while selecting a mode of transportation among several alternatives V ijk = a 1 x 1 + a 2 x 2 + … + a n x n • The disutility function represents a combined “worth” of the trip from i to j via mode k. • The model is probabilistic (this is the output of the model) • The model reflects individual choice behavior • The model can be calibrated with responses from a stated preference survey and using Maximum Likelihood techniques Virginia Tech 66 of 81 Variables Used in all Four Models Variables Used Captive Riders Business Travelers Non-Business Travelers f(TT,TC) f(TT,TC) Choice Riders f(TT,TC, Level of Use) f(TT,TC, Level of Use) TT = travel time (hrs) TC = scaled relative travel cost (dim) Level of Use = percent of trips made via GA Virginia Tech 67 of 81 Logit Model Layout ATS: American Travel Survey Auto:Automobile CA: Commercial Airline GA: General Aviation ATS DATABASE CA CA/Auto CAPTIVE Travelers TRAVELERS CA GA Accessible CHOICE Travelers TRAVELERS NON BUSINESS TRIP NON BUSINESS TRIP TOP TOP TOP AUTO BUSINESS TRIP BUSINESS TRIP TOP AUTO CA GA CA AUTO CA AUTO Virginia Tech CA GA 68 of 81 Extracting Data From ATS Virginia Tech 69 of 81 Travel Time Assumptions in the Logit Model Automobile Speed Urban areas: 32.5 (mph) (or Travel Highways : 60 (mph) time) Access/egress Distance Processing Time Detouring (3) ratio Airline GA Table function(1) Table function(2) (4) 30 (miles) 15 (miles) Orig. airport = 60 (min) Dest. airport = 30 (min) Orig. airport = 30 (min) Dest. airport = 20 (min) (3) 1.2 - 1) Travel distance vs. flight time, Airline (min) Miles 300 600 3000 3300 3600 Time 50.0 89.0 397 443 485 Data: Boeing 737-800 BC/A Data: 2) Travel distance vs. flight time, GA (min) Miles 300 600 2700 3000 Time 100.0 178.0 702 974 3) 4) Data: BC/A for Various GA aircraft Accounts for incremental trip distance due to the connecting flights. Data extracted from NPTS data. Virginia Tech 70 of 81 Travel Costs in the Logit Model Automobile Cost per mile (Cents/mile) Access/egress Distance Lodging cost3) Average Occupancy 1) Airline1) GA 31 (cents/mile) Equations2) Combined Cost 4) - 30 (miles) 15 (miles) 150 ($/day) Business trip: 1.2 Non-business trip: 3.0 (travelers/car) - 150 ($/day) - All trips: 1.2 (travelers /flight) It is assumed that 9% of air travelers purchase first and business class tickets 2) Airline fares: fare = distance / ( -0.26 + 0.027 * distance0.727) , For distance > 100 statute miles fare = distance / (-0.67 + 0.241 * distance0.3508), For distance > 100 statute miles 3) If driving time (or flight time for GA) is longer than maximum hours a day, the lodging cost is added to the total trip cost. We assume the maximum driving/flight hours/day to be 8 hours. 4) GA cost is obtained by combining costs of three GA aircraft types (SE, ME, JE) weighted by distance traveled. Virginia Tech 71 of 81 Calibrated Logit Model Synthetic trips are generated for every passenger in the ATS database. Travel costs and travel times are computed based on supply costs functions. The following model parameters are obtained: Parameter Non-business Trip Business Trip TTIME relativeCost TTIME relativeCost Estimate t-Value -0.0073 -4.0405 -0.0104 -3.0835 -4.34 -41.54 -2.95 -19.92 approx. Pr > |t| <.0001 <.0001 0.0032 <.0001 TTIME = travel time (hrs) TTIME relativeCost = scaled