Calibrating and Adjustment of System Planning Models

Calibrating and Adjustment of System Planning Models - December 1990

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NOTICE

This document is disseminated under the sponsorship of the
Department of Transportation in the interest of information
exchange. The contents of this report reflect the views of the
authors, who are responsible for the facts and accuracy of the
data presented herein. The contents do not necessarily reflect
the official policy of the Department of Transportation.

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Table of Contents
Page

1.0 Introduction 1
1.1 Calibration Versus Validation 1

2.0 Networks 5
2.1 Centroid Connectors 5
2.2 Speed and Capacity 7
2.3 Intersection Penalties 9
2.4 Intrazonal Times 10
2.5 Coding Errors 12

3.0 Trip Generation 14
3.1 Socioeconomic Data 14
3.2 Household Income 14
3.3 Production/Attraction Rates 15
3.4 Special Generators 16
3.5 Trip Balancing Factors 16

4.0 Auto Occupancy 17

5.0 Trip Distribution 18
5.1 Mean Trip Length 18
5.2 Estimating Trip Length 23
5.3 Employment Distribution Problems 23
5.4 Other Trip Purposes 24

6.0 Traffic Assignment 25
6.1 All-or-Nothing Assignment 25
6.2 Capacity Restraint Assignment - BPR Speed-Volume
Curves 26
6.2 Changing the Definition of capacity 28
6.3 Calibration with Equilibrium Assignment 28
6.3.1 Speeds and Travel Times with
Equilibrium Assignment 29
6.3.2 Determining Free Travel Times
and Free Speeds on Links 29

7.0 Transit Ridership Effects on Highway Volumes 30

8.0 External Stations 31

9.0 System Changes Versus Local Changes 32

10.0 Expected and Required Accuracy 33
10.1 Performance Measures Based on Observed Counts
10.2 Performance Measures Based on VMT 35

11.0 Conclusions 37

12.0 Trouble Shooting 38

References 41

Appendix 42

LIST OF TABLES

TABLE PAGE

1 Speed and Capacity Reference Table 8

2 Trip Table For Two Zone Study Area 12

3 Modified Trip Table 12

4 Reasonable Values of Person Trips
per Dwelling Unit 14

5 Sample Problem 15

6 Typical Ranges For Auto Occupancy 17

7 Friction Factor Table 21

8 Gravity Model Relationships 21

9 Gravity Model Adjustments 22

10 Capacity Relationships 28

11 Percentages Of External-To-External
Travel For Cities of Various sizes 31

LIST OF FIGURES
FIGURE PAGE

1 Screenlines And Cutlines 4

2 Centroid Connector Example 5

3 Modified Centroid Connectors 5

4 Centroid Connector Sample 1 6

5 Centroid Connector Sample 2 6

6 Centroid Connector And Intersection-Incorrect 7

7 Centroid Connector And Intersection-Correct 7

8 Sample Network 9

9 Trip Types For Two Zone Study Area 11

10 Skim Tree For Zone 1 13

11 Sample Network 18

12 Sample Urban Area 22

13 Sample Problem 25

14 Speed Volume Curve 26

15 Maximum Desirable Error for Link Volumes 34

iii

1.0 INTRODUCTION

The four-step transportation modeling process, as applied at the
regional level, has traditionally been dependent upon an extensive and
reliable origin-destination (O-D) data base. In the early years of such
models, this data base was developed largely through household surveys,
a time-consuming and expensive undertaking. Such surveys were
instrumental in developing the transportation models that have been used
during the past 30 years. Since 1980, over 30 urban areas have
conducted new home interview surveys to update their data base and
ensure the validity of their modeling process. However, given limited
resources, many planning agencies have had to rely on other means to
validate their system models.

This manual describes quick and simple procedures for calibrating and
adjusting systemwide transportation models so as to replicate existing
ground counts and thus be used with some validity for forecasting. The
four-step modeling process will not be described in detail. More
detailed information on this process can be found in the documents
listed in the reference section, or from documentation of various
software packages. For this manual to be useful, the reader should have
some basic knowledge of transportation planning. In addition, this
manual is not intended to replace the need for good O-D data. Clearly,
model calibration and validation is best undertaken with such data. In
its absence, however, there are several approaches that can be adopted.
This manual discusses the appropriate manner of their use. It is
oriented to the smaller urban areas but many of the techniques are
applicable to larger areas as well.

1.1 Calibration Versus Validation

Calibration in the traditional four-step modeling process was
accomplished by modifying model parameters until the models replicated
the travel patterns exhibited by the O-D survey. After the models were
calibrated, a validation effort was undertaken. Validation consisted of
running the calibrated models with current socioeconomic data and
comparing the simulated link volumes with ground counts. Over the
years, however, the use of large scale O-D surveys for this purpose has
generally declined due to their expense. Rather, default values for
trip generation and trip distribution models developed from past surveys
have been used. Sometimes, very limited small sample surveys have been
conducted to update the model parameters. Also, the Census Journey-to-
Work data are available every 10 years to calibrate a work trip
generation and distribution model. As a result, the practical
application and meaning of calibration and validation have changed over
the years.

With the decline of large scale O-D surveys, calibration and
validation have merged into one process. Initial default parameters are
used in the models. The models are then used to simulate link volumes,
which are compared with ground counts. If this comparison shows
significant differences, key model parameters are modified until the
model replicates ground counts with an acceptable degree of accuracy.
When modifying the model parameters, it is important to keep the values
reasonable and not have the end justify the means. If the only way the
model will replicate ground counts is by using unusual parameters, then
the entire process should be checked, including the validity of the
ground counts and the socioeconomic data.

Before any calibration or validation process is initiated it is
extremely important that the transportation planner verify the accuracy
of the socioeconomic and network system data. If the socioeconomic and
network system data are accurate, the level of effort needed to
calibrate or validate the transportation planning models will be greatly
reduced. Usually, inaccuracies in data and networks are the most common
cause of error in travel demand forecasting models. It is necessary
that the accuracy of the traffic counts used in comparison with the
simulated volumes be checked as well.

The following steps summarize the overall model calibration and
adjustment process.

Step 1. Run the region-wide transportation system models using
default values for model parameters. If old model
parameters are available from previous studies or O-D
surveys, they are used in the initial runs. More recent
data, such as that from small sample surveys, are used to
update these parameters.

Step 2. From the initial results of the model runs, develop region-
wide values such as trips/person and VMT/person.

Step 3. Compare the region-wide values developed under Step 2 with
typical values shown in appendix A.

Step 4. Develop screenlines and cutlines for your area. An example
of screenlines and cutlines is shown in Figure 1.
Screenlines should be established to intercept major traffic
flows through the region and should be located so that
"double' crossings of the screenlines are minimized. A
screenline located along a physical barrier such as a river
or railroad track is desirable since the number of crossings
is minimized. More than one screenline may be used to
intercept a variety of major flows such as between a major
suburban area and the downtown area and between the suburban
area and an outlying commercial and industrial area. It is
sometimes useful to establish such a line to intercept all
travel into and out of the central area.
A series of traffic counts must be taken at each roadway
location crossed by a screenline or cutline. These counts
must be factored to one time period such as 1990 peak
traffic season or 1990 ADT.

Step 5. Having evaluated the results from the above steps, determine
whether systemlevel, local or a combination of problems have
occurred in the application of the model. Modifications to
the model can be made by adjusting various equations,
parameters or variables as described in the following
sections of the manual. In some cases, adjustments to more
than one item may be necessary to obtain appropriate
results. Simulated volumes from the traffic model can be
raised or lowered to match ground counts by examining and
modifying, either individually or in combination, the
following:

- Network.Characteristics
- Centroid Connectors
- Roadway Speeds and Capacities
- Intersection Penalties
- Intrazonal Times
- Coding Errors

- Trip Generation Rates
- Socioeconomic Data
- Household Income
- Production and Attraction Rates
- Special Generators
- Trip Balancing Factors

- Auto Occupancy

- Trip Distribution
- Mean Trip Length
- Estimating Trip Length
- Employment Distribution
- Non-work Trip Purposes

- Traffic Assignment
- All-or-Nothing
- Capacity Restraint
- Equilibrium

The remainder of this manual is organized to discuss each one of
these model variables or steps.

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Cutlines and screenlines serve a similar purpose; cutlines, however are
shorter and cross corridors rather than intercept major regional flows.
Cutlines should be established to intercept travel along only one axis
(see Figure 1).

Figure 1 - Screenlines and Cutlines in Daneville Study Area

2.0 NETWORKS

Second only to errors in socioeconomic data, errors in network
development and link data coding are the most likely sources of error in
the modelling process. Building and checking networks is labor-
intensive, time-consuming, expensive, and tedious. In this section,
possible sources of network error are discussed.

2.1 Centroid Connectors

The location and number of centroid connectors can have a
significant impact on how
traffic is assigned to the network. Figure 2 shows a sample centroid
connector.

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If 1,000 trips are produced at the centroid, the trips will have to
use either link 4-3 or link 4-5 to reach a destination. By adding
additional centroid connectors, trip assignment could be significantly
impacted. For example, by adding an additional connector as shown in
Figure 3, the assignment of the 1000 trips could change. The north
connector as well as the south connector are now part of the possible
paths to reach network destinations. These trips could now use links 6-
1 and 6-2, as well as links 4-3 and 4-5.

