Integrating Parking Cost into Transit Generalized CostAn Application of Using Matrix Convolution.
Beth Jirong Xie Ph.D.
Metra, 547 W. Jackson Boulevard, Chicago, IL 60661
and
Kermit Wies Ph.D.
Chicago Area Transportation Study, 300 West Adams, Chicago, IL 60606
Presented to the 16th Annual International EMME/2 User's Group Conference
Albuquerque, New Mexico, USA
September 24-26, 2001
Integrating Parking Cost into Transit Generalized Cost-An Application
of Using Matrix Convolution
By
Beth Jirong Xie Ph.D.
Metra, 547 W. Jackson Boulevard, Chicago, IL 60661
and
Kermit Wies Ph.D.
Chicago Area Transportation Study, 300 West Adams, Chicago, IL 60606
Presented to the 16th Annual International EMME/2 User's Group Conference
Albuquerque, New Mexico, USA
September 24-26, 2001
Abstract
Chicago Area Transportation Study is the primary agency for the development
and maintenance of travel forecasting methods for the northeastern Illinois region. The
region has one of the most extensive public transportation systems in North America1.
About fifty percent work trips to the Chicago CBD are transit person trips. Many
commuters drive and park to take transit to the employment places in the Chicago CBD.
Parking costs have effects not only on mode choices to destinations, but also on mode
choices to transit facilities, primarily commuter rail. Under-estimated parking costs in
the CBD would cause the mode choice model to produce too many auto trips to the CBD.
Whereas an assumption of free parking for park-and-ride would make the transit cost low
and driving to transit facilities unrealistically inexpensive and attractive.
A method has been developed to integrate generalized parking costs into transit
generalized costs by using matrix convolution. Other than transit-oriented park-and-ride
facilities and CBD off-street facilities, there is no regional parking inventory. To
represent the regional reality that some areas have both fee parking lots and free street
parking as well, and some areas only have parking lots but no free parking, a variable
area type was used in addition to parking fee and parking capacity to calculate the
generalized parking costs. The calculation was added to a park-and-ride application in a
matrix convolution based on the example found in the Emme/2® documentation, in
which highway assignment was used to estimate drive costs, and the station access links
were used to identify station zones. The generalized parking costs were then added to the
total generalized transit cost through the matrix convolution. The advantage of this
method is that no detailed park-and-ride drive link coding or extra station or parking lot
matrix building was involved, leaving the model transferable between applications.
1
Chicago Area Transportation Study, 2020 Regional Transportation Plan 2000 Edition, TIP
Transportation Improvement Program for Northeastern Illinois FY 2001-2006, Appendix B,2000
1
I.
PURPOSE AND BACKGROUND
Chicago Area Transportation Study (CATS) is the primary agency for the
development and maintenance of travel forecasting methods for the northeastern Illinois
region. The region has one of the most extensive public transportation systems in North
America1. Transit service is provided by seven different transit modes, including
commuter rail, heavy rail, express bus and local bus in both urban and suburban areas of
six counties of a total 7.8 million population. In 1999 there were more than 23 million
person trips in the region, of which more than 20.9 million were auto person trips and
more than 2.14 million were transit person trips 2. Of these 23 million person trips, 1.8
million person trips go to the Chicago Central Business District (CBD), of which more
than 1.1 million were home based work trips to the CBD3. About fifty percent work trips
to the Chicago CBD are transit person trips. Many commuters, especially commuters
from surrounding counties drive and park to take transit to the employment places in the
Chicago CBD. Map One at the end of the paper presents the planning region and the
networks of the commuter rail, heavy rail and suburban bus.
