Value of Travel Time Estimation for PANYNJ and NJ Turnpike Facilities via Hierarchical
Bayesian Mixed Logit Approach
Paper No: 10-2810
Ozlem Yanmaz-Tuzel, M.Sc.1, Kaan Ozbay, Ph.D.1
Jose Holguin-Veras, Ph.D.2
1Rutgers
Intelligent Transportation Systems Laboratory, Rutgers University
2Rensselaer Polytechnic Institute
Travel Surveys
ABSTRACT
This paper investigates value of travel time (VOTT) of commuters traveling on
Port Authority of New York and New Jersey (PANYNJ) and New Jersey Turnpike
(NJTPK) toll facilities in the presence of time-of-day pricing. The methodology
proposed to estimate VOTT develops Hierarchical Bayesian Mixed Logit (HB-ML)
models using travel surveys conducted as part of evaluation studies of PANYNJ
and NJTPK facilities. The proposed approach is a novel way used to examine the
commuters’ behavior based on more flexible model specifications. Empirical
results show that travel time, toll, income, and departure time are statistically
significant parameters affecting VOTT of PANYNJ toll facility commuters. Mean
VOTT estimates are found to be around 16.5$/hr for PANYNJ E-ZPass peak users,
and around 15.15$/hr for PANYNJ E-ZPass off-peak users, with standard deviation
estimates close to 6.45 $/hr during peak periods and 5.72 $/hr during off-peak
hours. Similarly, mean VOTT estimates are found to be around 16.3$/hr for NJTPK
E-ZPass peak users, and around 14.79$/hr for NJTPK E-ZPass off-peak users,
with standard deviation estimates close to 5.48$/hr during peak periods and
4.56$/hr during off-peak hours.
INTRODUCTION
• For many years transportation policy strategies, such as time-of-day pricing
programs, have been proposed to reduce peak-period congestion by providing
higher tolls under congested conditions and lower tolls at less congested times.
• As a part of the evaluation study of PANYNJ’s and NJTPK’s time-of-day pricing
initiatives, passenger travel surveys were conducted for both of the toll facilities.
Rutgers University’s Eagleton Institute was in charge of conducting the computer
aided telephone interviews.
• Travel survey data collected for the PANYNJ facility contain 505 complete
observations. Among them 467 respondents are current regular users. Of those
surveyed, 392 respondents reside in NJ; among 103 of which use both facilities.
• Since the focus of this study is to investigate the VOTT of commuters traveling
within NJ and NYC using PANYNJ facilities, only the commuters using the Holland
and Lincoln tunnels are included in the estimation process.
NJTPK Time-of-day Pricing Program
• Since September 30, 2000, time-of-day pricing has been applied at NJTPK to
encourage peak-period commuters to shift to off-peak periods to reduce the
congestion during peak-periods. Only passenger cars with E-ZPass tag are eligible
for time-of-day pricing, and cash users pay higher tolls compared to E-ZPass users
irrespective of time-of-day.
Travel choice
E-ZPass Peak
E-ZPass Off-peak
Cash
41%
35%
24%
42%
30%
28%
1.24
0.35
1.7
0.39
Mean
1.86
2.31
Standard Deviation
0.53
0.58
E-ZPass peak
E-ZPass off-peak
Cash
5
4
6
0.45-5.45
0.35-4.85
0.45-6.45
68.80%
31.20%
70.51%
29.49%
Education
Graduate degree or higher
Less than graduate degree
PANYNJ
NJTPK
Annual Income
Toll ($)
<$25K
$25-55K
$55-75K
$75-100K
>$100K
3.18%
19.80%
11.31%
19.44%
46.25%
2.19%
7.11%
10.53%
14.1%
66.07%
18 ~ 24
25 ~ 29
30 ~ 39
24.93%
7.10%
8.20%
1.61%
8.32%
29.5%
40 ~ 49
19.40%
Age
50 ~ 59
60 ~ 64
> 64
Refused to answer
18.30%
7.10%
6.60%
3.70%
22.52%
21.45%
8.04%
10.46%
2.67%
METHODOLOGY
Toll Structure
Toll
• Comparing VOTT functions along these two similar toll roads helps the
practitioners and policy planners to better understand how different toll levels,
facility properties, and commuters’ trip and socio-economic characteristics affect
the VOTT around New Jersey (NJ) and New York City (NYC) areas.
Cash all day
E-ZPass peak
E-ZPass off peak
E-ZPass (weekend)
EMPIRICAL SETTING
Toll
PANYNJ Time-of-day Pricing Program
•Tolls are collected in the NYC bound direction only. establishes a high cash toll at
all times of day, with discounted E-ZPass tolls set at higher levels during peak
hours and at lower levels during the off-peak hours.
