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Trip Distribution Lecture 8 Norman W. Garrick and Hamed Ahangari

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Theories Of Migration IB SL.

Airport Forecasting. Forecasting Demand Essential to have realistic estimates of the future demand of an airport Used for developing the airport master.

Norman Washington Garrick CE 2710 Spring 2014 Lecture 07

CE 254 Transportation Engineering

What is the Model??? A Primer on Transportation Demand Forecasting Models Shawn Turner Theo Petritsch Keith Lovan Lisa Aultman-Hall.

Sequential Demand Forecasting Models CTC-340. Travel Behavior 1. Decision to travel for a given purpose –People don’t travel without reason 2. The choice.

CE 2710 Transportation Engineering

Trip Generation Input: Socioeconomic Data Land Use Data Output:

Lec 10, TD Part 3: ch5.4.2 & H/O, pp : Trip Distribution Trip distribution: why is it needed? The Fratar Method (read, not covered in class; get.

Trip Generation Modeling—Cross-Classification

Norman W. Garrick CTUP. Norman W. Garrick Transportation Forecasting What is it? Transportation Forecasting is used to estimate the number of travelers.

1 The Four-step Travel Model GEOG 111 & 211A – Fall 2004 October 14.

Norman W. Garrick Transportation Forecasting What is it? Transportation Forecasting is used to estimate the number of travelers or vehicles that will use.

CEE 320 Fall 2008 Transportation Planning and Travel Demand Forecasting CEE 320 Anne Goodchild.

Norman W. Garrick Trip Assignment Trip assignment is the forth step of the FOUR STEP process It is used to determining how much traffic will use each link.

Planning Process ► Early Transport Planning  Engineering-oriented  1944, First “ O-D ” study  Computational advances helped launch new era in planning.

TRIP ASSIGNMENT.

GEOG 111/211A Transportation Planning Trip Distribution Additional suggested reading: Chapter 5 of Ortuzar & Willumsen, third edition November 2004.

Lowry Model Pam Perlich URBPL 5/6020 University of Utah.

Source: NHI course on Travel Demand Forecasting (152054A) Session 10 Traffic (Trip) Assignment Trip Generation Trip Distribution Transit Estimation & Mode.

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Trip Distribution Modeling Part III - PowerPoint PPT Presentation

Trip Distribution Modeling Part III

Trip distribution modeling. part iii. ce 573 transportation planning ... step 1: set bj to 1.0, determine initial trip matrix, and solve ... with new ai ... – powerpoint ppt presentation.

• CE 573 Transportation Planning
• Growth factoring
• Types of constraints
• XFUTURE XNOW(growth factor)
• Applications
• Beyond regional scope
• Gravity model inadequate
• Too difficult to forecast independent variables
• The trip matrix total T
• Tij is the number of trips going from origin i to destination j.
• TLDk is the number of trips in cost-bin k
• Typical trip matrix constraints
• t initial OD matrix
• Uniform growth factor?Tij ttij.
• Singly constrained growth-factor methods
• Doubly constrained growth factors?have growth factors for origins and destinations (), where
• instead of ai and bj being the growth factors for origin i and destination j, they are adjustments made to each O-D pair volume in order to achieve the target values Oi and Dj required by the growth factors for the origins and destinations
• BI-PROPORTIONAL ALGORITHM
• Step 1 Set bj to 1.0, determine initial trip matrix, and solve for ai that meet origin constraints, given the latest bj values.
• Recalculate Tij with new ai values
• Step 2 Solve for bj that meet the destinations constraints given the latest ai values and the previous bj values.
• Recalculate Tij with new bj values and the latest ai values.
• m-1 indicates previous iteration
• Step 3 Keeping the bj values fixed solve for ai that satisfy origin constraints given the ai from the last iteration (iteration m-1).
• Repeat steps 2 and 3 until changes in ai and bj are sufficiently small.
• Note This algorithm assumes that both sets of constraints can be satisfied simultaneously. In other words, the following must be true
• Disadvantages
• requires an initial O-D matrix
• no consideration given to changes in transport costs

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Travel Demand Forecasting: Parameters and Techniques (2012)

Chapter: chapter 1 - introduction.