Connecting a centroid to a network could also affect the assignment
of traffic to a freeway versus an arterial. An example of this is shown
in Figures 4 and 5. Trips going from Centroid 1 to 10 in Figure 4 use
the shortest path, which is via the freeway (path 1-2-34-5-9-10). The
freeway path travel time of 16 minutes compares favorably to the
arterial time path (path 1-2-6-12-7-11-8-9-10) of 20 minutes. However,
by adding centroid links 112 and 10- 1 1 as shown in Figure 5, the
arterial path now becomes path I- 12-7-1 1- 10 with a travel time of 10
minutes. Thus, trips going from centroids I to 10 would use the freeway
in Figure 4; but they would use the arterial path in Figure 5. A
different centroid connector configuration can therefore influence the
results of the assignment process.

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As a rule of thumb, centroid connectors should be attached to links
on all four sides of traffic zones, and networks should have 8-10 links
per zone. Connectors should represent, as closely as possible, the
local streets within the zone and reasonable access points to the
collectors/arterials in the system. A centroid connector should not be
added to either a baseyear or forecast-year network if access to a given
link is blocked by a canal, rail line, park, undevelopable land, freeway
control of access or if there is no highway or street facility in the
area. That is, centroid connectors should represent, as closely as
possible, the local streets within the zone and reasonable access points
to collectors/arterials in the system.

One must also be concerned about where centroid connectors are
"attached" to the network. Generally, centroid connectors should not
connect to an intersection as shown in Figure 6. In such a situation,
turning movements for intersection 3 could be distorted. This is
especially true if the model forecasted turning movements for
intersection 3. A better network representation is shown in Figure 7.
Note also that the assignment for link 4-3 in Figure 6 will most likely
be different than that for link 4-5-3 in Figure 7.

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2.2 Speed and Capacity

The network speed and capacity logic used to code the link data needs
to be clearly defined and consistently applied. Some urban areas are
coding capacities and speeds using a look-up (reference) table based on
functional classification, the number of lanes, and the area locational
characteristics of the zone. Each link in the network is coded as a
type of facility that exhibits the type of characteristics found in the
look-up table. The advantage of a lookup table is that modifications to
either speeds or capacities can be made easily without having to modify
data link-by-link. The look-up table permits the testing of alternative
speed and capacity logic. Small urban areas sometimes input capacities
and volumes on a link-by-link basis. An example look-up table with
acceptable ranges of speeds and capacities is shown in Table 1.

Planners in small cities have observed that many drivers try to minimize
distance rather than travel time. In minimizing distance rather than
time, drivers may be using the local road system rather than the
freeways. An indication that distance minimization might be

occurring is unexpectedly large forecasted volumes (relative to counts)
on higher-speed facilities in outlying areas and low forecasted volumes
on CBD links. To compensate for distance minimization, speeds can be
increased on low-speed links and decreased on highspeed links. For
example, it may be necessary to decrease freeway speeds to 45 mph or
lower in order to compensate for the extra distance involved in trips on
freeways. Lowering the speeds on the freeways would compensate for this
travel characteristic of drivers in small urban areas.

The methods for using speeds and capacities to calibrate a system model
are covered in the Distribution and Assignment sections of this manual.

Table 1--Speed and Capacities Reference Table
MPH
FACILITY TYPE SPEED CAPACITY NO. OF LANES

FREEWAYS 50-60 1500-2000 PER LANE
20-45 700-1000 1 LANE

ARTERIALS
(W/LEFT TURN 25-45 1400-2000 2 LANES
BAYS) 25-45 2100-3000 3 LANES
15-45 500-800 1 LANE

ARTERIALS
(NO LEFT 20-45 1200-1800 2 LANES
TURN BAY) 20-45 1900-2800 3 LANES

CENTROID
CONNECTORS 10-20 N/A N/A

* Arterial speed and capacity varies depending on the area type (CBD,
Central City, Urban, Suburban, Rural) and the percentage of green
time at intersections.

2.3 Intersection Penalties

Many models not only calculate travel times by looking at link
speeds, but also include time for traversing an intersection. Actually,
for travel along a congested arterial most of the travel time is
accumulated at the intersection. Especially for sub-area models,
intersection penalties can be an important means of producing results
that replicate observed volumes more closely. For example, to go from
node I to node 7 in Figure 8, three logical paths are available: path 1-
2-3-7 with a travel time of 6 minutes; path 1-5-6-7, with a travel time
of 6 minutes; and path 1-2-6-7 with a travel time of 6 minutes. If
intersection delay was considered, path 1-2-3-7 would be chosen because
it includes a right turn (2-3-7), versus path 1-5-6-7 which includes a
left turn (1-5-6), and path 1-2-6-7 which includes both a left turn (2-
6-7) and a right turn (1-2-6). This result, of course, assumes that
left turns require more travel time than right or through movements.
Typically, a left turn takes 30 or more seconds to complete compared to
10 or 15 seconds for a through movement or right turn.
The model, therefore, should normally choose paths which have fewer left
turns, assuming close-to-equivalent travel times on the travel links.
This is accomplished by having the left turn penalties larger than right
or through turn penalties.

One approach for coding turn penalties is to apply default penalty times
to all turns. Defaults are then adjusted at specific locations where
special circumstances exist. That is, the overall time at the
intersection would be increased or decreased to obtain an accurate
penalty for that intersection. The codes at each intersection could
therefore be a positive or negative number.

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FIGURE 8-Sample Network

It has been found that good traffic forecasts can be performed
without a heavy dependence on large turn penalties. Consequently, many
of the forecasting packages distributed in the United States lack full
support for turn penalties. Care should be taken to observe and adhere
to the limits of a particular forecasting package. There are two
particularly prevalent limitations:

1. In many (but not all) packages, the algorithm for finding the
shortest path between centroids does not perfectly account for turn
penalties at intersections. It is possible for these algorithms to -
occasionally overlook a moderately large turn penalty (i.e., I to 5
minutes). The solution to this problem is to keep the turn penalties
as small as possible. If a large penalty is required and your
forecasting package cannot accomodate it, it will be necessary to
explicitly show that turning movement as a link in the network. To
prohibit selected movements, you should not encounter problems using
very large penalties (e.g., 100 minutes).

2. In many forecasting packages, traffic assignment algorithms do not
account for congestion-related delays during turns. There are three
possible ways around this limitation. First, include that movement
as a link, and use the speed-volume function to calculate a delay.
Second, incorporate the delay (or as much as possible) on the links
approaching the intersection. Third, manually step through the
assignment algorithm, adjusting the penalties at each iteration. The
last method is practical only for very small networks.

Given a tendency for drivers to avoid making turns, the modeled
network should not exhibit large numbers of circuitous paths. Turn
penalties can be used to straighten paths between origins and
destinations. An effective means of straightening paths is to place a
small left-turn penalty (i.e., 0. I to 0.25 minutes) on all the
intersections in the network.

Turn penalties should not be used in only one section of the network.
Otherwise, the assignment algorithm will tend to avoid that section, and
forecasted volumes on the network links in this section will be too
small. It is best to develop a single strategy for establishing turn
penalties and to apply that strategy uniformly across the network.

2.4 Intrazonal Times

Two types of internal trips are found in the four-step modeling
process--intrazonal and interzonal. Intrazonal trips are trips that
begin and end in the same zone as shown in Figure 9. Interzonal trips
begin and end in different zones.

An interzonal trip between centroids 9 and 10 would use path 9-7-6-5-
10. For intrazonal trips, the network would not be used and trips would
not be assigned. Thus, the higher the percentage of intrazonal trips
the lower the volume on the network. The following example illustrates
this point.

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FIGURE 9-Trip Types for Two Zone Study Area

Figure 9 represents two zones having four possible types of trip
interchanges. These are:

Trips from 9 to 10 (interzonal)
Trips from 9 to 9 (intrazonal)
Trips from 10 to 10 (intrazonal)
Trips from 10 to 9 (interzonal)

The trip table shown in Table 2 is a hypothetical distribution of
trips in this zonal system. Based on this Table, 100 out of 300 or 1/3
of the trips from zone 9 are intrazonal trips. Thus, trips on path 9-7-
6-5-10 would be 200 (the trips going from zone 9 to zone 10). If
intrazonal trips increased, then the trips assigned to the network would
decrease. For example, if traffic shifted as shown in Table 3,
intrazonal trips would represent 50% or 150 out of 300 trips. Then the
trips on path 9-7-6-5-10 would be 150.

By increasing the percentage and number of intrazonal trips, the
number of interzonal trips and volumes on the network will be reduced.
By decreasing the percentage and number of intrazonal trips, the number
of interzonal trips and volumes on the network will be increased. Thus,
link volumes can be modified by varying the number of intrazonal trips.

Click HERE for graphic.

The best way to control intrazonal trips is by adjusting intrazonal
times in the gravity model trip distribution process. The smaller the
intrazonal travel times, the greater the intrazonal trips. The larger
the intrazonal travel times, the fewer the intrazonal trips. A second
method for controlling intrazonal trips is by modifying the average trip
lengths through the gravity model. Shortening the trip lengths will
increase the intrazonal trips since intrazonal trips are normally
shorter in travel time than interzonal trips. An additional explanation
of this principle is given in the trip distribution chapter.

A third method for influencing intrazonal trips is in the definition
of the zones. In order to have intrazonal trips, a zone must have both
productions and attractions (dwelling units and employment). Traffic
zones containing only dwelling units or only employment will have
intrazonal trips only for the nonhome based trip purpose.

If zones are large, intrazonal trips will be high. If zones are too
large then any single loading may automatically call for a road widening
from two to four lanes or four to six lanes. In a well designed zonal
and network system, centroid connector loadings should generally be less
than 10,000 to 15,000 vehicles per day.