relative travel cost (dim) Virginia Tech 72 of 81 Computational Example • For a traveler with annual household income of $35,000 and synthesized travel cost and time by mode for a 328-mile trip are as follows: Travel Time (hr) Travel Cost ($) Relative Travel Cost (Cost/HHIncome) Automobile 5.47 32.00 0.09371 Airline 4.54 282.80 0.80800 GA 1.92 492.00 1.40571 Note: HHIncome is scaled to $/100 Virginia Tech 73 of 81 Sample Problem Output (Business) The following probabilities apply to limited choice intercity travelers (remember a limited choice rider is one that can only go via auto or commercial airline) • P auto P airline For a business traveler: ( – 0.0104 ) ( 5.47 ) + ( – 3.0835 ) ( 0.09371 ) = ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ( – 0.0104 ) ( 5.47 ) + ( – 3.0835 ) ( 0.09371 ) + ( – 0.0104 ) ( 4.54 ) + ( – 3.0835 ) ( 0.808 ) ( – 0.0104 ) ( 4.54 ) + ( – 3.0835 ) ( 0.808 ) = ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ( – 0.0104 ) ( 5.47 ) + ( – 3.0835 ) ( 0.09371 ) + ( – 0.0104 ) ( 4.54 ) + ( – 3.0835 ) ( 0.808 ) P auto = 0.90 P airline = 0.10 Virginia Tech 74 of 81 Sample Problem Output (Non-Business) The following probabilities apply to limited choice intercity travelers (remember a limited choice rider is one that can only go via auto or commercial airline) • P auto P airline For a non-business traveler: ( – 0.0073 ) ( 5.47 ) + ( – 4.0405 ) ( 0.09371 ) = ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ( – 0.0104 ) ( 5.47 ) + ( – 3.0835 ) ( 0.09371 ) + ( – 0.0104 ) ( 4.54 ) + ( – 3.0835 ) ( 0.808 ) ( – 0.0073 ) ( 4.54 ) + ( – 4.0405 ) ( 0.808 ) = --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ( – 0.0073 ) ( 5.47 ) + ( – 4.0405 ) ( 0.09371 ) + ( – 0.0073 ) ( 4.54 ) + ( – 4.0405 ) ( 0.808 ) P auto = 0.95 P airline = 0.05 Virginia Tech 75 of 81 0.4 Business Trips 0.35 Percent Travel by Commercial Air) Percent Travelers by Commercial Air Sensitivity Analysis (Income Changes) 0.3 0.25 0.2 0.15 TextEnd 0.1 0.05 0 3.5 4.5 5.5 6.5 7.5 8.5 Income ($) Income ($) Virginia Tech 9.5 10.5 11.5 12.5 x 104 76 of 81 Percent Travelers by Commercial Air Percent Travel by Commercial Air) Sensitivity Analysis (Income) 0.35 Non-Business Trips 0.3 0.25 0.2 0.15 TextEnd 0.1 0.05 0 3.5 4.5 5.5 6.5 7.5 8.5 Income ($) Income ($) Virginia Tech 9.5 10.5 11.5 12.5 x 104 77 of 81 Transportation Network Analysis Airbus A320 Jacksonville - Miami Virginia Tech 78 of 81 Remarks About Logit Models • Require careful evaluation and individual choice behavior survey methods • Require calibration using Maximum Likelihood techniques • Relatively simple to use once they have been calibrated • Have been used in the analysis of air transportation in other context: - Airline consolidation and market share analysis - Route choice - Airport choice - Economics Virginia Tech 79 of 81 Sample Model Used in NAS Simulator LMI Economic Impacts Module FAA Policy Module Exogenous Database NAS Level of Service Module (UMD) Woods and Poole Database Trip Demand (Tij) NAS Capacity Modules (UMD/VT) Trip Distribution Analysis (Tijk) (Tijk) Airline Fleet Module (UCB) Mode Split Model (Tijkm) No Sustainable? Yes Airline Operations Module (MIT) Virginia Tech 80 of 81 Sample Airport Choice Model Virginia Tech 81 of 81 ...
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