Some Issues in Transportation Demand
Modeling and ITS Deployment Planning
Paul Metaxatos
Urban Transportation Center
University of Illinois at Chicago
CTS-IGERT – Weekly Seminar
May 14, 2009
Some Computational Considerations
In Transportation Demand Modeling
The Gravity Model
E ( Nij )  Tij  Ai B j Fij

Fij  exp 
 k

k (k )
 cij 


Estimation Procedures
Ai
(2 r 1)
 Oi /
DSF
Ai 's
B j 's
Bj
(2 r )
B
j  j 1
I
 D j /  Ai
(2 r  2)
j
(2 r 1)
i 1
 k 's
ML Estimation
J
Fij i  I
Fij j  J
Ti   Ni  i
T j  N  j j
cij

ij
Tij   cij
(k )
ij
(k )
Nij k
O-D Distance Measures
•Straight-line (Euclidean) distance
•Travel distance
•Travel time
•Generalized cost
•Functional distance
•Taxonomical distance
1 Mode – 1 Commodity – 1 Travel Time Parameter – National Level
Geography
Size of Origin
– Destination
Table (Cells)
Size of ML
Estimation
Problem
(I+J+1) –
System of
Equations
Storage Requirements
50 states
2,500
101
20 KB of RAM
3141 counties
9,865,881
6,283
~ 78 MB of RAM
33,000 zip codes
1,089,000,000
66,001
~ 8 GB of RAM
65,000 census
tracts
4,225,000,000
130,001
~ 33 GB of RAM
Covariance Matrices
Cov(T )  1  Cov( A, B,  )  1
1  diag (T )  M 
diag (1/ A(1),...,1/ A( I ),1/ B(1),...,1/ B( J ),1,,,1)
M – the coefficient matrix of the right-hand side of
tij  a (i )  b( j )    k cij
k
(k )
tij  log(Tij )
ai  log( Ai )
b j  log( B j )
1 Mode – 1 Commodity – 1 Travel Time Parameter – National Level
Size of Covariance Matrix –
(I*J, I*J) cells
Geography
Size of Origin
– Destination
Table (Cells)
50 states
2,500
3141 counties
9,865,881
33,000 zip codes
1,089,000,000
1,185,921,000,000,000,000
~ 9 EB of RAM
65,000 census tracts
4,225,000,000
17,850,625,000,000,000,000
~ 142 EB of RAM
6,250,000
97,335,607,906,161
Storage Requirements
50 MB of RAM
~ 778 TB bytes of RAM
Two Applications
In Transportation Demand Modeling
5115 Study
1. Measure the ton-miles and value-miles of international
trade traffic carried by highway for each State
2. Evaluate the accuracy and reliability of such measures
for use in the formula for highway apportionments
Small-Area
Estimation
of O-D Flows
Trip Generation and
Small Household Travel Surveys (HTS)
Issues with Small HTS and Trip Generation
Average Number of Trips per Household
(number of households in parenthesis)
• Unusual observations
• Small number of observations
• No observations
Number of
Workers
Household Size
1
2
3
4+
0
6.28
(53)
9.22
(40)
16.00
(3)
8.00
(3)
1
6.09
(87)
10.42
(45)
10.94
(18)
9.06
(15)
2
(-)
9.56
(46)
10.81
(11)
15.46
(28)
3
(-)
(-)
11.00
(2)
11.83
(6)
4
(-)
(-)
(-)
10.66
(3)
-: indicates category not possible in this classification.