2.5 Coding Errors

Before calibrating a network model, the network should be checked for
coding errors by visual inspection of network maps and computer output.
The forecasting software can automatically check for only the most
obvious errors. Every available device in your software should be used
for finding:

a. One-way links going the wrong direction;
b. Socioeconomic data entered incorrectly;
c. Speed, capacity, or free travel time entered incorrectly;
d. Extra links between pairs of nodes;
e. Links connected to the wrong nodes;
f. Missing nodes or links;
g. Centroids blocking trips through the network (in packages where
trips cannot pass through centroids);
h. Links with incorrect lengths; and
i. Geometry of intersections inconsistent with the turn penalties at
that intersection.

The best method for finding these errors will depend upon your
software package.

Skim trees can be especially helpful in finding coding errors. A
skim tree is a network showing the minimum path from one zone to all
other zones. There can be as many skim trees as there are centroids.
Careful inspection of a few skim trees can reveal most errors relating
to network geometry. An example of a skim tree is shown in Figure 10.

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FIGURE 10--Skim Tree For Zone 1

For additional network related information Reference 3 is recommended
for review.

3.0 TRIP GENERATION

3.1 Socioeconomic Data

Socioeconomic data can be an important source of error in system
modelling. If there are errors in the number of dwelling units or zonal
population, important inputs to trip generation, the number of trips
assigned to the network will be incorrect.

As an initial step in calibration, the regional total of the trips
produced should be evaluated for reasonableness. The total region-wide
trips produced should be divided by the total number of dwelling units
to determine the average number of trips per dwelling unit. Table 4
summarizes reasonable values of person trips per dwelling unit. This
Table refers to total trip generating dwelling units versus occupied
dwelling units. These rates may not directly apply to vacation areas
and other regions where occupancy varies across the year. Additional
data on person trips per dwelling unit are shown in the appendix A,
Table A2. If trips per dwelling unit are significantly different than
Table 4, the socioeconomic data may need further examination. First,
the region-wide number of dwelling units should be rechecked. Second,
the production rates used by the model should be checked. If errors are
found or the rates are not within a reasonable range, the rates may be
raised or lowered to modify the total number of trips produced (see
Production-Attraction Rate section).

Table 4--Reasonable Values of Person Trips Per Dwelling Unit

Population Person Trips Per Dwelling Unit*

50,000 - 100,000 14.1
100,000 - 250,000 14.5
250,000 - 750,000 11.8
750,000 + 7.6

* Includes internal and external trips

Source: Reference 5

3.2 Household Income

Where household income is used to estimate trips, care must be
taken to maintain a common dollar value over all analysis periods.
If the production rate table is based on 1980 household income and
the base year for socioeconomic data at the zonal level is 1989,
the model will over estimate the trip productions. A simple
example is shown below.

Table 5-Sample Problem

Production Rates Socioeconomic Data

1980 Trip Productions Zone # Dwelling 1989
Income Per Dwelling Unit Units Income

0-5,000 8 1 100 $8,000
5,000-10,000 10 2 200 $12,000
10,000-20,000 12 3 100 $16,000

Based on the information in Table 5, zone 3 would produce 1200
trips (12 x 100). However, the production rates are based on year
1989 income of $16,000. If the Consumer Price Index doubles from
the year 1980 to 1989 then the year 1989 income is equal to $8,000
($16,000/2) in 1980 dollars. Therefore, the trips produced in zone
3 for the year 1989 would be 1000 trips (10 x 100), where the 10 is
the number of trip productions per dwelling unit with an average
income of $8,000 in 1980 dollars.

3.3 Production And Attraction Rates

Trip generation production and attraction rates offer an
important area of adjustment in the modelling process. Quite
often, trip generation rates are based on old data, are borrowed
from other areas or are based on recent small sample surveys. As
such, they may not truly represent the trip generation
characteristics of the base year in a specific urban area. In some
cases, they may represent overall regional rates, but may not be
able to represent adequately the trip generation rates in different
sub-areas of the region.

The trip characteristics that influence trip generation include
the percent of trips by trip purpose as well as the trip rates by
purpose. After applying the trip generation procedure, the balance
between productions and attractions across the entire region should
be checked (see section 3.5, Trip Balancing Factors). The results
of trip generation for the entire region should be compared with
the trip rates per dwelling unit and per capita and for other areas
for reasonableness. Table 4 provided such rates for comparison
purposes. Additional data on person trips are shown in the
appendix A, Table A2.

There are a number of changes that might be made at this point
in the calibration. Trip rates can be raised or lowered to better
reflect region-wide trips produced. If data are available for some
land use types for which there is information (e.g., the Institute
of Transportation Engineers trip generation publication for trips
in and out of shopping centers, residential areas, etc.), the trip
rates can be compared to these and adjustments made as necessary.
This would be most appropriate in instances where "special
generator rates"

supercede the results of the trip generation model (see section
3.4, Special Generators and Reference 7). When using published
trip rates such as those provided by ITE, be aware that most travel
models generate person trips by purpose (work, shop, etc.) whereas
ITE trip rates are vehicle trips with no breakdown by purpose.

Another opportunity for making adjustments in trip generation rates
occurs after trip distribution and traffic assignment. Comparisons
of traffic assignment volumes and traffic counts across the
screenline(s) may indicate that trip rates should be raised or
lowered. Comparisons across cutlines may indicate that trips to or
from certain areas are high or low with one possible explanation
being that trip generation rates do not recognize the differences
between these areas. Such differences may indicate adjustments are
necessary for the trip generation of productions and attractions.
Clearly, such comparisons could also indicate other problems, so
any adjustments should be coordinated with other possible
adjustments.

3.4 Special Generators

Special generators are used for zones or activity centers that
have trip rates significantly different from standard trip rates.
Special trip generators in this category include commercial
airports, regional recreational facilities, universities, regional
retail malls, military bases, etc. A significant difference
between assigned and counted traffic volumes in a particular area
may indicate the need to specify a special generator location and
adjust the trip generation rates accordingly.

3.5 Trip Balancing Factors

Balancing total trip productions and attractions provides an
initial check on the quality of the socioeconomic data and the trip
rates. The ratio of region-wide productions to attractions by trip
purpose should be in the range of 0.90 to 1. 10 prior to any
adjustment. If the ratio falls outside of this range, there may be
a problem with the socioeconomic estimates, the trip rates, or
both. Any discrepancy should be resolved prior to proceeding to
trip distribution. Generally, non home-based (NHB) trips are the
most difficult to get good trip rates for and, consequently, the
trip purpose that is most often out of balance.

4.0 AUTO OCCUPANCY

Auto occupancy is used to convert person trips into vehicle
trips. Changes in auto occupancy can result in significant changes
in trips. The following example illustrates this point.

The total number of home-based work person trips estimated for a
study area is 138,000. If the auto occupancy rate for work trips
is 1.38 the total number of vehicle trips would be 138,000/1.38 or
100,000 vehicle trips. However, if an auto occupancy rate of 1. 15
is used then the vehicle trips would be 138,000/1.15 or 120,000.
Thus a change of auto occupancy from 1.38 to 1.15 results in a 20%
increase in vehicle trips (100,000 to 120,000).

By adjusting auto occupancy rates the vehicle trips can be
adjusted up or down. Typical ranges for auto occupancies for
different trip purposes are shown in Table 6. Additional

occupancy rates are shown in the appendix A, Table A9. If local
data are available, they should be used.

Table 6. Typical Ranges for Auto Occupancy

HBW 1.07 - 1.20

HBNW 1.40 - 1.71

NHB 1.24 - 1.65

TOTAL 1.31 - 1.54

Source: References 5 and 6

5.0 TRIP DISTRIBUTION

5.1 Mean Trip Length

One of the most powerful methods for adjusting traffic volumes
on highway links is through the trip distribution process.
Shortening or increasing the average trip lengths through the
distribution process will raise or lower the traffic volumes on
links. Trip lengths resulting from a gravity model distribution
are controlled by changing the gravity model input parameters. To
explain this process first we will look at the gravity model using
the information in Figure 1 1.

ZONE TO ZONE TRAVEL TIME

1-1 3
1-2 5
1-3 10

Click HERE for graphic.

Productions Attractions

1 100 100
2 300 200
3 200 300

Figure 11--Sample Problem

The basic formula for the gravity model is as follows:

A * FF
j ij
Tij = P * ------------
i n
� (A * FF )
1 j ij

where:
Tij = Trips going from zone i to zone j
Pi = Trips produced at zone i
Aj = Attractions in zone j
FFij = Friction factor for trips going from zone i to
zone j.
n = number of zones

Using the information in Figure 11, the number of trips going
from zones 1 to 2, 1 to 3, and 1 to 1 can be determined by using
the gravity model. The one additional piece of information needed
is the friction factor. The friction factor is normally determined
by using one of the following equations:

Power Function Exponential Function
1 1
FF = ---- FF = ----
x tx
t e

where: t = travel time between zone i and j
x = distribution parameter
e = value of e

Using the sample problem data and the power function, where the
distribution parameter is equal to 2, for the friction factors, the
gravity model will distribute the 100 trips from zone 1 as follows:

2
200 * (1/5 )
T = 100 x [ --------------------------------------- ] = 36
1-2 2 2 2
200 * (1/5 ) + 300 * (1/10 ) + 100 * (1/3 )

3
T = 100 x [ ----- ] = 14
1-3 22

11
T = 100 X [ ----- ] = 50
1-1 22

If the distribution parameter of 2 is raised to a value of 3 the
friction factors will change and the gravity model will distribute
the trips as follows:

3
200 * (1/5 )
T = 100 x [ --------------------------------------- ] = 36
1-2 3 3 3
200 * (1/5 ) + 300 * (1/10 ) + 100 * (1/3 )

.3
T = 100 x [ ----- ] = 5
1-3 5.6

3.7
T = 100 X [ ----- ] = 66
1-1 5.6

By raising the distribution parameter from 2 to 3, shorter trips
become more attractive. With a distribution parameter of 2, the
gravity model produces 50 intrazonal trips in zone 1, the zone with
the shortest travel time of 3 minutes. When the distribution
parameter is raised to 3, these intrazonal trips increase to 66.
The other longer trips (zone 1-2 and 1-3) decrease respectively by
7 and 9 trips. The longest trips (zone 1-3) have the highest
percentage decrease in trips.