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

1 1.1 Background In 1978, the Transportation Research Board (TRB) published NCHRP Report 187: Quick-Response Urban Travel Estimation Techniques and Transferable Parameters (Sosslau et al., 1978). This report described default parameters, factors, and manual techniques for doing planning analysis. The report and its default data were used widely by the transportation planning profession for almost 20 years. In 1998, drawing on several newer data sources, including the 1990 Census and Nation- wide Personal Transportation Survey, an update to NCHRP Report 187 was published in the form of NCHRP Report 365: Travel Estimation Techniques for Urban Planning (Martin and McGuckin, 1998). Since NCHRP Report 365 was published, significant changes have occurred affecting the complexity, scope, and context of transportation planning. Transportation planning tools have evolved and proliferated, enabling improved and more flexible analyses to support decisions. The demands on trans- portation planning have expanded into special populations and broader issues (e.g., safety, congestion, pricing, air quality, environment, climate change, and freight). In addition, the default data and parameters in NCHRP Report 365 need to be updated to reflect the planning requirements of today and the next 10 years. The objective of this report is to revise and update NCHRP Report 365 to reflect current travel characteristics and to pro- vide guidance on travel demand forecasting procedures and their application for solving common transportation problems. It is written for “modeling practitioners,” who are the public agency and private-sector planners with responsibility for devel- oping, overseeing the development of, evaluating, validating, and implementing travel demand models. This updated report includes the optional use of default parameters and appropriate references to other more sophisticated techniques. The report is intended to allow practitioners to use travel demand fore- casting methods to address the full range of transportation planning issues (e.g., environmental, air quality, freight, multimodal, and other critical concerns). One of the features of this report is the provision of trans- ferable parameters for use when locally specific data are not available for use in model estimation. The parameters pre- sented in this report are also useful to practitioners who are modeling urban areas that have local data but wish to check the reasonableness of model parameters estimated from such data. Additionally, key travel measures, such as average travel times by trip purpose, are provided for use in checking model results. Both the transferable parameters and the travel measures come from two main sources: the 2009 National Household Travel Survey (NHTS) and a database of model documentation for 69 metropolitan planning organizations (MPOs) assembled for the development of this report. There are two primary ways in which planners can make use of this information: 1. Using transferable parameters in the development of travel model components when local data suitable for model development are insufficient or unavailable; and 2. Checking the reasonableness of model outputs. This report is written at a time of exciting change in the field of travel demand forecasting. The four-step modeling process that has been the paradigm for decades is no longer the only approach used in urban area modeling. Tour- and activity-based models have been and are being developed in several urban areas, including a sizable percentage of the largest areas in the United States. This change has the potential to significantly improve the accuracy and analytical capability of travel demand models. At the same time, the four-step process will continue to be used for many years, especially in the smaller- and medium- sized urban areas for which this report will remain a valuable resource. With that in mind, this report provides information on parameters and modeling techniques consistent with the C h a p t e r 1 Introduction