The CATS existing mode choice model's transit utility function includes many
components including the congested time of auto access and the cost of base fares and
zonal fares in addition to the in-vehicle time, out-vehicle time, waiting time and boarding
time, but considers no parking cost. An effective mode choice model should adequately
include as many variables as possible to represent a traveler’s choice of each specific
mode over other modes. The traveler’s decision to drive to a park-and ride lot to take
transit, or take a bus to get to a rail facility depends on the generalized transit cost. The
generalized transit cost (time and monetary cost) is associated with the costs of all modes
of access and the transit trip to the final destination. The cost of driving to a park-andride lot should include both the driving cost and parking cost. Parking cost has effects
not only on mode choices to destinations, like auto trips to the CBD, but also on mode
choices to transit facilities, primarily commuter rail. Free parking or under-estimated
parking costs in the CBD would cause the mode choice model to produce too many auto
trips to the CBD. Further, an assumption of free parking for park-and-ride would make
the transit cost low and driving to transit facilities unrealistically inexpensive and
attractive. As a consequence, the model would predict too many park-and-ride trips but
too few bus trips to commuter rail.
There are 1790 transportation analysis zones in the CATS planning region. Other
than transit-oriented park-and-ride facilities and the central area of the CBD off-street
facilities, there is no regional parking inventory. In a parking facility database compiled
by Metra, the region’s commuter railroad, by January 2001, there were 232 Metra
stations, including the stations in the CBD. But parking information, such as parking
capacities and parking fees, are available for only 188 of the total 232 Metra stations.
These 188 stations are all located outside the Chicago CBD area. A wide variety of
1
Chicago Area Transportation Study, 2020 Regional Transportation Plan 2000 Edition, TIP
Transportation Improvement Program for Northeastern Illinois FY 2001-2006, Appendix B 2000
2
Chicago Area Transportation Study, 2020 Regional Transportation Plan-Destination 2020. 2000.
3
Summarized approximately from CATS 1999 trip tables.
2
parking and fee arrangements exist in many urbanized and suburban areas in the region
because most of the parking is managed by the municipalities, not by Metra. Further,
Metra's parking database does not include any of the South Shore's Indiana stations.
A parking inventory of the central area of the CBD was compiled in 19864. A
previous study by Ronald Eash5 used this inventory of on and off-street parking spaces to
predict the parking location choices of auto commuters and non-work travelers to the
Chicago central area. The inventory included parking information for 49 of the 76 CBD
zones, and these 49 zones were defined as the Chicago Central Area in Eash’s study.
Eash summarized 1990 central area parking conditions that there were 4 zones with more
than 4000 parking spaces, 7 zones with 3000 to 4000 spaces, 7 zones with 2000 to 3000
spaces, and the rest of zones each with less than 2000 parking spaces. In the 49 central
area zones, 2 zones had the highest daily parking fees greater than $12.50, 20 zones had
the parking fees from $7.50 to $12.50, and the parking costs were from less than $5.00 to
$7.50 in the rest of the zones. On-street parking in the central area of the CBD is only
available to a limited extent, usually metered, costly, and restricted to short term parking.
This means that on-street parking is not available for all-day parking for work trips5.
Within the CATS transportation planning region, parking capacities and parking
fees vary widely from the Chicago CBD to other urbanized areas and to suburban areas.
Some areas have fee parking lots and free street parking as well, some areas have both
free parking lots and free street parking, and some areas only have fee parking lots but no
free parking at all. The daily parking fee varies from $0.00 in a remote park-and-ride
facility to over $18.00 charged by a lot in the Chicago CBD.
Chicago Transit Authority (CTA) - the service provider of heavy rail, express and
local buses in the City of Chicago - also operates fee lots at approximately 12 heavy rail
stations. Pace - the operator of the suburban local, express and feeder buses - also runs
lots at several locations, most of them are free. Furthermore, in many suburbs, local
downtowns have fee-based on- and off-street parking. However, at the time of this study,
there was no regional parking inventory other than the above two cited Metra and the
CBD off-street parking data sources, and it is obvious that these two data sources do not
adequately represent the current regional parking conditions.
A methodology was developed to calculate generalized parking cost (in terms of
minutes) as an input to mode choice model, taking into considerations of general parking
conditions in the Chicago CBD, in the park-and ride lots, and in all other urbanized, less
urbanized and suburban areas.
4
5
Downtown Research Corporation, The 1986 Downtown Chicago Parking Survey, Chicago Association of
Commerce and Industry , Downtown Parking Task Force, 1986. The database was updated by CATS in
1999.
