Lecture 4Four transport modelling stages with emphasis on public transport (hands on training)

Dr. Muhammad Adnan

Lecture Outline

• Trip Generation• Trip Distribution• Modal Choice• Trip Assignment- Car Traffic• Trip Assignment – Public transport

Traffic Analysis Zones (TAZs)• Geographic areas dividing the planning region into relatively

similar areas of land use and land activity. Zones represent the origins and destinations of travel activity within the region… every household, place of employment, shopping center, and other activity… are first aggregated into zones and then further simplified into a single node called a centroid. (TRB Report-365)

• TAZs serve as the primary unit of analysis in a travel demand forecasting model. They contain socioeconomic data related to land use. TAZs are where trips begin and end

Guidelines for Delineating TAZs• The following can serve as a checklist summarizing recommendations on the best practices in

delineating TAZs– The number of people per TAZ should be greater than 1,200, but less than 3,000 for the base and

future years;– Each TAZ yields less than 15,000 person trips in the base and future year;– The size of each TAZ is between 0.25 to one square mile in area;– There is a logical number of intrazonal trips in each zone, based on the mix and density of the land

use;– Each centroid connector loads less than 10,000 to 15,000 vehicles per day in the base and future

year;– The study area is large enough so that nearly all (over 90 percent) of the trips begin and end within

the study area;– The TAZ structure is compatible with the base and future year highway and transit network;– The centroid connectors represent realistic access points onto the highway network;– Transit access is represented realistically;– The TAZ structure is compatible with Census, physical, political, and planning district/sector

boundaries;– The TAZs are based on homogeneous land uses, when feasible, in both the base and future year – Special generators and freight generators/attractors are isolated within their own TAZ.

Trip Generation

Modelling Methods

•Linear regression method

•Cross-classification (category analysis) method/trip rate method

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Trip generation

•Productions & Attractions

•Home-based & non-home based

trips

J

I

Zones

Example• City X has recently conducted a travel survey

of its 10 TAZs. The collected data is summarized in the table. Based on the given information

• Predict the total number of trips that will be produced by each zone in 10 yrs. (Assume zonal population in 10 yrs is known)?

• Relate Y (total trips produced by a zone) to X1 (zonal population)?

• Expected total number of trips for a zone with a population of 5,000?

• How confident you are about your estimates?

Excel Method

Another Data

Trip Distribution Models (1)• People decide on Possible destinations is

function of– Type and extent of transportation activities– Pattern (location and intensity) of land use– Socio-Economic characteristics of population

• Modelling Assumptions– Number of trips decrease with COST between zones– Number of trips increase with zone “attractiveness”

Trip Distribution Models (2)I. Growth Factor Models (Uniform, Average

Factor, Fratar and Detroit)

II. Theoretical Models (Gravity Model, Intervening opportunity Model, Entropy Models)

Growth Factor Models (General)

• Future trips can be found by proportioning the relative growth in those zones

• Iterative in Nature– Start with existing– New proportions established– Iteration continues till we reach stable numbers

Uniform Growth Factor Model

F= P*/P0

P* = Design Year TripsP0 = Base year Trips (Total)

Tij = F tij for each pair i and j

Tij = Future Trip Matrix tij = Base-year Trip Matrix F= General Growth Rate

Uniform Growth Factor Model

The Uniform Growth Factor is typically used for over a 1 or 2 year horizon. However, assuming that trips grow at a standard uniform rate is a fundamentally flawed concept.

This method suffers from the disadvantages that it will tend to overestimate the trips between densely developed zones, which probably have little development potential, and underestimate the future trips between underdeveloped zones, which are likely to be extremely developed in the future.

Gravity Model (Mathematical Form)

K-Factors• K-factors account for socioeconomic linkages • K-factors are i-j TAZ specific • If i-j pair has too many trips, use K-factor less

than 1.0 • Once calibrated, keep constant? for forecast • K-Factors are used to force estimates to agree

with observed trip interchanges

Example

Input Data

Travel times into friction factors

Modal Choice

Logit Models (Discrete Choice Models)

• Binomial Logit Models• Multinomial Logit Models• Nested Logit Models

• These models worked on the principle of Random Utility Maximization

Concept of Utility

• Utility Function measures the degree of satisfaction that people derive from their choices.