2four-step process and Chapter 4, which contains the key information on parameters and techniques, is organized con- sistent with the four-step approach. Chapter 6 of this report presents information relevant to advanced modeling practices, including activity-based models and traffic simulation. This report is organized as follows: • Chapter 1—Introduction; • Chapter 2—Planning Applications Context; • Chapter 3—Data Needed for Modeling; • Chapter 4—Model Components: – Vehicle Availability, – Trip Generation, – Trip Distribution, – External Travel, – Mode Choice, – Automobile Occupancy, – Time-of-Day, – Freight/Truck Modeling, – Highway Assignment, and – Transit Assignment; • Chapter 5—Model Validation and Reasonableness Checking; • Chapter 6—Emerging Modeling Practices; and • Chapter 7—Case Studies. This report is not intended to be a comprehensive primer for persons developing a travel model. For more complete information on model development, readers may wish to consult the following sources: • “Introduction to Urban Travel Demand Forecasting” (Federal Highway Administration, 2008); • “Introduction to Travel Demand Forecasting Self- Instructional CD-ROM” (Federal Highway Administra- tion, 2002); • NCHRP Report 365: Travel Estimation Techniques for Urban Planning (Martin and McGuckin, 1998); • An Introduction to Urban Travel Demand Forecasting— A Self-Instructional Text (Federal Highway Administration and Urban Mass Transit Administration, 1977); • FSUTMS Comprehensive Modeling Online Training Workshop (http://www.fsutmsonline.net/online_training/ index.html#w1l3e3); and • Modeling Transport (Ortuzar and Willumsen, 2001). 1.2 Travel Demand Forecasting: Trends and Issues While there are other methods used to estimate travel demand in urban areas, travel demand forecasting and mod- eling remain important tools in the analysis of transportation plans, projects, and policies. Modeling results are useful to those making transportation decisions (and analysts assisting in the decision-making process) in system and facility design and operations and to those developing transportation policy. NCHRP Report 365 (Martin and McGuckin, 1998) pro- vides a brief history of travel demand forecasting through its publication year of 1998; notably, the evolution of the use of models from the evaluation of long-range plans and major transportation investments to a variety of ongoing, every- day transportation planning analyses. Since the publication of NCHRP Report 365, several areas have experienced rapid advances in travel modeling: • The four-step modeling process has seen a number of enhancements. These include the more widespread incor- poration of time-of-day modeling into what had been a process for modeling entire average weekdays; common use of supplementary model steps, such as vehicle availability models; the inclusion of nonmotorized travel in models; and enhancements to procedures for the four main model components (e.g., the use of logit destination choice models for trip distribution). • Data collection techniques have advanced, particularly in the use of new technology such as global positioning systems (GPS) as well as improvements to procedures for performing household travel and transit rider surveys and traffic counts. • A new generation of travel demand modeling software has been developed, which not only takes advantage of modern computing environments but also includes, to various degrees, integration with geographic information systems (GIS). • There has been an increased use of integrated land use- transportation models, in contrast to the use of static land use allocation models. • Tour- and activity-based modeling has been introduced and implemented. • Increasingly, travel demand models have been more directly integrated with traffic simulation models. Most travel demand modeling software vendors have developed traffic simulation packages. At the same time, new transportation planning require- ments have contributed to a number of new uses for models, including: • The analysis of a variety of road pricing options, including toll roads, high-occupancy toll (HOT) lanes, cordon pricing, and congestion pricing that varies by time of day; • The Federal Transit Administration’s (FTA’s) user benefits measure for the Section 5309 New Starts program of transit projects, which has led to an increased awareness of model properties that can inadvertently affect ridership forecasts;