Ronald Eash, Modeling Parking Location Choices of Auto Commuters to the Chicago Central Area,
presented to Metropolitan Conference and Public Transportation Research, Chicago, 1997
3
II.
DATA AND METHODOLOGY
As the parking fee is the direct cost and the parking lot capacity also influences
the parking cost function, these two variables were used in the parking cost calculation,
with awareness that the data for these two variables are incomplete. Both these two
variables were compiled from Metra’s 2001 station parking database, which includes
parking information for 188 Metra stations and includes no parking information for the
CBD. These two variables were compiled from the parking lot information only. While
Metra's parking database also includes the information for station on-street parking, for
simplicity, the Metra’s on-street parking data was not used, but it was treated in the same
way as on-street parking in other urbanized and suburban areas in the region, and this will
be discussed later.
Many stations have multiple lots of different sizes, each of these lots charges
different parking fees, and the fees are paid based on different payment schedules such as
daily, monthly, quarterly, semi-annually and / or annually (usually at reduced prices).
There are a few cases with more than one station located in a single transportation
analysis zone; as a result, the 188 stations fall in 169 transportation analysis zones. The
parking capacity was aggregated from all parking lots for all stations in the zone. The
zonal parking capacity ranges from 0 spaces to 3355 spaces, and the smallest non-zero
parking capacity is 6 spaces. Map Two (at the end of this paper) presents the parking
capacity by zone.
The parking fee was calculated as the average daily parking fee in the zone that is
connected to the station(s). The calculation used a simple averaging method without
being weighted by the size(s) of the parking lot(s). The daily average parking fee varies
from 50 cents to 3 dollars. Several zones have small free parking lots only. The parking
conditions in the CBD were treated differently and are explained in the following
paragraphs.
Apart from the incompleteness in the data of parking fees and parking lots, the
situation is further complicated by the fact that on-street parking conditions vary widely
from less urbanized areas to urbanized areas and to the Chicago CBD, as described
previously. To represent the regional reality that some areas have parking lots and free
parking on the street as well, and some areas only have parking lots but no free parking at
all (CBD), a third variable - area type was used. No data from CTA park-and-ride lots or
Pace parking facilities were used in this study. The use of this third variable would also,
in a more general way to some extent, take care of the CTA and Pace parking conditions.
The data source for the variable area type is from CATS highway capacity zone
coverage6. This GIS coverage was originally developed for identify capacity zone
reference for each highway node and for calculating highway link capacities for highway
6
This GIS coverage was originally developed a few years ago for identify capacity zone reference for each
highway node and for calculating highway link capacities. For reference, also see Chicago Area
Transportation Study, 2020 Regional Transportation Plan 2000 Edition, TIP Transportation Improvement
Program for Northeastern Illinois FY 2001-2006, Appendix B 2000
4
assignment. In this coverage, the whole planning region is categorized as eleven area
types from insider CBD to external area labeled from 1 to 11.
In this study, the area types were further indexed by values that represent some
parking costs in terms of minutes from very expensive to inexpensive associated with the
area. Using the information on the parking fees in the central area of the CBD from
Eash’s study5, an average parking cost of $6.50 in 1990 dollars for the whole central area
of the CBD could be assumed. Then this dollar value could be converted into about 100
minutes by using a dollar minute conversion factor. This value of 100 was then indexed
to the zones inside the central area of the CBD. Similar logic was applied to every zone
of the remainder of the CBD and of other area types, and the value ranges from 70 to 4.
The determination of the lower end value of 4 was based on a recent Metra survey result
that in a less urbanized area the average walking time from a parking lot or an on-street
parking spot (so a free parking) to the platform is about 4 minutes. Table 1 presents the
description, label and the indexed values for different area types. Map Three shows the
distribution of all area types in the region.
Table 1.