Quite often a friction factor table rather than an equation is
used, especially if an O-D survey was once conducted in the urban
area. Also, the Census Journey-to-Work data available every ten
years allow calibration of a work trip model as was done when large
scale O-D surveys were conducted. The use of a friction factor
table provides additional flexibility as compared to a power or
exponential function given that portions of the table can be
adjusted easily to provide modified trip lengths. An example
friction factor table is shown in Table 7. Example data for
friction factor tables by trip purpose and urban area are contained
in Reference 8.

TABLE 7-Friction Factor Table

TRIP LENGTH FRICTION FACTOR NONHOME
MINUTES HOME BASED WORK HOME BASED NONWORK BASED

1 275 335 390
2 255 325 380
3 240 305 350
4 220 280 310
5 205 245 250
6 180 205 205
7 160 170 165
8 138 140 130
9 120 115 105
10 102 94 84
11 88 76 69
12 75 62 57
13 64 50 47
14 55 40 38
15 45 32 31
16 36 26 25
17 28 22 20
18 18 18 13
19 9 15 8
20 2 13 3

What does all this mean with respect to model calibration? By
changing the distribution parameter (the exponent in the friction
factor calculation) we can shorten or lengthen the average trip
length of the resulting trips. And if trip length is changed then
the volumes on the links can be raised or lowered. Table 8 shows
the relationships between model parameters and model products.
Table 8 shows the relationship between changes in the gravity model
parameters and resulting outputs.

Table 8-Gravity Model Relationships

IF THEN AND AND
Gravity Model Trip Length Link Intrazonal
Parameter Volumes Volumes

The situation shown in Figure 12 is typical of many cities.
Work trips have a much longer average travel time than shopping
trips. This condition can be reflected in the models by using
different distribution parameters for different trip purposes.
Trips will be distributed by trip purposes and will have
significantly different trip lengths. Table 9 provides default
values for distribution parameters by trip purpose. As noted in
this Table, the distribution parameter for the power function is
around 2.0 and the exponential function is 0. 1. Work trips should
have an average travel time greater than other trip purposes.
Additional information on average trip lengths is shown in appendix
A, Table A8.

Click HERE for graphic.

FIGURE 12--Sample Urban Area

Table 9--Gravity Model Adjustments

Parameter* Trip Length Minutes
Power Exponential Large Small
Pop. Pop.

Home-Based Work 2.0-2.2 0.1 15-20 7-10
Home-Based Non Work 1.9-2.0 0.1 13-17 6-9
Non Home-Based 1.8-2.0 0.1 13-17 6-8

* Different networks can produce different average trip lengths
even if the gravity model parameter is the same.

5.2 Estimating Trip Length for an Urban Area

The relevant trip length for calibration purposes is the total
travel time from origin to destination, including "excess" time.
Excess time includes walking time and parking time. Refer to
Reference I for additional information on the coding of excess
time.

The following relationships can give estimates of average trip
length in minutes based on the urban area population, P.

Home-Based Work: t = 0.98 x P0.19

Home-Based Social Recreation: t = 2.18 X P0.12

Home-Based Shopping: t = 8.1

NonHome-Based: t= 0.63 x P0.20

These trip length relationships were developed from origin-
destination studies done in the 1960's, but recent studies have
shown that trip length (for cities of a given size) has remained
roughly constant over the past 20 years (see reference 10).

5.3 Employment Distribution Problems

A common problem for urban areas with large central cities is
the matching of low income households with low income jobs in the
trip distribution process. Central business districts in large
urban areas have high income employment. The households filling
these jobs are in urban and suburban areas some distance from the
central business district. The households located nearest the
central business district are mostly low income. The problem
occurs when the trip distribution model matches low income
households with high income jobs if steps are not taken to prevent
it. Failure to prevent this mismatch can seriously distort the
trip length frequency distribution of HBW trips, underestimate VMT,
and underestimate the demand for transit if the person trip table
is used as an input to mode split.

Two approaches can be used to deal with this problem. One is to
disaggregate home based work trip productions and home-based work
trip attractions into income quartiles and treat each income
quartile as a separate trip purpose. This procedure was used by
the North Central Texas Council of Governments for their 1984 model
calibration. A household and work place survey as well as an
excellent socioeconomic inventory were available.
A second procedure is to use sector to sector bias factors (K
factors, see reference 1) in the trip distribution model that have
the effect of increasing the attractiveness of high income urban
and suburban sectors with the high income central business district
employment sectors. The bias factors are calibrated based on a
knowledge of the income attributes of the zones and are basically a
trial and error procedure followed by an evaluation of the sector
to sector trip interchanges. This procedure was used by the
Houston-Galveston Area Council to calibrate their 1984 model.

WARNING: K factors do not remain constant over time and are
generally discouraged.

5.4 Other Trip Purposes Requiring Special Treatment

In addition to extemal-to-external trips, two other common trip
purposes do not behave according to a gravity model. These are school
trips and truck trips. School trips by automobile are relatively small
in number and can sometimes be folded in with home-based-work trips
without seriously affecting forecasts of highway volumes. To the extent
that truck trips are external trips, they will be properly accounted for
during the calibration of external stations. Truck trips that are
strictly internal can sometimes be combined with the other internal trip
purposes, particularly nonhome-based trips.

Combining school trips and internal truck trips with other trip
purposes, however, could cause distortions in the forecast. Check for
this possibility. It may be necessary to supply a separate trip table
for each of these purposes. Normally, however, the distortions will be
insignificant and the trips can be folded into the other trip purposes.

For additional information on trip distribution, see references 1, 5
and 8.

6.0 TRAFFIC ASSIGNMENT

Within the traffic assignment process, steps can be taken to provide
a better match between link volumes simulated by the models and measured
base year traffic counts. The three most common traffic assignment
procedures, to be discussed below, are: (1) all or nothing; (2) capacity
restraint; and (3) equilibrium. Capacity restraint and equilibrium are
variations on the all-or-nothing assignment process. Additional
information on traffic assignment can be found in reference 3.

6.1 All-or-Nothing Assignments

All-or-nothing assignment assigns all vehicle trips between two zones
in a trip table to the links in the highway network comprising a single
minimum time path. Assignments using this technique do not take into
account delay caused by limited capacity of the links (i.e., the
resulting congestion) comprising the minimum time path. A minimum path
assignment simply shows the route that would be used if there was
unlimited capacity on the routes. Figure 13 shows a simple network.
There are two logical paths from zone 11 to 12-path 11-2-3-4-12 with a
total travel time of 2+3+3+2= 10 minutes and path 11-98-7-12 with a
travel time of 12 minutes. All the trips from zone 11 to 12 would be
assigned to the minimum time path 11-2-3-4-12.

Figure 13-All-or-Nothing Traffic Assignment Example

A simple table for coding link speeds was shown in Table 1. In Figure
13, if link 2-3 has a length of 1 mile and a speed of 20 miles per hour,
the travel time will be 3 minutes as shown. If the speed is dropped to
10 miles per hour, travel time for link 2-3 will increase to 6 minutes.
Ile minimum path for trips between zone 11 to 12 would then become 11-9-
8-7-12, rather than 11-2-3-4-12. By decreasing the speed on link 2-3,
traffic is diverted to an alternate route. Lowering speeds on links
decreases their volumes. Correspondingly, increasing link speeds
decreases link travel time and thus can increase volumes assigned to the
links, assuming, of course, that the decreased link travel time causes
the path that uses it to be more attractive to trips.

Initial speeds for highway links should correspond to a level of
service of C for the facility. Level of service C speeds would be
equivalent to approximately 87% of the free flow speed. For example, if
a freeway has a free flow speed of 60 miles per hour, then the initial
speed might be 0.87 x 60 or 52 miles per hour.

6.2 Capacity Restraint Assignment

Capacity restraint assignment attempts to balance assigned volumes
with coded link capacity and speed. An iterative procedure is used.
'Me first iteration is an all-or-nothing assignment. On successive
iterations, link speeds are adjusted based on a volume delay or speed
volume curve. The BPR formula is probably the most common speed volume
curve used. However, different equations have been calibrated for
different urban areas. New minimum paths are computed and another all-
or-nothing assignment is made using the new paths. There is no
assurance that the volumes will converge to a stable value. The final
assignment may be an average of the assigned volumes from each
iteration, or the volumes from some (usually later) iterations may be
weighted more heavily.

For capacity restraint assignment techniques, the coded link capacity
will affect link speeds on the second and subsequent iterations
according to Formula 1, and as illustrated in Figure 14.