3 • The evaluation of alternative land use patterns and their effects on travel demand; and • The need to evaluate (1) the impacts of climate change on transportation supply and demand, (2) the effects of travel on climate and the environment, and (3) energy and air quality impacts. These types of analyses are in addition to several traditional types of analyses for which travel models are still regularly used: • Development of long-range transportation plans; • Highway and transit project evaluation; • Air quality conformity (recently including greenhouse gas emissions analysis); and • Site impact studies for developments. 1.3 Overview of the Four-Step Travel Modeling Process The methods presented in this report follow the conven- tional sequential process for estimating transportation demand that is often called the “four-step” process: • Step 1—Trip Generation (discussed in Section 4.4), • Step 2—Trip Distribution (discussed in Section 4.5), • Step 3—Mode Choice (discussed in Section 4.7), and • Step 4—Assignment (discussed in Sections 4.11 and 4.12). There are other components commonly included in the four-step process, as shown in Figure 1.1 and described in the following paragraphs. The serial nature of the process is not meant to imply that the decisions made by travelers are actually made sequentially rather than simultaneously, nor that the decisions are made in exactly the order implied by the four-step process. For example, the decision of the destination for the trip may follow or be made simultaneously with the choice of mode. Nor is the four-step process meant to imply that the decisions for each trip are made independently of the decisions for other trips. For example, the choice of a mode for a given trip may depend on the choice of mode in the preceding trip. In four-step travel models, the unit of travel is the “trip,” defined as a person or vehicle traveling from an origin to a destination with no intermediate stops. Since people traveling for different reasons behave differently, four-step models segment trips by trip purpose. The number and definition of trip purposes in a model depend on the types of information the model needs to provide for planning analyses, the char- acteristics of the region being modeled, and the availability of data with which to obtain model parameters and the inputs to the model. The minimum number of trip purposes in most models is three: home-based work, home-based nonwork, and nonhome based. In this report, these three trip purposes are referred to as the “classic three” purposes. The purpose of trip generation is to estimate the num- ber of trips of each type that begin or end in each location, based on the amount of activity in an analysis area. In most models, trips are aggregated to a specific unit of geography (e.g., a traffic analysis zone). The estimated number of daily trips will be in the flow unit that is used by the model, which is usually one of the following: vehicle trips; person trips in motorized modes (auto and transit); or person trips by all modes, including both motorized and nonmotorized (walking, bicycling) modes. Trip generation models require some explanatory variables that are related to trip-making behavior and some functions that estimate the number of trips based on these explanatory variables. Typical variables include the number of households classified by characteristics such as number of persons, number of workers, vehicle availability, income level, and employment by type. The output of trip generation is trip productions and attractions by traffic analysis zone and by purpose. Trip distribution addresses the question of how many trips travel between units of geography (e.g., traffic analysis zones). In effect, it links the trip productions and attractions from the trip generation step. Trip distribution requires explanatory variables that are related to the cost (including time) of travel between zones, as well as the amount of trip-making activity in both the origin zone and the destination zone. The outputs of trip distribution are production-attraction zonal trip tables by purpose. Models of external travel estimate the trips that originate or are destined outside the model’s geographic region (the model area). These models include elements of trip generation and distribution, and so the outputs are trip tables represent- ing external travel. Mode choice is the third step in the four-step process. In this step, the trips in the tables output by the trip distri- bution step are split into trips by travel mode. The mode definitions vary depending on the types of transportation options offered in the model’s geographic region and the types of planning analyses required, but they can be generally grouped into auto mobile, transit, and nonmotorized modes. Transit modes may be defined by access mode (walk, auto) and/or by service type (local bus, express bus, heavy rail, light rail, commuter rail, etc.). Nonmotorized modes, which are not yet included in some models, especially in smaller urban areas, include walking and bicycling. Auto modes are often defined by occupancy levels (drive alone, shared ride with two occupants, etc.). When auto modes are not modeled separately, automobile occupancy factors are used to convert the auto person trips to vehicle trips prior to assignment. The outputs of the mode choice process include person trip tables by mode and purpose and auto vehicle trip tables.

4Time-of-day modeling is used to divide the daily trips into trips for various time periods, such as morning and afternoon peak periods, mid-day, and evening. This division may occur at any point between trip generation and trip assignment. Most four-step models that include the time-of-day step use fixed factors applied to daily trips by purpose, although more sophisticated time-of-day choice models are sometimes used. While the four-step process focuses on personal travel, commercial vehicle/freight travel is a significant component of travel in most urban areas and must also be considered in the model. While simple factoring methods applied to per- sonal travel trip tables are sometimes used, a better approach is to model such travel separately, creating truck/commercial vehicle trip tables. The final step in the four-step process is trip assignment. This step consists of separate highway and transit assignment processes. The highway assignment process routes vehicle trips from the origin-destination trip tables onto paths along Forecast Year Highway Network Forecast Year Transit Network Forecast Year Socioeconomic DataTrip Generation Model Internal Productions and Attractions by Purpose Trip Distribution Model Mode Choice Model Person and Vehicle Trip Tables by Purpose/Time Period Time of Day Model Person and Vehicle Trip Tables by Mode/Purpose/Time Period Highway Assignment CHECK: Input and output times consistent? Transit Assignment Highway Volumes/ Times by Time Period Transit Volumes/ Times by Time Period Input Data Model Output Model Component Decision Feedback Loop Yes No Truck Trip Generation and Distribution Models Production/Attraction Person Trip Tables by Purpose Truck Vehicle Trip Tables by Purpose Truck Time of Day Model Truck Vehicle Trip Tables by Time Period External Trip Generation and Distribution Models External Vehicle Trip Tables by Time Period Figure 1.1. Four-step modeling process.