Unusual Observations
Problem
• Outliers
• Influential observations
Remedy
• Examine diagnostics from equivalent regression problem
- studentized residualsi  2
- DFFITSi  2[(k  1) / n]1/ 2 for n  k
Small Number of Observations
Problem
• Reliability of trip generation rates
Remedy
• CART analysis
- non-parametric
- binary recursive partitioning algorithm
CART Example Using Two Independent Variables
Before CART
After CART
Average Number of Trips per Household
(number of households in parenthesis)
Number of
Workers
Household Size
Average Number of Trips per Household
(number of households in parenthesis)
Number of
Workers
1
2
3
4+
0
6.28
(53)
9.22
(40)
16.00
(3)
8.00
(3)
1
6.09
(87)
10.42
(45)
10.94
(18)
2
(-)
9.56
(46)
3
(-)
4
(-)
Household Size
1
2
3
4+
0
6.28
(53)
9.22
(40)
11.67
8.89
9.06
(15)
1
6.09
(87)
10.42
(45)
(21)
(18)
10.81
(11)
15.46
(28)
2
-
9.56
(46)
10.85
15.46
(28)
(-)
11.00
(2)
11.83
(6)
3
-
-
(13)
(-)
(-)
10.66
(3)
4
-
-
-
-: indicates category not possible in this classification.
11.44
(9)
-: indicates category not possible in this classification.
Another CART Example
Before CART
After CART
Trip Rates by Household Size and Trip Purpose
Trip
Purpose
HB-Work
Number of cases
Trip Rates by Household Size and Trip Purpose
Household Size
Trip
Purpose
1
2
3
4+
1.90
71
2.43
70
2.60
25
2.64
36
Household Size
1
2
3
4+
HB-Work
Number of cases
1.94
171
2.33
223
HB-Shop
Number of cases
1.64
42
2.26
76
2.50
20
2.81
32
HB-Shop
Number of cases
HB-School
Number of cases
2.19
58
2.26
23
1.22
9
2.72
11
HB-School
Number of cases
HB-Other
Number of cases
2.44
93
4.00
105
3.97
29
6.14
47
HB-Other
Number of cases
2.44
93
4.00
105
NHB
Number of cases
2.82
99
3.61
107
4.48
29
4.61
41
NHB
Number of cases
2.83
99
3.62
107
2.72
79
4.22
58
6.15
47
4.61
41
Trip Rates by Household Size, Number of Workers
and Trip Purpose (after CART Analysis)
Trip Rates by Household Size, Number of Workers
and Vehicle Availability (after CART Analysis)
Workers
0
1
2
3
4
Vehicle
Availability
0
1
2
3+
0
1
2
3+
0
1
2
3+
0
1
2
3+
0
1
2
3+
1
Household Size
2
3
10.14
8.73
9.09
14.89
6.16
8.86
9.09
14.89
-
4+
8.86
9.89
15.46
-
10.85
-
11.44
Row-column Decomposition Analysis
As an Imputation Method
Average Number of Trips per Household
(number of households in parenthesis)
Number of
Workers
Household Size
1
2
3
4+
0
6.28
(53)
9.22
(40)
16.00
(3)
8.00
(3)
1
6.09
(87)
10.42
(45)
10.94
(18)
9.06
(15)
2
(-)
9.56
(46)
10.81
(11)
15.46
(28)
3
(-)
(-)
11.00
(2)
11.83
(6)
4
(-)
(-)
(-)
10.66
(3)
barijij
-: indicates category not possible in this classification.
yij    ai  b j  rij
 is the grand mean;
ai is the effect of the ith row;
b j is the effect of the jth column;
rij is the residual in the ith row and jth column.
Row-column Decomposition Analysis
As an Imputation Method (cont.)