S
FORMULA 1: S = -----------------
1 + .15 (v/c)4

SPEED
where: S = actual speed
So = Free Flow Speed
v/c = volume to c capacity ratio
c = capacity at level of service C
v = volume

FIGURE 14-Speed-Volume Curve

The following is an example of how capacity alters assigned volumes:

Link Characteristics

Link Length = 1 mile
0----------O So = 60 mph
1 2 Capacity = 3000 VPH
Assigned Volume = 3000 VPH

Using Formula 1, the speed for link 1-2 would be as follows:

60
S = ---------------------------
4
1 + .15 (3000/3000)

60 60 60
S = --------- = ---------- = --------
4
1 + .15(1) 1 + .15 1.15

S = 52 MPH

With a speed of 52 MPH the travel time for link 1-2 would be 1. 15
(60/52) minutes. If the capacity of link 1-2 is lowered to 1500 VPH the
speed would be reduced using Formula 1.

60
S = ---------------------------
4
1 + .15 (3000/1500)

60 60 60
S = --------- = ---------- = --------
4
1 + .15(2) 1 + 2.4 3.4

S = 18 MPH

For a travel speed of 18 MPH, the travel time for link 1-2 would
increase to 3.3 minutes.

As shown earlier in this chapter, an increase in the travel time of a
link will likely lower the assigned volume. Correspondingly, a decrease
in travel time will increase the assigned volume. Therefore, as shown
in the example, lowering the speed during the application of the
capacity restraint traffic assignment process, either by starting with a
lower speed 'S' or by adjusting the value of capacity 'C', will increase
the travel time which in turn will lower the assigned volume on
congested links.

If assigned volumes for entire classifications of facilities are high
or low, speeds or capacities can be used to correct the inconsistencies.
Table 9 summarizes these relationships. For an assignment where
assigned freeway volumes are low and arterials are high, one way to
correct the problem is to raise the speed or capacity of the freeways or
lower the speed or capacity of the arterials. It is important to
remember that capacity will only affect assigned volumes if a capacity
restraint assignment process is used, whereas changes in speed will
affect assigned volumes no matter what type of assignment procedure is
used.

Table 10-Capacity Relationships

IF THEN AND AND
Link Speed Travel Time Assigned
Capacity Volume

6.2.1 Changing the Definition of Capacity

Some planners opt to use a different definition of capacity in the
speed-volume function. Instead of design capacity (flow at level of
service C), they use ultimate capacity (flow at level of service E).
Such a change in definition requires a change in the parameters of the
speed-volume function. Specifically, the parameter that multiplies the
volume-to-capacity ratio must be a larger number when the definition of
capacity is taken to be ultimate capacity. A value of 0.80 (instead of
0. 15) is approximately correct for most facilities. It may be
necessary to vary this parameter to obtain good speed estimates. An
excellent source of information about the relationship between speed and
ultimate capacity is the 1985 Highway Capacity Manual.

6.3 Calibration with Equilibrium Assignment

It is very difficult on congested networks to obtain good estimates
of link volumes with an all-ornothing assignment. There is more control
possible with an iterative capacity restraint process that weights the
iteration results. However, with the above two methods, volumes on
individual links can be erratically sensitive to small changes in link
travel time or turn penalties. This sensitivity to small changes in
link travel times or turn penalties makes the process of arriving at
just the right combination of speeds on the various links especially
difficult.

Equilibrium assignment techniques are based on similar concepts used
in the previous two methods. In an equilibrium assignment, there are
usually several equally good paths through the network for each origin-
destination pair. These extra paths help produce a more accurate
assignment, and they also have an important benefit during calibration.
The extra paths buffer the effect of link speeds on link volumes, that
is, a small change in speed will cause an appropriately small change in
volume.

Because they are iterative procedures, equilibrium assignment
algorithms are time-consuming. Nonetheless, their advantages may be
substantial. Equilibrium assignments require many iterations to
converge. It is recommended that at least 3 iterations (or 4
increments) be used for initial calibration and that at least 10
iterations (or 11 increments) be used for final calibration and
comparisons of alternatives. Even more iterations may be necessary if
there are fewer than 100 zones in your network.

A word of caution:

Equilibrium and capacity restraint assignments are beneficial if
congestion exists. For small urbanized areas with minimal congestion,
an all-or-nothing assignment may be more appropriate and give adequate
results.

6.3.1 Speeds and Travel Times with Equilibrium Assignment

An equilibrium assignment algorithm (or an algorithm that produces
similar results) will calculate a speed (or travel time) for each link.
The initial settings of speeds and travel times are less important than
the free speeds and free travel times. Adjustments to initial speeds
during calibration have almost no effect on the forecasted volumes,
unless your package has a means of approximating free speeds (or free
travel times) from the given initial speeds. Check the documentation of
the software package. It may be required that initial speeds always be
entered as if traffic were moving at level of service C.

6.3.2 Determining Free Travel Times and Free Speeds on Links

Free travel time is defined as the time it would take a vehicle to
traverse a link if it were the only vehicle on the road. The link is
normally measured from stop line to stop line (i.e., the free travel
time usually includes the delay associated with passing through at least
one intersection). Consequently, links in areas with many signalized
intersections tend to have large free travel times (or low speeds). On
a road with good progressive signalization, a free travel time should be
approximately 10% greater than the time it would take to traverse the
link at the speed limit. In other words, traffic moves about 10% slower
than the speed limit when there are few vehicles on a road having
several intersections. You may need to vary free travel time in order
to obtain reasonable agreement with ground counts.

7.0 TRANSIT RIDERSHIP EFFECT ON HIGHWAY VOLUMES

If a study area has significant amounts of transit ridership,
forecasted highway assignment volumes may be too large if this transit
ridership is not taken into account. The following methods can be used
for small and medium size urban areas to adjust for transit ridership
without having to build and process a transit network. If the trip
generation process included transit trips, the following adjustments may
be necessary.

1. Increase automobile occupancy by the percentage of persons using
transit. For example, if the current transit ridership is 5 % and
the actual automobile occupancy is 1.38, then the model automobile
occupancy should be 1.45 (1.38 times 1.05), thus reducing the
number of vehicles on the highway links.

2. Decrease trip production or trip attractions rates to represent
the percentage of transit ridership. Rates for both productions
and attractions need not be adjusted. Depending upon the
balancing option in the trip generation step, only one set of
rates controls the total number of trips in the system. If trip
production rates are modified, it is desirable to vary the mode
split by income category.

3. Modify the productions or attractions in individual zones. To do
this, first obtain current ridership data from the local transit
agency. Productions and attractions can be varied by either (1)
making downward adjustments to population and employment estimates
for zones or (2) directly modifying the productions and
attractions after they have been calculated in the trip generation
step.

* A word of caution. For small and medium size urban areas, transit
patronage may be insignificant and a transit adjustment will be
unnecessary.

8.0 EXTERNAL STATIONS

External stations are used to represent trips coming to or going from
the study area. Analytically, external stations work much like
centroids in the network, that is, a trip can have either its origin or
destination at that node. Practically speaking, an external station
represents a point on a road; it does not have socioeconomic
characteristics. Consequently, productions and attractions by trip
purpose for external stations are prepared by observing and matching the
relevant ground counts.

Some forecasting packages make a distinction between two classes of
external trips: internal-to external (I-E) and exterrial-to-internal (E-
1); and external-to-external (E-E). E-1 and I-E trips are handled in
the same manner as internal-to-intemal trips, but E-E trips require
special treatment. E-E trips pass through the study area without
stopping. Assuming that there is information about the number of E-E
trips at the external stations, there are ways of accounting for them in
the forecast. If there are relatively few E-E trips, then they can be
added to the E-I and I-E trips assignment. Many of the E-E trips will
be assigned to the wrong roads, but the overall assignment may still be
acceptable. When there is a significant amount of E-E trips, the
following procedures should be considered:

- If the E-E trips always follow specific paths through the network,
then those trips can be manually assigned to the correct links
(check the documentation of your forecasting package for the
proper method of doing this). An example of such a situation
would be a major interstate highway passing through a small
community.

- Create an E-E trip table and assign it to the network along with
the other trip purposes. You should not expect a gravity model to
accurately represent E-E trips.

Table 10 gives approximate percentages of all external trips that are
E-E trips. Local data about trips at external stations should be
obtained. Surveys of drivers at external stations are comparatively
inexpensive and are quite helpful in improving the quality of your
forecasts.

Table 11-- Percentages of External-to-External Travel for Cities of
Various Sizes

Urban Area % of All External Trip
Population That are E-E

50,000 - 100,000 21
100,000 - 250,000 15
250,000 - 750,000 10
750,000 - 2,000,000 4

Source: Reference 5

9.0 SYSTEM CHANGES VERSUS LOCAL CHANGES

Model calibration requires a determination of whether differences
between simulated volumes and ground counts are system-wide, more local
in nature, or a combination of both. Three levels of comparison should
be made:

1. System-wide (e.g. across screenlines)
2. By major movement (e.g. across cutlines)
3. By link

If volumes are consistently high or low across the region then system
wide characteristics must be changed to correct the problem. For
example, all screenlines are found to be 15 to 20% low. To correct this
problem, a number of system wide changes should be considered.
Characteristics that affect system wide volume changes are:

1. Auto occupancy rates
2. Trip generation rates
3. Trip length
4. Intrazonal time (all zones)
5. Socioeconomic data - income, dwelling units (all zones)

Quite often, regional totals will adequately reflect the travel in
the region, but there will be major differences across cutlines or
between major areas. These differences may indicate that adjustments
are necessary for major movements within the region such as between a
major residential area and employment center or along a major corridor.