Are Type Description
Inside CBD
Remainder of CBD
Remainder of Chicago
Inner suburbs
Remaining Chicago urban area
Indiana urbanized area
Other Illinois urbanized areas
Inside other Indiana urbanized area
Remainder of NE. of Illinois urban area
Rural
External area
Area Type Label
1
2
3
4
5
6
7
8
9
10
11
Indexed Parking Cost
100
70
25
15
10
10
6
6
4
4
0
The generalized parking cost now consists of three components, the average daily
parking fee, the parking capacity and the area type. The parking fee was converted from
1999 dollars to 1990 dollars and into minutes by using a 1990 dollar-to-minute
conversion factor. The size of the parking capacity is considered as a utility in the
generalized parking cost function. The utility of the parking capacity was assumed to rise
with the capacity size at a diminishing rate, and a maximum capacity value was assumed
as a ceiling so that there would be very little or no extra utilities above the maximum
capacity value. The capacity values were transformed into log values and an exponential
value was taken. Figure 1 shows parking space utility. As there was no data available
for estimation, the model was calibrated by trial and error to get the calculated values to
5
be reasonable and in scale with the in-vehicle time, the out-vehicle time, and the costs of
the base fares and the incremental fares. The generalized parking cost now is in a form:
Generalized parking cost =area type value + 0.7*parking fee –0.3*Ln(parking capacity)1.2
Figure 1. Parking Space Utility
Parking Space Utility
14.00
12.00
utility
10.00
8.00
Series1
6.00
4.00
2.00
0.00
0
1000
2000
3000
4000
5000
6000
Parking Spaces
The three input variables were entered into the Emme/2® calculations as three
extra attributes. The calculation was added to a park-and-ride application in a matrix
convolution based on the example found in the Emme/2® documentation, in which
highway assignment was used to estimate the driving cost, and the station access links
were used to identify station zones. The station zones are the zones that have commuter
rail station(s), heavy rail station(s) or / and bus station(s). The generalized parking costs
were calculated for all station zones. If a station zone is used as an intermediate zone
where park-and-ride would occur for any interchange zone pair, the generalized parking
cost associated with that particular station zone would be added to the total generalized
transit cost for the interchange zone pair. These generalized parking costs were stored in
an origin matrix and the matrix was used as the masking operator in the convolution. The
convolution formula is as follows:
Mf (combined auto and transit time)
pq
= min((mf(transit leg) + mf(auto leg) )+ mo(parking cost and station zone flag))
k
pk
kp
k
where mf is a full matrix and mo is an origin matrix, p are origins, q are destinations and
k are park-and-ride zones.
III.
RESULTS
The calculated generalized parking costs are 100 for all zones in the central CBD,
70 for all zones in the remainder of the CBD, 38 to 4 for the intermediate zones of other
6
area types with or without parking lots and with different parking fees. An intermediate
zone is a station zone where park-and ride occurs. The convolution produced the
following effects: 1). The parking costs in the CBD and in the remainder of the CBD are
so expensive that these areas are rarely used as intermediate zones; 2). The auto trips to
the destinations in the CBD would be more expensive with the parking costs in the CBD;
3). For a pair of origin and destinations zones, if an intermediate zone is used, there will
be some parking costs for that origin and destination pair. For example, given a zone of
area type 3 and indexed value 25, there would be three following outcomes. If there were
no off-street parking, the parking cost would be 25, the cost (in minutes) that a person
might drive to find a parking spot and walk to the station. If there were some free
parking lots, the parking cost would be cheaper than 25, a lower cost due to the time
saved because of the knowledge of the location and the size of the free parking lots. The
third outcome is that if there were some parking fees for the lots, the parking cost would
be higher than 25, the cost is associated with the parking fee in minute, the size of the
parking facility and the area type. Appendix 1. presents some examples of the calculation
results. Map Four shows the distribution of the generalized parking costs.
The methodology used in this study has several advantages. First, by using the
highway links as park-and-ride drive links and the highway congested time as the auto
access time, it is unnecessary to code the detailed park-and-ride drive links, which could
be tedious and time consuming. Second, by using the station access links to identify
station zones, it is unnecessary to build extra matrices for stations or parking lots, which
takes extra databank spaces and can be time consuming too. Third, by using the area type
variable, the parking conditions of the whole region can be accessed to some extent,
especially when the comprehensive parking inventory is not available. Another
advantage stemming from the above three advantages is that the model may be
transferable between applications or regions. The model has some limitations: the
parking demand is not constrained (cut off) by parking capacity; the parking cost does not
increase with the parking demand (as it gets harder to find a parking space); subsidized or
reimbursed parking fees were not considered; and finally the sensitivity of the model
needs to be further tested. It should be noted that the model is not intended to accurately
estimate the parking costs for individual parking lots nor reproduce the station choices,
but to represent the generalized transit cost for mode split, and so is more appropriate for
a regional model.