5 the highway network, resulting in traffic volumes on network links by time of day and, perhaps, vehicle type. Speed and travel time estimates, which reflect the levels of congestion indicated by link volumes, are also output. The transit assignment process routes trips from the transit trip tables onto individual transit routes and links, resulting in transit line volumes and station/ stop boardings and alightings. Because of the simplification associated with and the resul- tant error introduced by the sequential process, there is some- times “feedback” introduced into the process, as indicated by the upward arrows in Figure 1.1 (Travel Model Improvement Program, 2009). Feedback of travel times is often required, particularly in congested areas (usually these are larger urban areas), where the levels of congestion, especially for forecast scenarios, may be unknown at the beginning of the process. An iterative process using output travel times is used to rerun the input steps until a convergence is reached between input and output times. Because simple iteration (using travel time outputs from one iteration directly as inputs into the next iteration) may not converge quickly (or at all), averaging of results among iterations is often employed. Alternative approaches include the method of successive averages, constant weights applied to each iteration, and the Evans algorithm (Evans, 1976). Although there are a few different methods for implement- ing the iterative feedback process, they do not employ param- eters that are transferable, and so feedback methods are not discussed in this report. However, analysts should be aware that many of the analysis procedures discussed in the report that use travel times as inputs (for example, trip distribution and mode choice) are affected by changes in travel times that may result from the use of feedback methods. 1.4 Summary of Techniques and Parameters Chapter 4 presents information on (1) the analytical tech- niques used in the various components of conventional travel demand models and (2) parameters for these mod- els obtained from typical models around the United States and from the 2009 NHTS. These parameters can be used by analysts for urban areas without sufficient local data to use in estimating model parameters and for areas that have already developed model parameters for reasonableness checking. While it is preferable to use model parameters that are based on local data, this may be impossible due to data or other resource limitations. In such cases, it is common practice to transfer parameters from other applicable models or data sets. Chapter 4 presents parameters that may be used in these cases, along with information about how these parameters can be used, and their limitations. 1.5 Model Validation and Reasonableness Checking Another important use of the information in this report will be for model validation and reasonableness checking. There are other recent sources for information on how the general process of model validation can be done. Chapter 5 provides basic guidance on model validation and reasonable- ness checking, with a specific focus on how to use the informa- tion in the report, particularly the information in Chapter 4. It is not intended to duplicate other reference material on validation but, rather, provide an overview on validation consistent with the other sources. 1.6 Advanced Travel Analysis Procedures The techniques and parameters discussed in this report focus on conventional modeling procedures (the four-step process). However, there have been many recent advances in travel modeling methods, and some urban areas, especially larger areas, have started to use more advanced approaches to modeling. Chapter 6 introduces concepts of advanced model- ing procedures, such as activity-based models, dynamic traffic assignment models, and traffic simulation models. It is not intended to provide comprehensive documentation of these advanced models but rather to describe how they work and how they differ from the conventional models discussed in the rest of the report. 1.7 Case Study Applications One of the valuable features in NCHRP Report 365 was the inclusion of a case study to illustrate the application of the parameters and techniques contained in it. In this report, two case studies are presented to illustrate the use of the information in two contexts: one for a smaller urban area and one for a larger urban area with a multimodal travel model. These case studies are presented in Chapter 7. 1.8 Glossary of Terms Used in This Report MPO—Metropolitan Planning Organization, the federally designated entity for transportation planning in an urban area. In most areas, the MPO is responsible for maintaining and running the travel model, although in some places, other agencies, such as the state department of transportation, may have that responsibility. In this report, the term “MPO” is sometimes used to refer to the agency responsible for the model, although it is recognized that, in some areas, this agency is not officially the MPO.