Some possible areas for investigation are as follows:

- For volumes in a corridor that are too high or low, check:
- Auto occupancy rates for facilities in corridor
- Trip generation rates for zones contributing high volumes of
trips to the corridor
- Land use data for these same zones
- Centroid connectors in the area of the corridor
- Intrazonal times in zones near the corridor
- Intersection penalties

- Travel between major areas too high or too low (this may become
apparent through several cutlines in a portion of the region being
generally too high or too low):

- Trip generation rates in subarea
- Land use data in subarea
- Trip lengths
- Intrazonal time (selected zones)
- Vehicle occupancy

If total volumes for all links match the total ground counts, but
individual links are high or low, changes must be made that only affect
specific links. For local changes that affect only specific links, the
following characteristics could be modified:

1. Speed and capacity (link specific)
2. Intersection penalties (nodes for a specific
link)
3. Centroid locations
4. Special generators (near specific link)
5. Local network configuration

10.0 EXPECTED AND REQUIRED ACCURACY

As discussed in previous sections, a regional transportation planning
model consists of a complex series of steps with many built-in
assumptions. When calibrating a model, one should not be overly
optimistic about matching the simulated volume to ground counts. A
range of accuracy for such a comparison is shown in Figure 15.

A reasonable expectation is for the model to be accurate enough so
that it will not affect the number of lanes required to handle the
volume. For example, if the model forecasts an ADT of 5,000 and the
actual ADT is 2,000 a design change would not result. The number of
lanes necessary for an ADT of 5,000 is two lanes and the number of lanes
needed for an ADT of 2000 is still 2 lanes. In spite of having an error
of 150% the required number of lanes remains the same.

As the ADT on a facility increases, the expected accuracy of the
models should increase as well. For example, links with an ADT of
100,000 would have an acceptable range of accuracy of + 15% or 85,000 to
115,000. The number of required lanes would not change. Figure 15
shows the acceptable range of deviation from actual volumes. As shown
in this Figure, the lower the volume, the higher the anticipated
deviation.

A word of caution: When comparing forecasted volumes to ground
counts, it is important to recognize that the ground counts probably
contain a significant amount of error.

Traffic volumes vary greatly by season and by day of week. Count
errors can be caused by variation in the mix of vehicles in the traffic
stream. Regularly occurring local events, special events, and accidents
can distort the counts on large portions of the highway system. Errors
can also be due to mechanical counter failure, field personnel mistakes,
or improper counter location. Procedures have been developed to help
correct for some of this variation, but these procedures are imperfect.
There is often no way to ensure that ground counts correspond to the
same time period as base-case socioeconomic data.

Base-case ground counts should be thought of as approximations of
existing traffic, just as the basecase model estimate is an
approximation to existing traffic. There is a definite limit to how
well model estimates should match ground counts. Figure 15 also shows
the expected error in ground counts due to day-to-day variations in
traffic. A perfectly calibrated model would have the link estimates
clustered about the expected error in ground counts with about one-third
of the links with a higher error and about two-thirds of the links with
a lower error.

FIGURE 15

Click HERE for graphic.

10.1 Performance Measures Based on Observed Counts

Traffic assignment provides the best opportunity to evaluate the
reasonableness of the entire modeling process. However, if the assigned
volumes are judged to be unreasonable, it is difficult to know from an
assignment where the difficulty lies. For this reason, it is important
to test the trip generation model, the network definition, and the trip
distribution model as thoroughly as possible prior to performing
assignments.

--Percent Error Region-wide:

Ideally, ground counts are made for 100 percent of the network links
for the validation year. In practice, this is not possible. However,
ground counts need to be made for a high percentage (greater than 65
percent) of freeways and principal arterials and a reasonable percentage
of minor arterials and collectors. Estimation of traffic counts for
links that were not counted may be desirable if it can be done with a
high degree of accuracy. If it cannot be done with accuracy, it is
better to validate using only actual counts.

Percent error is the total assigned traffic volumes divided by the
total counted traffic volumes (ground counts) for all the links that
have counted volumes. The percent error region-wide should be less than
5 percent.

--Percent Error by Functional Classification:

This test will provide insight into whether the assignment model is
loading trips onto the ftinctionally classified systems in a reasonable
manner. The percent error by functional classification is the total
assigned traffic volumes divided by the total counted traffic volumes
(ground counts) for all links that have counted volumes, disaggregated
by functional classification. Suggested error limits are:

Freeways: Less than 7 percent.
Principal Arterials: Less than 10 percent.
Minor Arterials: Less than 15 percent.
Collectors: Less than 25 percent.
Frontage Roads: Less than 25 percent.

--Correlation Coefficient:

A sample correlation coefficient, r, calculated using pairs of
assigned and counted volumes typically will have a value greater than
0.88. Most modelling packages calculate this value.

10.2 Performance Measures Based on VNIT

An independent region-wide VMT estimate prepared annually, based on
traffic counts and a roadway inventory, provides a good check on the
reasonableness of the base-year traffic assignment. Depending on the
number of counts made annually, it is possible to develop independent
estimates of VMT by functional classification and area type as well. If
the comparison of assigned VMT and counted VMT is not satisfactory, the
most probable cause is an error in the trip length frequency
distribution.

--Region-wide VMT

If the urban area prepares an annual VMT estimate, the assigned VMT
should agree with the assignment estimated VMT within 5 percent.
However, care should be taken that the basis for the two estimates are
the same. Often the annual VMT estimate is for all roads in an area,
whereas assignments do not represent all roads. Appropriate adjustments
should be made prior to the comparison.

--VMT by Functional Classification:

Assigned VMT by functional classification provides an excellent check
of the reasonableness of an assignment. Typically, urban area VMT is
distributed as follows:

Small Medium Large
50-200K 200-1M >1M

Freeway/Expressway 18-23% 33-38% 40%

Other Principal Arterials 37-43% 27-33% 27%

Minor Arterials 25-28% 18-22% 18-22%

Collectors 12-15% 8-12% 8-12%

Source: Reference 9

--VMT Per Person:

The VMT per person needs to be reasonable for the validation year and
the forecast year. For a large urban area a reasonable range of VMT per
person is 17 to 24 miles. For a small urban area a reasonable range is
10 to 16 miles. If an annual independent region-wide VMT estimate is
made this can be converted to an estimated VMT per person and compared
to the assigned VMT per person value. Annual urban area population
estimates are usually available. See appendix A, Table A7 for
additional data on VMT per person.

--VMT Per Household:

The daily VMT per household needs to be reasonable for the validation
year and the forecast year. For a large urban area, a reasonable range
of daily VMT per household is 40-60 miles. For a small urban area a
reasonable range is 30-40 miles.

11.0 CONCLUSIONS

This manual has identified several key issues relating to model
calibration and validation. As noted on the first page, a good origin-
destination data base is the most preferred basis for calibration and
validation. In the absence of such a data base, however, planners often
need to make adjustments to model parameters so that model results
better replicate actual trip volumes. In so doing, planners must be
careful about the variable relationships that are inherent in these
models. T'he problem of modelgenerated link volumes not replicating
ground counts can be caused by many different factors. Careful
consideration needs to be given to any steps taken to modify model
parameters. Do real-world conditions justify the scope and magnitude of
such modifications?

In addition, each planning software package has often unique
approaches and assumptions. They are based on a similar theory of
travel behavior. However, the user-interface varies greatly across
packages. Avoid mistakes by fully understanding all features of the
software. If the model is producing unreasonable results or if it will
not respond as expected to changes in parameters or data, additional
information should be obtained on how to make the model function
properly. The reference manual is likely to contain the solution to the
problem; If the answer cannot be found there, contact another
experienced user or the person responsible for technical support of the
package.

12.0 TROUBLESHOOTING

This section describes problems that may result during model
calibration and validation and some possible solutions. Each possible
solution should be evaluated to determine if an individual or a
combination of solutions would be most appropriate for resolving the
identified problems. Solutions are not given in a priority order nor
are they all encompassing.

PROBLEM POSSIBLE SOLUTIONS

1. Systemwide volumes higher a. Raise auto occupancy
than ground counts rates
b. Lower trip production rates
c. Lower number of dwelling
units
d. Lower average income or
average auto ownership
e. Lower average trip lengths
f. Increase intrazonal trips

2. Systemwide volumes lower a. Lower auto occupancy
than ground counts rates
b. Raise trip production rates
c. Raise number of dwelling
units
d. Raise average income or
average auto ownership
e. Raise average trip lengths
f. Decrease intrazonal trips

3. Total systemwide volumes a. Modify speed and capacity
match ground counts but of specific link
specific links do not b. Modify local network
c. Add or delete nearby centroid
connectors
d. Add or delete intersection
penalties leading to or from
link
e. Check nearby special
generators
f. Check socioeconomic data
of nearby zones

4. Bridge crossing volumes a. Modify speed, capacity,
do not match ground counts or length of bridge links
b. Modify nearby network
c. Modify average trip length

5. Freeway volumes are high a. Lower the speed or capacity
of freeway links
b. Raise the speed or capacity
of parallel arterial links
c. Adjust nearby centroid
connectors
d. Raise intersection penalties
on links leading to freeway

6. Freeway volumes are low a. Raise speed or capacity of
freeway links
b. Lower the speed or capacity
of parallel arterial links
c. Adjust nearby centroid
connectors
d. Lower intersection
penalties on
links leading to freeway

7. Arterial volumes are low a. See Solutions Problem #5

8. Arterial volumes are high a. See Solutions Problem #6

9. High volume facilities overloaded a. Use capacity restraint or
beyond capacity equilibrium assignment
(Note: This is important infor- b. Increase the number of
mation for your planning. Such a assignment iterations
condition may remain even after (see Traffic Assignment
all reasonable adjustments have Section)
been made in the model process. c. Lower speeds and capacities
of high high volume
facilities
d. Increase speed and capacities
of low volume roads

10. A resulting link speed is a. Increase the free travel
too high time
b. Decrease the capacity
c. Decrease the traffic
assignment coefficient
multiplying the volume-to-
capacity ratio (esp.
multiple-hour assignments)

11. A resulting link speed is too low a. Decrease the free travel
time
b. Increase the capacity
c. Increase the traffic
assignment coefficient
multiplying the volume-to-
capacity ratio

12. Paths between origins and a. Recheck the network for
destinations are unreasonable coding errors
b. Decrease the size of turn
penalties in dense portions
of the network
c. Decrease the number of turn
penalties in specific parts
of the network
d. Set link speeds so that they
consider the effects of
distance minimization
e. Use an assignment algorithm
(e.g., equilibrium) that
properly accounts for the
volumes on links)

General Hints

1. If a specific link is significantly different than the ground
count check the volumes of nearby links. This may make it
possible to trace where trips are going and assist in
identifying the error. Selected link analysis is useful for
this purpose as well as for other evaluation of model results.
This procedure allows the determination of the origins and
destinations of trips using a specific link(s).