ACHNOWLEDGMENTS
The authors of this paper thank Christopher Wilson of Metra for his valuable comments
and suggestions.
7
APPENDIX 1. Examples of the Calculation Results.
zone Area type Area value Average fee capacity generalized cost
2
3
25
0
28
23.73
4
3
25
100
223
31.21
14
3
25
100
1149
30.36
42
3
25
100
55
31.90
51
3
25
0
11
24.14
171
3
25
100
44
32.00
174
3
25
0
28
23.73
177
3
25
100
65
31.82
183
3
25
100
28
32.21
188
3
25
100
363
30.96
189
3
25
100
139
31.45
194
3
25
100
86
31.68
197
3
25
100
316
31.03
200
4
15
113
324
22.12
201
3
25
100
133
31.47
208
3
25
100
189
31.29
220
4
15
100
1240
20.32
225
4
15
100
795
20.56
267
4
15
100
262
21.13
281
4
15
100
275
21.11
296
4
15
100
90
21.66
309
4
15
100
167
21.36
321
3
25
100
147
31.42
334
3
25
0
6
24.40
343
3
25
100
68
31.80
344
3
25
100
61
31.85
360
3
25
0
20
23.88
375
4
15
100
112
21.55
419
3
25
100
85
31.69
429
4
15
84
477
19.46
433
4
15
100
553
20.75
462
4
15
0
18
13.93
467
5
10
95
482
15.39
471
5
10
100
1003
15.43
481
5
10
102
583
15.89
506
5
10
106
733
16.11
512
5
10
113
1691
16.26
522
5
10
100
725
15.60
529
5
10
100
690
15.63
559
5
10
100
229
16.20
560
4
15
88
302
20.04
574
4
15
88
105
20.57
581
4
15
88
306
20.03
582
3
25
100
168
31.35
607
5
10
100
314
16.04
609
4
15
100
103
21.60
617
5
10
100
129
16.48
8
625
4
15
100
205
21.25
626
4
15
100
47
21.97
627
4
15
100
109
21.57
650
4
15
84
45
20.64
656
4
15
68
22
19.61
664
5
10
100
151
16.41
684
9
3
95
148
8.99
700
5
10
100
91
16.66
702
5
10
100
201
16.26
707
9
3
100
385
8.93
710
9
3
100
157
9.39
712
5
10
100
1641
15.17
722
5
10
100
488
15.81
741
5
10
100
360
15.97
824
5
10
88
1657
14.15
843
5
10
107
329
16.61
847
5
10
95
1396
14.83
848
9
3
88
332
7.99
869
5
10
84
554
14.39
870
5
10
100
138
16.45
893
5
10
92
495
15.12
895
5
10
88
680
14.62
931
5
10
99
56
16.80
935
5
10
95
96
16.21
937
5
10
91
251
15.39
970
5
10
80
1452
13.54
998
5
10
114
723
16.79
1001
5
10
95
640
15.25
1003
5
10
108
413
16.58
1023
5
10
105
986
15.87
1040
5
10
108
349
16.66
1079
5
10
0
48
8.48
1082
5
10
100
100
16.61
1100
5
10
50
536
11.52
1137
5
10
100
100
16.61
1145
5
10
88
316
15.02
1181
5
10
100
288
16.08
1184
5
10
100
221
16.22
1188
5
10
100
182
16.31
1191
5
10
100
628
15.68
1193
7
6
100
76
12.74
1200
7
6
100
115
12.54
1206
7
6
100
185
12.31
1210
7
6
100
643
11.67
1213
9
3
100
145
9.43
1235
7
6
100
272
12.11
1238
7
6
100
71
12.78
1266
7
6
100
516
11.78
1277
7
6
100
142
12.44
1282
7
6
100
410
11.90
9
1337
7
6
117
971
12.89
1409
7
6
100
109
12.57
1419
7
6
88
873
10.49
1432
7
6
100
606
11.70
1433
7
6
100
292
12.07
1446
9
3
100
424
8.88
1478
10
3
100
138
9.45
1509
5
10
95
709
15.19
1521
9
3
100
172
9.34
1522
9
3
100
1108
8.38
1551
7
6
100
602
11.70
1581
7
6
84
205
10.90
1757
11
0
100
141
6.44
10
Appendix 2. Macro for the generalized parking cost in the matrix convolution.