NJTPK
Departure time (hr)
• This paper aims to estimate VOTT functions in the presence of time-of-day
pricing and investigate the impacts of individual preference heterogeneity on how
commuters value travel time.
• On March 25, 2001, a new pricing structure was initiated with tolls varying
according to time-of-day and payment technology.
Respondent Characteristics
PANYNJ
Mean
Standard Deviation
• The relationship between toll, travel time and consequently the efficiency of timeof-day pricing raises a fundamental question of how much commuters are willing to
pay to save travel time, i.e. commuters’ value of travel time (VOTT).
• PANYNJ controls some of the most important transportation facilities in NYC and
NJ, including the NYC’s and Northern NJ’s airports, port facilities and the Hudson
River Crossings.
Trip Characteristics
Total Trip Travel time (hr)
• In the existence of time-of-day pricing, commuters can either pay higher tolls to
save on travel time; they can shift to off-peak periods, or use alternative
routes/modes to avoid tolls but experience higher travel times.
• A new Hierarchical Bayesian Mixed Logit (HB-ML) model is estimated using
travel surveys conducted as part of evaluation studies of PANYNJ and NJTPK
time-of-day pricing programs.
Summary Statistics
Cash all day
E-ZPass peak
E-ZPass off peak
E-ZPass (weekend)
PANYNJ tolls
Before
March 2001
March 2008
$4.00
$6.00
$8.00
$4.00
$6.00
$8.00
$3.60
$5.00
$8.00
$3.60
$4.00
$6.00
NJTPK tolls (Exit 1 – Exit 18E, mileage = 111 miles)
Before
Sept. 2000
Jan. 2003
Jan. 2006
$4.60
($ 0.04/mile)
$5.50
($ 0.05/mile)
$6.45
($ 0.06/mile)
$6.45
($ 0.06/mile)
-
$4.95
($ 0.04/mile)
$5.45
($ 0.05/mile)
$6.45
($ 0.06/mile)
-
$4.60
($ 0.04/mile)
$4.85
($ 0.04/mile)
$4.85
($ 0.04/mile)
-
$4.95
($ 0.04/mile)
$5.45
($ 0.04/mile)
$6.45
($ 0.06/mile)
In this paper, VOTT functions are estimated via HB-ML models. Unlike the
classical approach, in Bayesian statistics, parameters are treated as random
variables, and prior knowledge about parameter vector is represented by a prior
distribution. Given the parameter vector θ, the probability of traveler n’s observed
choices, conditional on θ is represented by:
Then, the probability not conditional on θ is the integral of P(yn| θn) depending on
the prior distribution:
where Φ(θ|b,∑) is the normal density with mean b and variance ∑. The hyperpriors on these parameters are:
Value of Travel Time Estimation for PANYNJ and NJ Turnpike Facilities via Hierarchical
Bayesian Mixed Logit Approach
Paper No: 10-2810
Ozlem Yanmaz-Tuzel1, Kaan Ozbay1
Jose Holguin-Veras2
In Bayesian approach, there is a precise relationship between prior and the
posterior distribution linked through the likelihood function. Let L(Y| θ) be likelihood
function of the observed data, formulated as:
Then, based on Bayes’ rule, the posterior distribution of the parameter vector,
f(θ|Y), is represented as:
1Rutgers
Intelligent Transportation Systems Laboratory, Rutgers University
2Rensselaer Polytechnic Institute
VALUE OF TRAVEL TIME ESTIMATION
RESULTS
• In the context of time-of-day pricing, VOTT can be defined as the marginal rate of
substitution of travel time for money in a commuter’s utility function; which
represents the relative desirability of available alternatives.
• When the utility function is estimated via discrete choice models, VOTT for
commuter n is calculated as the ratio between the partial derivative of the utility
function with respect to travel time and with respect to travel cost.
where f(b) is Normal(b|b0, S0) with large variance and f(∑) is IW(∑|ψ,m)
ESTIMATION RESULTS
• This section describes the HB-ML estimation results, where travelers choose their
departure time in the presence of time-of-day pricing. The available alternatives for
the travelers are (a) off-peak travel with E-ZPass, (b) peak travel with E-ZPass, or
(c) peak travel with manual payment (cash).
CONCLUSIONS
• This paper aims to investigate VOTT of commuters traveling on PANYNJ and
NJTPK toll facilities in the presence of time-of-day pricing.