6Model area—The area covered by the travel demand model being referred to. Often, but not always, this is the area under the jurisdiction of the MPO. The boundary of the model area is referred to as the cordon. Trips that cross the cordon are called external trips; modeling of external trips is discussed in Section 4.6. Person trip—A one-way trip made by a person by any mode from an origin to a destination, usually assumed to be without stops. In many models, person trips are the units used in all model steps through mode choice. Person trips are the usual units in transit assignment, but person trips are converted to vehicle trips for highway assignment. Trip attraction—In four-step models, the trip end of a home-based trip that occurs at the nonhome location, or the destination end of a nonhome-based trip. Trip production—In four-step models, the trip end of a home-based trip that occurs at the home, or the origin end of a nonhome-based trip. Vehicle trip—A trip made by a motorized vehicle from an origin to a destination, usually assumed to be without stops. It may be associated with a more-than-one-person trip (for example, in a carpool). Vehicle trips are the usual units in highway assignment, sometimes categorized by the number of passengers per vehicle. In some models, vehicle trips are used as the units of travel throughout the modeling process. Motorized and nonmotorized trips—Motorized trips are the subset of person trips that are made by auto or transit, as opposed to walking or bicycling trips, which are referred to as nonmotorized trips. In-vehicle time—The total time on a person trip that is spent in a vehicle. For auto trips, this is the time spent in the auto and does not include walk access/egress time. For transit trips, this is the time spent in the transit vehicle and does not include walk access/egress time, wait time, or time spent transferring between vehicles. Usually, transit auto access/ egress time is considered in-vehicle time. Out-of-vehicle time—The total time on a person trip that is not spent in a vehicle. For auto trips, this is usually the walk access/egress time. For transit trips, this is the walk access/ egress time, wait time, and time spent transferring between vehicles. In some models, components of out-of-vehicle time are considered separately, while in others, a single out-of- vehicle time variable is used.

TRB’s National Cooperative Highway Research Program (NCHRP) Report 716: Travel Demand Forecasting: Parameters and Techniques provides guidelines on travel demand forecasting procedures and their application for helping to solve common transportation problems.

The report presents a range of approaches that are designed to allow users to determine the level of detail and sophistication in selecting modeling and analysis techniques based on their situations. The report addresses techniques, optional use of default parameters, and includes references to other more sophisticated techniques.

Errata: Table C.4, Coefficients for Four U.S. Logit Vehicle Availability Models in the print and electronic versions of the publications of NCHRP Report 716 should be replaced with the revised Table C.4 .

NCHRP Report 716 is an update to NCHRP Report 365 : Travel Estimation Techniques for Urban Planning .

In January 2014 TRB released NCHRP Report 735 : Long-Distance and Rural Travel Transferable Parameters for Statewide Travel Forecasting Models , which supplements NCHRP Report 716.

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Trip Distribution

Jul 14, 2012

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Trip Distribution. Additional suggested reading: Chapter 5 of Ortuzar & Willumsen, third edition. November 2004. Trip Distribution Objectives. Replicate spatial pattern of trip making

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• spatial distribution
• estimate friction factor parameters
• mode split process
• trip length characteristics
• distribution models
• calculate friction factor matrix

Presentation Transcript

Trip Distribution • Additional suggested reading: Chapter 5 of Ortuzar & Willumsen, third edition November 2004

Trip Distribution Objectives • Replicate spatial pattern of trip making • Account for spatial separation among origins and destinations (proximity in terms of time, cost, & other factors) • Account for attractiveness among TAZs • Reflect human behavior

Destinations TAZ P 15 13 26 18 8 13 93 A 22 6 5 52 2 6 93 Origins 1 2 3 4 5 6 Sum T11 T12 T13 T14 T15 T16 O1 T21 T22 T23 T24 T25 T26 O2 T31 T32 T33 T34 T35 T36 O3 T41 T42 T43 T44 T45 T46 O4 T51 T52 T53 T54 T55 T56 O5 T61 T62 T63 T64 T65 T66 O6 D1 D2 D3 D4 D5 D6 1 2 3 4 5 6 Sum 1 2 3 4 5 6 Sum Trip Distribution • Convert Production and Attraction Tables into Origin - Destination (O - D) Matrices