~/GENERALIZED PARKING COST
s=1999
~/*****************************************
~/ Area type from capacity zone coverage
~/ 1=inside CBD (zone 54-100)
~/ 2=inside remainder of CBD (zone 101-129)
~/ 3=inside remainder of Chicago
~/ 4=inside inner suburbs
~/ 5=inside remaining Chicago urban area
~/ 6=inside Indiana urbanized area
~/ 7=inside other IL urbanized areas (Joliet, McHenry)
~/ 8=inside other Indiana urbanized areas
~/ 9=inside remainder of NE. IL urban area
~/ 10=rural
~/ 11=external area
~/ 0=points of entry or outside region.
~/
~/*****************************************************************
~/ calculate auto generalized cost
3.21
~+;1;y;mf26;n
~+;(2.16*mf10) + (0.88*mf7) + (0.0812*mf7) + 0.812; ; ;n;1; ;4
~/
~/*****************************************************************
~/ identify station zones using access links;
2.41
~+;1;y;ul3;0;;all;4
~+;1;y;ui1;0;;all;4
~+;1;y;ui2;0;;2;i=1,1790;;4
~+;1;y;ui3;0;;2;i=1,1790;;4
~/
~+;1;y;ul3;1;; mod=uvw;;4
~+;1;y;ui1;ul3;;2;i=1,1790;;4;6
3.21
~+;1;y;mo4;n;0; ; ;n;1;
~+;1;y;mo1;n;0; ; ;n;1;
~+;1;y;mo1;n;ui1; ; ;n;1; ;4
~/
~/ Index area type
2.41
1
y
ui2
(@atype .eq. 1)*100+
(@atype .eq. 2)*70+
(@atype .eq. 3)*25+
(@atype .eq. 4)*15+
((@atype .ge. 5) .and.(@atype .le. 6))*10+
((@atype .ge. 7) .and.(@atype .le. 8))*6+
((@atype .ge. 9) .and.(@atype .le. 10))*4+
((@atype .eq. 0) .or. (@atype .ge.11))*0
i=1,1790
11
4
~/
~/ Data manipulation and log transformation of the data.
~/
~+;1;y;ui3;(@pspac + 5000*(@pspac .eq. 0));;2;i=1,1790;;4
~/
~/
~+;1;y;ui1;0;;all;4
~+;1;y;ui1;(ln(ui3));;2;i=1,1790;;4
~/
~+;1;y;ui3;0;;2;i=1,1790;;4
1
y
ui3
((ui1)*(ui1 .ne. (ln(5000)))+
(0)*(ui1 .eq. (ln(5000))))
i=1,1790
4
~/ generalized cost calculation.
~/
~+;1;y;ui1;0;;2;i=1,1790;;4
1
y
ui1
ui2+ 0.7*(@pcost/8.25)-0.3*((ui3)^1.2)
i=1,1790
4
6
~/
3.21
~/
~+;1;y;mo4;n;((mo1 .eq. 1)*(ui1)); ; ;n;1;
~+;1;y;mo4;n;99999; ;mo4;0,0,in;n;1; ;4
~/~+;1;y;mo4;n;mo4-1; ; ;n;1; ;4
~/
~/ Now the station zones in mo4 have values 99999 for non-station
zones, 100 for central CBD, 70 for the remainder of CBD, 38 to 4 for
the zones of different area type with or without parking lots. These
values are to be used in the masking in the matrix convolution.
~/
~/******************************************************************
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