• In order to test the performance of the proposed HB-ML model, we compared
model diagnostics of the HB-ML model with classical ML model. In particular, for
each model we have calculated pseudo-r2 value expressed as:
where:
D: Posterior expectation of the deviance (=-2*log(likelihood))
D0: Log likelihood at zero (β=0, except constants)
• The estimation results revealed pseudo-r2 value of 0.236 classical ML model and
pseudo-r2 value of 0.274 for the proposed HB-ML model.
• These diagnostics confirm that the proposed HB-ML model performs and fits the
data better and ML model may have converged to a local maximum. Thus, in
situations where it is uncertain whether a global maximum has been obtained or
the sample size is small, Bayesian procedures can be recommended, since they
do not require the maximization of a likelihood function.
Estimation results for PANYNJ and NJTPK facilities
PANYNJ
Variables
Constant
Tr Time
(Tr Time)2
Toll
Toll2
Tr Time*toll
Dep. Time
(Dep. Time)*(Tr Time)
Income
(Income)*(Tr Time)
Education
Age
Employment
Gender
E-ZPass peak E-ZPass off-peak
mean st dev mean
st dev
-1.408 0.078 -1.312
0.079
-0.949 0.078
-0.97
0.079
-0.353 0.077 -0.454
0.079
-0.169 0.078 -0.199
0.079
-0.032 0.008 -0.039
0.009
-0.331 0.078 -0.318
0.081
-0.643 0.078 -0.681
0.078
0.357 0.067
0.501
0.068
-0.459
0.06
-0.509
0.062
2.034 0.076
2.043
0.077
0.22
0.046
0.166
0.047
2.092 0.079
2.069
0.08
2.086 0.078
2.084
0.078
NJTPK
E-ZPass offE-ZPass peak
peak
mean
st dev
mean st dev
-1.229
0.049
-1.455 0.070
-1.591
0.244
-1.69
0.278
-0.429
0.106
-0.491 0.110
-0.892
0.112
-0.847 0.131
-0.49
0.110
-0.422 0.091
-0.97
0.146
-0.85
0.131
0.39
0.092
0.34
0.084
-0.497
0.071
-0.481 0.069
1.71
0.368
1.15
0.256
0.105
0.022
0.079
0.018
1.567
0.100
1.12
0.071
1.937
0.152
1.439
0.119
•The methodology proposed to estimate VOTT develops HB-ML models using
travel surveys conducted as a part of evaluation study of PANYNJ and NJTPK
time-of-day pricing program.
• Mean VOTT estimates are found to be around 16.5$/hr (PANYNJ) and 16.3$/hr
(NJTPK) for E-ZPass peak users, and around 15.15$/hr (PANYNJ) and 14.79$/hr
(NJTPK) for E-ZPass off-peak users.
• The standard deviation of VOTT estimates is close to 6.45$/hr (PANYNJ) and
5.48$/hr (NJTPK) during peak periods and 5.72$/hr (PANYNJ) and 4.56$/hr
(NJTPK) during off-peak hours.
• When compared with commuters traveling over the entire NJTPK commuters, the
estimation results for NJTPK commuters using PANYNJ facilities show a similar
behavior.
• The mean VOTT values for each toll facility are very close to each other, while
standard deviation values are slightly lower for commuters traveling over the entire
NJTPK.
•Empirical results obtained from travel survey data shows that the interaction terms
involving travel time, toll, income and departure time, and their statistically
significant coefficients, reveal a significant degree of observable heterogeneity in
how commuters value the travel time provided by PANYNJ facilities.
• The proposed HB-ML estimation methodology provides the researchers with a
new way to examine the commuters’ behavior based on more flexible model
specifications.
• Estimation of heterogonous VOTT functions helps the practitioners and policy
planners to better understand how different toll levels, facility properties, and
commuters’ trip and socio-economic characteristics affect the valuation of travel
time around New York Metropolitan area.
•The comparison results with classical ML models reveal that, in situations where it
is uncertain whether a global maximum has been obtained,
•Bayesian approach is recommended, since it performs better and does not require
maximization of the likelihood function. Even when the researcher is not interested
in Bayesian interpretive approach, HB methodology may be pursued since the
mean of the posterior should be close to the classical mean estimate.
•Alternatively, classical estimators can be used where the researcher is uncertain
whether the Bayesian procedure has converged to draws from the posterior. Thus,
it is our view that Bayesian and classical estimators complement each other.
•If the researcher is interested in individual-level coefficients, or the sample size is
small, Bayesian procedures may result in better estimates compared with classical
approaches.