Crude approximation for HBW

Trip Distribution, Methodology • General Equation: • Tij = Ti P(Tj) • Tij = calculated trips from zone i to zone j • Ti = total trips originating at zone i • P(Tj) = probability measure that trips will be attracted to zone j • Constraints: • Singly Constrained • Sumi Tij = Dj OR Sumj Tij = Oi • Doubly Constrained • Sumi Tij = Dj AND Sumj Tij = Oi

Trip Distribution Models • Growth Factor / Fratar Model • Tij = Ti (Tj / T) • Tij = present trips from zone i to zone j • Ti = total trips originating at zone i • Tj = total trips ending at zone j • T = total trips in the entire study • Tij* = Tij (Fi Fj) / F • Fi = Ti* / Ti • Fj = Tj* / Tj • F = T* / T • * = estimated future trips

a Aj / Cij Trip Distribution Models You can consider this as the probability spatial distribution P(Tj) • Gravity Model • Tij = Ti • Tij = trips from zone i to zone j • Ti = total trips originating at zone i • Aj = attraction factor at j • Ax = attraction factor at any zone x • Cij = travel friction from i to j expressed as a generalized cost function • Cix = travel friction from i to any zone x expressed as a generalized cost function • a = friction exponent or restraining influence a Sum (Ax / Cix)

Trip Distribution Models • Intervening - Opportunities Model • Tij = Ti (e - e ) • Tij = trips from zone i to zone j • T = trip destination opportunities closer in time to zone i than those in zone j • Ti = trip end opportunities in zone i • Tj = trip end opportunities in zone j • L = probability that any destination opportunity will be chosen -LT -LT(T + Tj)

Model Advantages Disadvantages Growth Factor Gravity Intervening - Opportunities Simple Easy to balance origin and destination trips at any zone Specific account of friction and interaction between zones Does not require origin - destination data Claimed to bear a better “fit” to actual traffic Does not reflect changes in the frictions between zones Does not reflect changes in the network Requires extensive calibration Long iterative process Accounts for only relative changes in time - distance relationship between zones Arbitrary choice of probability factor Model Comparison New: Destination choice models build on intervening opportunities

Gravity Model Process • Create Shortest Path Matrix - Minimize Link Cost between Centroids • Estimate Friction Factor Parameters - Function of Trip Length Characteristics by Trip Purpose • Calculate Friction Factor Matrix • Convert Productions and Attractions to Origins and Destinations • Calculate Origin - Destination Matrix • Enforce Constraints on O - D Matrix - Iterate Between Enforcing Total Origins and Destinations

Shortest Path Matrix • Matrix of Minimum Generalized Cost from any Zone i to any Zone j (see OW p. 153) • Distance, Time, Monetary Cost, Waiting Time, Transfer Time, etc.. may be used in Generalized Cost • Time or Distance Often Used • Matrix Not Necessarily Symmetric (Effect of One - Way Streets) TAZ ID TAZ ID 1 2 3 4 5 6 C11 C12 C13 C14 C15 C16 C21 C22 C23 C24 C25 C26 C31 C32 C33 C34 C35 C36 C41 C42 C43 C44 C45 C46 C51 C52 C53 C54 C55 C56 C61 C62 C63 C64 C65 C66 1 2 3 4 5 6

Example: travel time matrix for 6 TAZs

Friction Factor Models • Exponential: • f(cij) = e c > 0 • Inverse Power: • f(cij) = cijb > 0 • Gamma: • f(cij) = a cij e a > 0, b > 0, c > 0 - c (cij) - b - b - c (cij) Trip Purpose a b c HBW 28507 0.020 0.123 HBP 139173 1.285 0.094 NHB 219113 1.332 0.010 ref. NCHRP 365 / TransCAD UTPS Manual pg. 80