2. Confirm that centroids and centroids connectors are accurately
represented in the network.

3. Check the network to ensure the number of links is compatible
with the number of zones. See Reference 3.

4. Generally links should form the boundaries of zones.

5. Strive to make changes that make sense and are predictable in
the future. Try not to be arbitrary in making the changes.

REFERENCES

(1) Calibrating and Testing a Gravity Model for Any Size Urban
Area, by U.S. Department of Transportation, Federal Highway
Administration, August 1983

(2) Highway Traffic Data for Urbanized Area Project Planning and
Design, by N.J. Pederson and D.R. Samdahl, JHK & Associates,
Transportation Research Board, Washington, D.C., December
1982

(3) Traffic Assignment, by Comsis Corporation, For Federal
Highway Administration, August 1973

(4) An Analysis of Urban Area Travel by Time of Day, by Peat,
Marwick, Mitchell & Co., For Federal Highway Administration,
January 1972

(5) Quick-Response Urban Travel Estimation Techniques and
Transferable Parameters, by Art Sosslau, Comsis Corporation,
National Cooperative Highway Research Program, Report 187,
Washington, D.C., 1978

(6) Characteristics of Urban Transportation Demand, by U.S.
Department of Transportation, UMTA, July 1988

(7) Trip Generation Analysis, by Comsis Corporation, For Federal
Highway Administration, August 1975

(8) Urban Trip Distribution Friction Factors, by U.S. Department
of Transportation, Federal Highway Administration, 1974

(9) Increasing the Capacity of Urban Highways -- The Role of
Freeways, by Christopher Fleet and Patrick DeCorla-Souza,
presented at the 69th Annual Meeting of the TRB, January 7-
11, 1990

(10) Factors and Trends in Trip Length, by Alan M. Voorhees and
Associates, NCHRP Report #48, 1968

APPENDIX

TABLE A-1

COMPARISON OF TRANSPORTATION PLANNING DATA FOR URBANIZED AREAS
BASED ON THE U.S. CENSUS FOR 1960, 1970, AND 1980

URBANIZED AREA FACTOR 1960 1970 1980

Total number of areas a 202 248 366
Total population 91,322,864 118,440,006 139,182,696
Total number of households 28,107,216 37,791,508 50,549,711
Total housing units 29,756,224 39,557,589 53,824,097
Percent renter-occupied housing 43.7 41.1 39.2
Workers as percent of population 38.5 40.3 45.7
Autos per household 1.0 1.2 1.3
Persons per auto 3.3 2.6 2.1
Workers per auto 1.3 1.1 0.9
Persons per household 3.2 3.1 2.8
Workers per household 1.3 1.3 1.3
Percent of workers making work trip by
Auto(b) 73.4 77.3 83.4(b)
Rail 8.2 4.9 3.4
Bus 16.4 8.7 6.1
Percent of households with
0 Auto 25.3 20.1 16.7
1 Auto 54.6 45.5 44.6
2 Autos 17.8 29.0 30.3
3+ Autos 2.3 5.4 8.4

A-1

TABLE A-2

TRIP GENERATION: PER PERSON, PER HOUSEHOLD

Persons Persons Vehicles Vehicle
Study Area Person Trips per per per per Trips per
Study Area Year Description Person Household Household Vehicle Household Household

Atlanta 1972 1,640,000 2.49 7.2 2.9 2.1 1.38 ---
Baltimore 1977 T.P.A. 2.9 8.3 2.8 --- --- ---
Buffalo, 1973 1,234,000 2.5 7.5 3.0 2.5 1.2 ---
Chicago 1979 City 1.6 4.6 2.9 --- -- ---
Chicago 1979 SMSA 2.4 7.2 3.0 --- --- ---
Dallas 1984 T.P.A. 3.40 8.68 2.6 1.4 1.84 6.4
Detroit(a) 1980 7 County 2.59 7.47 2.9 --- --- ---
Denver 1980 T.P.A. --- --- --- --- 2.27 8.3
(U.A.)
Denver 1971 T.P.A 2.83 8.76 3.10 2.21 1.40 ---
Duluth 1970 157,000 2.83 8.23 2.91 2.88 1.01(b) --
El Paso 1970 362,800 2.53 8.68 3.43 3.03 1.13(b) ---
Fresno/Clovis 1972 295,000 3.00 8.25 2.74 2.21 1.21(b) ---
Greensboro 1970 182,000 2.44 8.29 3.40 2.43 1.40(b) ---
Huntington 1972 215,000 2.86 9.09 3.18 2.89 1.10(b) ---Los
Angeles 1976 6 County 2.99 8.15 2.8 1.8 1.6 ---
Louisville 1975 Urban Areas 2.19 6.34 2.90 1.91 1.52 5.0
Miami 1980 SMSA 3.2 --- --- -- --- ---
Milwaukee 1972 7 County 2.5 7.9 3.2 2.6 1.24(b) 6.1
Minn./St. Paul 1982 7 County 3.37 -- -- -- 1.58 6.9
Philadelphia 1977 SMSA (+) 2.45 7.66 2.5 2.45 1.27 6.0
Phoenix 1980 T.P.A. 2.44 6.58 2.7 -- -- ---
Portland 1977 SMSA 3.67 8.66 2.4 --- --- ---
Rochester 1974 735,000 2.56 8.03 3.14 2.75 -- ---
Sacramento 1978 3 County 3.39 9.34 2.6 1.6 1.6 ---
San Antonio 1980 County -- -- --- 1.39 -- ---
San Diego 1977 County 3.5 9.8 2.8 1.71 1.64 ---
San Francisco 80/81 CMSA (-) 3.40(a) 8.71 2.56 1.52 1.70 ---
Seattle 1977 T.P.A. -- 6.63 -- -- --- ---
Springfield, MA 1981 2 County -- --- -- --- 1.51 ---
Washington, DC 1968 2,114,000 2.17 --- -- 2.58 -- ---
NPTS 1969 USA 2.02(d,e) 6.36(d,e) 3.2 --- 1.2 3.8(d)
NPTS 1977 USA 2.72(d) 7.20(d) 2.8 1.77 1.6 4.0(d)
NPTS 1983 USA 2.68(d) 7.69(d) 2.7 1.60 1.7 4.1(d)

Key to Notes:
a Recession may have reduced trip rates. d Based on 365 days per year.
b Autos per household. e Does not include walk and bicycle trips
made
c Trips per person 5 years and older equals 3.63. by persons under 5 years old.

SOURCE: Reports from individual study area.

A-2

TABLE A-3

PERSON TRIPS GENERATED PER HOUSEHOLD
BY AUTO OWNERSHIP
Area Autos per Household All
Study Area Year Description 0 1 2 3+ Households

Buffalo 1973 1,234,000 1.6 6.9 11.5 16.9 7.5
Cincinnati 1972 T.P.A. 2.0 6.5 ----11.6---- ---
Chicago(a) 1979 City 1.9 5.3 7.7 9.5 4.6
Chicago(a) 1979 SMSA 1.7 6.4 10.7 12.7 7.2
Fresno 1971 295,000 1.3 6.7 ----12.0---- 8.2
Los Angeles 1976 6 County 2.0 5.8 ----11.0---- 8.1
Milwaukee 1972 7 County 1.9 7.0 11.5 16.0 7.9
Minn./St.Paul 1982 7 County 1.8 6.5 11.1 16.4 9.1
Monterey 1970 T.P.A 1.2 6.6 ----12.0---- ---
Portland 1977 SMSA 3.0 6.8 ----11.5---- 8.7
Rochester 1974 735,000 2.2 7.1 11.1 14.0 8.0
San Diego(b) 1977 County 3.0 6.6 ----13.0---- 9.8
San Francisco 80/81 CMSA (-) 4.0 6.3 10.1 13.4 8.7
Washington, DC 1968 2,714,000 2.1 5.9 9.7 10.6 ---

Key Notes:

a -- Shown are person trips per occupied dwelling unit.
b -- Person trips not including motorcycle, bicycle, walking.

SOURCE: Reports from individual study areas.