Step 1: Column Means Subtracted
Workers
0
1
2
3
4
Column
Fit
1
0.10
-0.10
U*
U
U
6.18
Household Size
2
3
-0.51
3.81
0.69
-1.25
-0.17
-1.38
U
-1.19
U
U
9.73
12.19
*U - unavailable
Examples
Column fit = means of column;
e.g., 6.18=(6.28+6.09)/2
Cell value = observed value – column fit;
e.g., 0.10=6.28-6.18
Step 2: Row Means Subtracted
Workers
4+
-3.00
-1.94
4.46
0.83
-0.34
11.00
Household Size
1
2
3
-0.00 -0.61 3.71
0.55
1.34 -0.60
U
-1.14 -2.35
U
U
-1.01
U
U
U
0
1
2
3
4
Column
Effects -3.60
-0.04
2.41
4+
-3.10
-1.29
3.49
1.01
0
Row
Effects
0.10
-0.65
0.97
-0.18
-0.34
Grand Mean
1.23
9.78
Examples
Row effect = mean of step one row; e.g., 0.10=(0.10-0.51+3.81-3.00)/4
Residuals = cell value of step one – row effect; e.g., -0.00=0.10-0.10
Grand mean = mean of column fits; e.g., 9.78=(6.18+9.73+12.19+11.00)/4
Column effect = column fit – grand mean; e.g., -3.60=6.18-9.78
Original cell value = grand mean + row effect + column effect + residual;
e.g., 6.28=9.78+0.10-3.60-0.00
Workers
0
1
2
3
4
Row-column
Decomposition
Analysis (cont.)
Logarithmic
Transformation
of Trip Rates
Workers
0
1
2
3
4
Column
Fit
Workers
0
1
2
3
4
Column
Effects
Household Size
1
2
3
4+
1.84
2.22
2.77
2.08
1.81
2.34
2.39
2.20
U*
2.26
2.38
2.74
U
U
2.40
2.47
U
U
U
2.37
Step 1: Column Means Subtracted
Household Size
1
2
3
4+
0.02
-0.05
0.29
-0.29
-0.02
0.07
-0.09 -0.17
U
-0.02 -0.11
0.37
U
U
-0.09
0.10
U
U
U
-0.01
1.82
2.27
2.49
2.37
Step 2: Row Means Subtracted
Household Size
1
2
3
4+
0.03
-0.04
0.30
-0.28
0.04
0.12
-0.04 -0.12
U
-0.10 -0.19
0.29
U
U
0.09
0.09
U
U
U
0.00
-0.42
0.04
0.25
0.13
Row
Effects
-0.01
-0.05
0.08
0.01
-0.01
Grand Mean
2.24
COMPUTER ASSISTED SCHEDULING
AND DISPATCHING SYSTEMS
IN PARATRANSIT
Alternative CASD Deployment Scenarios
CASD
Scenario
Hardware
Software
Centralized
One central
server serves
all operators
One
statewide
system
Decentralized
One server
per operator
One or more
different
systems
Regional
One server
per region
One or more
different
systems
Centralized
Approach
Advantages
•Facilitates centralized coordination at the state level
•Lower software costs
Disadvantages
•Need for reliable Internet connections
•Fear of loosing control of services and operations
Decentralized
Approach
Advantages
Offers strong local control
No need for high speed Internet connections
Disadvantages
•More on-site technical support
•Possibility of multiple standards
•Difficult to coordinate among multiple providers
•Increased ownership costs
Regional
Approach
Advantages
•Little worry about maintaining and updating software and
hardware
•Facilitates monitoring of contract performance by State DOT
•Facilitates implementation of brokerage
•Proximity to client facilitates maintenance, training and service
of client software
Disadvantages
•Communication needs less than centralized but more than
decentralized approaches
Focus Group Overall Findings
•Centralized approach too difficult for smaller agencies
•Fear of loosing control triggers desire to as much
decentralization as possible
•Decentralized approach is most desired but with
standardization
•Fear of half-way implementation
•State DOT should pay for software, hardware, implementation,
technical support, contractual support with vendor
Cost Analysis – Summary of Findings
•The cost of a decentralized implementation for a typical
agency was about $65,000 (first year) and
$25,000 annually thereafter (2000 dollars)
•The respective costs for the regional approach were about
$60,000 initially and $18,000 annually thereafter
•Regional approach could potentially save more than
$10,000 per agency per year on average.
•This amounts to more than $300,000 savings per year
for the 30 (5311) providers in Illinois