Example friction factors using travel times alone Friction ij = 1/exp(-0.03* Timeij)

Friction Factor Matrices • Matrix of Friction from any Zone i to any Zone j, by Trip Purpose • Each Cell of a Friction Factor Matrix is a Function of the Corresponding Cell of the Shortest Path Matrix • Each Trip Purpose has a separate Friction Factor Matrix Because Trip Making Behavior Changes for Each Trip Purpose TAZ ID TAZ ID 1 2 3 4 5 6 F11 F12 F13 F14 F15 F16 F21 F22 F23 F24 F25 F26 F31 F32 F33 F34 F35 F36 F41 F42 F43 F44 F45 F46 F51 F52 F53 F54 F55 F56 F61 F62 F63 F64 F65 F66 1 2 3 4 5 6

Trip Conversion(Approximate) • Home Based Trips: Non - Home Based Trips: • Oi = (Pi + Ai) / 2 Oi = Pi • Di = (Pi + Ai) / 2 Di = Ai • Oi = origins in zone i (by trip purpose) • Di = destinations in zone i (bytrip purpose) • Pi = productions in zone i (by trip purpose) • Ai = attractions in zone i (by trip purpose) • Note: This Only Works for a 24 Hour Time Period • If our models are for one period in a day we prefer to work directly with Origins-Destinations

O - D Matrix Calculation • Calculate Initial Matrix By Gravity Equation, by Trip Purpose • Each Cell has a Different Friction, Found in the Corresponding Cell of the Friction Factor Matrix • Enforce Constraints in Iterative Process • Sum of Trips in Row i Must Equal Origins of TAZ i • If Not Equal, Trips are Adjusted Proportionally • Sum of Trips in Column j Must Equal Destinations of TAZ j • If Not Equal, Trips are Adjusted Proportionally • Iterate Until No Adjustments Required

Destinations Origins 1 2 3 4 5 6 Sum T11 T12 T13 T14 T15 T16 O1 T21 T22 T23 T24 T25 T26 O2 T31 T32 T33 T34 T35 T36 O3 T41 T42 T43 T44 T45 T46 O4 T51 T52 T53 T54 T55 T56 O5 T61 T62 T63 T64 T65 T66 O6 D1 D2 D3 D4 D5 D6 1 2 3 4 5 6 Sum O - D Matrix Example:

Attraction/friction matrix

Aj / frictionij Gravity model probability Sum (Ax / frictionix)

Trip Interchange - iteration 1 For each cell value we apply the gravity equation once - in this iteration - after this we use the ratio to adjust the values in the cells - until row and column targets are satisfied - see also OW - chapter 5

Trip interchange - iteration 2 Using the ratios from before we succeed in getting the targets for the sums of cells for each column - look at the other ratios

Trip interchange - iteration 3

Trip interchange - iteration 4 We get both rows and columns to produce the sums we want!

Multiple Matrices • For each trip purpose obtain different Origin-Destination Tij matrices • Usually these are 24 hour Matrices (number of trips from one zone to another in a 24 hour period) • In assignment we will need a matrix of vehicles moving from a zone to another during a specific period (peak usually) in a typical day

Final O - D Matrix (simplified) • Combine (Add) O - D Matrices for Various Trip Purposes • Scale Matrix for Peak Hour • Scale by Percent of Daily Trips Made in the Peak Hour • 0.1 Often Used (10% of daily trips) • Scale Matrix for Vehicle Trips • Scale by Inverse of Ridership Ratio to Convert Person Trips to Vehicle Trips • 0.95 to 1 Often Used • Note: Mode Split Process / Models More Accurate, - we will explore them in class

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Trip distribution

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Trip distribution is another of the major aspects of the transportation simulation process and although generation, distribution and assignment are often discussed separately, it is important to realise that if human behaviour is to be effectively simulated then these three processes must be conceived as an interrelated whole.

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Salter, R.J. (1976). Trip distribution. In: Highway Traffic Analysis and Design. Palgrave, London. https://doi.org/10.1007/978-1-349-06952-1_7

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