A-3

TABLE A-4

PERSON TRIPS GENERATED PER HOUSEHOLD
BY HOUSEHOLD INCOME

Study Area $0- $5- $10- $15- $25- $35- All
Study Area Year Description 4,999 9,999 14,999 24,999 34,999 $50,000 50,000+ Income Notes

Baltimore 1977 T.P.A. ------5.0------ 8.1(a) ------------------11.6(a)------------ 8.3
Chicago 1979 SMSA ------3.0---- 5.8 7.0 ------------11.9----------- 7.2 b
Los Angeles 1976 6 County 4.2 6.1 8.1 10.9 12.2 ------12.6------- 8.1 c
Milwaukee 1972 7 County 3.4 7.2 10.7 12.2 -----------13.9------------ 8.8 c
Minn./St. Paul 1982 7 County ------3.9------ 6.3 8.6 11.2 -------12.9------ 9.1
Phoenix 1980 T.P.A. 3.4 4.6 5.6 7.1 ------------8.6------------ 6.7 c
Portland 1977 SMSA ------4.6------ ------8.9------- -----------12.6------------ 8.1 d
San Diego 1977 County 3.2(h) 7.0(h) 8.9(h) 12.3(h) 14.6 14.1 15.8 9.5 e,f
San Francisco 80/81 CMSA(-) 3.6 5.7 7.2 8.5 10.9 11.1 12.5 8.7 g
NPTS 1983 USA ------5.3------ 10.2(i) 14.7(i) 14.5(i) -----19.7(i)----- 11.1

Key to Notes:
a - Income categories are $10,000-18,999 and $19,000 and over.
b - Income categories are 0-$9,000 and $9,001-15,000.
c - Recomputed from different income groupings.
d - Income categories are 0-$7,999, $8-29,000, and $20,000 and
over.
e - Income in 1977 dollars.
f - Does not include trips by motorcycle, bicycle, walking.
g - Average equals 9.06 for households reporting income.
h - Calcluated by simple averaging over smaller income categories.
i - Income categories are $10-19,999;$20-29,999;$30-39,999; and
$40,000 and over.

SOURCE: Reports from individual study areas.

TABLE A-5

AVERAGE DAILY VEHICLE TRIPS PER HOUSEHOLD BY FAMILY INCOME AND VEHICLE
OWNERSHIP (1983/4)

Family
Income Number of Household Vehicles
(Dollars) 1 2 3 4+ All
0- 9,999 2.6 3.7 5.1 6.8 1.9
10-19,999 3.1 4.9 5.5 7.0 3.3
20-29,999 3.4 5.1 5.9 8.5 4.9
30-39,999 3.1 5.4 7.0 8.2 5.6
40,000+ 2.9 5.7 6.9 9.2 6.2
All 3.0 5.1 6.3 8.4 4.1

SOURCE: Federal Highway Administration, Survey Data Tabulations: 1983-
1984 Nationwide Personal Transportation Study, November 1985,
p.11.

A-5

TABLE A-6

PERSON TRIPS BY HOME-AND NONHOME-BASED
Percentage Distribution
___________________________
Home- Home-
Study Area Based Based
Study Area Year Description Work NonWork Based Total

Atlanta 1972 1,640,000 25.4 55.4 19.2 100
Baltimore 1977 1,749,125 22.3 54.7 23.0 100
Cincinnati 1978 T.P.A. 28.7 53.3 18.0 100
Dallas 1980 T.P.A. 19.9 59.7 20.4 100
Denver 1982 Urbanized Area 25.2 54.0 20.8 100
Detroit 1980 7 County 20.3 53.8 25.9 100
El Paso 1970 363,000 19.7 55.9 24.4 100
Evansville 1978 T.P.A. 19.1 46.9 34.0 100
Indianapolis 1970 T.P.A. 25.4 53.4 21.2 100
Kansas City 1970 8 County 18.7(a) 59.1 22.2 100
Los Angeles 1976 6 County 19.2 52.7 28.2 100
Louisville 1975 Urbanized Area 26.6 54.1 19.3 100
Milwaukee 1972 7 County 33.0 47.0 20.0 100
Minn./St. Paul 1982 7 County 17.9 53.7 28.4(b) 100
Pensacola 1970 T.P.A. 14.8 59.2 26.0 100
Philadelphia 1977 SMSA(+) 23.0 55.0 22.0 100
Phoenix 1980 T.P.A. 25.7 53.5 20.8 100
Portland 1977 SMSA 19.3 57.9 22.8 100
Sacramento 1978 3 County 13.9 58.8 27.3 100
San Diego 1977 County (-) 14.6 57.5 28.0 100
San Francisco 1980 9 County 18.2 51.4 30.4 100
Washington,, DC 1968 2,714,000 24.4 62.8 12.8 100

Key to Notes

a --"Serve Passenger" not included in Home-Based Work trip purpose.
b -- 45 percent are Nonhome-Based Work trips.

Source: Reports from individual study areas.

A-6

TABLE A-7

DAILY VMT: TOTAL AND PER PERSON

Total Daily
Study Area VMT VMT per
Study Area Year Description (000,000) Person

Atlanta 1972 1,640,000 12.6 13.8
Chicago 1970 8 County 95.6 12.6
Chicago 1975 SMSA 99.0 ----
Dallas 1983 County 40.6 24.7
Denver 1983 Urbanized Area 25.6 16.4
Detroit 1980 7 County 56.3 ----
Evansville 1970 175,000 1.8 10.3
Honolulu 1970 750,000 8.9 11.9
Houston 1977 2,300,000 41.0 17.8
Los Angeles/ 1982 Urbanized Area 165.4 17.4
Long Beach
Louisville 1975 Urban Area 10.8 12.7
Louisville 1981 Urban Area 13.0 15.6
Milwaukee 1972 Urbanized Area 13.0 ----
Milwaukee 1972 7 County 20.1 11.1
Minn./St. Paul 1980 7 County 36.1 18.2
New York City 1980 City 41.8 5.9
Philadelphia 1977 SMSA 57.71(a) 11.3
Phoenix 1979 T.P.A. 10.3(b) 9.0
Portland 1977 SMSA 10.7 11.1
Sacramento 2982 Urbanized Area 15.2 19.1
San Diego 1982 Urbanized Area 30.8 18.1
San Francisco/ 1982 Urbanized Area 52.6 16.5
Oakland
San Jose 1982 Urbanized Area 22.0 17.7
Seattle 1975 1,800,000 23.6 13.1
St. Louis 1972 2,400,000 20.2 8.4
Tucson 1973 407,000 5.0 12.5
Washington,, DC 1980 SMSA 45.4(c) ----

NPTS 1969 USA ---- 10.6
NPTS 1983 USA ---- 11.9

Key to Notes:
a -- Includes 10.2 million VMT by truck.
b -- Major streets and freeways only.
c -- Includes 5.6 million VMT by truck.

SOURCE: Reports from individual study areas.

A-7

TABLE A-8

AVERAGE AUTO TRIP TIMES BY TRIP PURPOSE
(In Minutes)
Home--Based
Study Area ___________________________________________________ Nonhome- All External-
Study Area Year Description Work School Shop Soc./Rec. Other Based Trips Internal

Baltimore 1977 T.P.A. 15.6 ---- ---- ---- 10.9 12.6 ---- ----
Denver 1971 U.A. 18.6 ---- 10.6 ---- 14.1 ---- 15.1 33.0
Los ARPIN 1976 6 County 30.1 ---- 16.4 ---- 21.7 21.7 23.5 ----
Lag ARPIN 1967 9,008,400 17.8 ---- 5.4 ---- 9.7 8.2 11.0 ----
Minn./St.Paul 1970 1,874,400 19.2 27.0 11.4 17.3 ---- ---- 16.9 ----
Philadelphia 1977 SMSA (+) ---- ---- --- ----- ---- ---- 17.8 44.1
Sacramento 1979 3 County(-) 17.1 ---- 11.1 ---- 12.6 12.9 13.2 ----
Son Diego 1977 County(-) 24.6 ---- 14.8 ---- 19.0 18.5 19.6 ----
San Francisco 80/81 CMSA(-) 24.5 17.2 --- 18.6 14.5 16.3 18.0 ----
San Francisco 1965 4,400,000 15.8 ---- 9.5 11.5 9.4 9.1 ---- ----
Wilmington 1970 T.P.A. 9.5 ---- ---- ---- 7.7 7.3 8.9 11.9

SOURCE: Reports from individual study areas.

A-8

TABLE A-9
AUTO OCCUPANCY BY DESTINATION TRIP PURPOSE

Study Area Personal Social
Study Area Year Description Home Work Business Recreatin Shop Other All

Albuquerque 1981 T.P.A -- 1.22 -- 1.88 1.57 -- 1.51
Chicago 1979 SMSA 1.33 1.14 -- -- -- 1.44 1.33
Detroit 1980 7 County -- 1.22 -- -- -- -- 1.41
El Paso 1970 362,800 -- 1.2 1.4 1.7 -- 1.5 1.5
Milwaukee 1972 7 County 1.43 1.15 1.35 1.91 1.46 -- 1.41
Portland 1977 SMSA 1.45 1.13 --- 1.12 1.51 -- 1.50
San Diego 1977 County(-) 1.44 1.14 1.22 1.78 1.56 1.42 1.49
San Francisco 80/81 CMSA(-) -- 1.1 -- 1.7 1.2 -- 1.3
Springfield, MA 1980 2 County -- 1.14 -- -- -- -- 1.35

NPTS 1969 USA -- 1.4 1.9 2.5 2.0 -- 1.9
NPTS 1977 USA -- 1.4 1.8 2.4 1.9 -- 1.9
NTPS 1983 USA -- 1.3 1.8 2.2 1.7 -- 1.8

A-9

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