• A disutility function represents the generalized cost associated with each choice

Example

• Auto Utility Equation: UA= -0.025(IVT) -0.050(OVT) - 0.0024(COST)• Transit Utility Equation: UB= -0.025(IVT) -0.050(OVT) – 0.10(WAIT) – 0.20(XFER) - 0.0024(COST)• Where:• IVT= in-vehicle time in minutes• OVT = out of vehicle time in minutes• COST = out of pocket cost in cents• WAIT = wait time (time spent at bus stop waiting for bus)• XFER = number of transfers

• Question: what is the implied cost of IVT? OVT? WAIT? XFER?

Binary logit Example

Example

• Mode OVT IVT Cost (cents)

• 1 person 5 17 200.0• 2-person carpool 5 21 100.0• 3-person carpool 5 23 66.6• 4-person carpool 5 25 50.0 • Transit 7 33 160.0

Part 1: CALCULATE MODE PROBABILITIES BY MARKET SEGMENT

• Overview: Calculate the mode probabilities for the trip interchanges. Use the tables on the next pages.

• Part A: Calculate the utilities for transit as follows:– Insert in the table the appropriate values for OVT, IVT, and COST.– Calculate the utility relative to each variable by multiplying the variable by the

coefficient which is shown in parenthesis at the top of the column; and– Sum the utilities (including the mode-specific constant) and put the total in the

last column. • Part B: Calculate the mode probabilities as follows:

– Insert the utility for transit in the first column;– Calculate eU for transit– Sum of eU for transit and put in the “Total” column; and– Calculate the probability for transit using the formula:– Sum the probabilities (they should equal 1.0)

Say, from trip distribution, the number of trips was 14,891. Calculate the number of trips by mode using the probabilities calculated.

Mode Trips

(Zone 5 to Zone 1)

Solo Driver

2-Person Carpool

3-Person Carpool

4-Person Carpool

Transit

Total 14, 891

Trip Assignment- Car Traffic

Equilibrium Assignment (capacity Restraint Assignment)

Two link problem with an O-D pair

Example-2

• All or Nothing Assignment

Problem formulation

• User Equilibrium

Solution

For Large Networks- Frank-wolfe Algorithm

• Initial UE guess: AON based on free-flow times• Find link travel times at current UE guess• Find Latest AON based on link travel times

above• New UE guess: Find best λ to combine old UE

guess and latest AON solution through Z function

• Repeat second step

t2(V2)=2+V2

t1(V1)=1+3V1

Example -3

O D

t3(V3)=3+2V3

O-D Demand constraint

V1+V2+V3=10

Solution- FW algorithm• See excel Worksheet

• A: Initial estimates of travel time

• B: First AON Solution

• C: As we don’t yet have any other information, the AON solution in B becomes our first equilibrium flow estimate

• D: The corresponding equilibrium travel time estimates are obtained by substituting the flows C in the travel time functions

• E: the input travel times to the next step

• F: The AON solution

• G: This is the first time we have to do some work to calculate these values –the first combination step of the FW algorithm, combination of a mix of C and F

– New (V1, V2, V3)= (1-λ)(10,0,0) + λ(0,10,0) = (10-10λ, 10λ, 0), – Put these volumes in Z function, calculate λ, =0.725 GOTO step D and repeat this until travel times equate each other

Trip Assignment- Public Transport

Transit Assignment

• Links include different services running between stops or stations.

• Involves movement of passengers, not vehicles• Complex interchange patterns associated with

passengers• Impedance functions includes fare structure• Some paths offer more than one parallel service with

complex associated choices (e.g., express bus versus local bus service)

• In-vehicle time• Initial wait time• Transfer wait time• Access time

Egress time

Dwell time

Number of transfers

Costs

To ensure consistency with mode choice, variables used and their weights should be consistent with mode choice utilities

Assignment attributes and weighting factors:

In-vehicle time factor = 1.0Auxiliary (walk) travel time factor = 2.0Wait time factor = 2.0Wait time = Headway/ 2Boarding time = 5 minBoarding time factor =1.0