A Microscopic Simulation Study of Automated Headway Control of Buses on the Exclusive Bus Lane on the Lincoln Tunnel Corridor

1
Rutgers Intelligent Transportation Systems (RITS)
Laboratory Department of Civil Environmental
Engineering
A Microscopic Simulation Study of Automated
Headway Control of Buses on the Exclusive Bus
Lane on the Lincoln Tunnel Corridor
Paper 10-3495 Kaan Ozbay, Ph.D., Teja
Indrakanti and Ozlem Yanmaz-Tuzel, M.Sc.
Rutgers, The State University of New Jersey
Abstract This paper studies the feasibility of
automating the exclusive bus lane (XBL) in the
Lincoln tunnel corridor, that helps in increasing
the capacity of the bus lane and avoids the
construction of new lanes. Three different bus
controllers that adjust the speed of the bus
based on its speed and the spacing with respect
to the bus ahead were implemented in a simulation
model developed in Paramics, a traffic
micro-simulation software. Then, the performance
of each of the bus controller and the travel
times were examined and the results were compared
with the simulation model that represents the
existing case. In addition, the performance of
the bus controllers under emergency conditions is
investigated. A cost-benefit analysis indicated
that automation of the bus lane was beneficial.

Traffic volumes for the existing conditions were
estimated by traveling in the XBL and accessing
the travel time information available on websites
such as the Port Authoritys website and
traffic.com. The model was then calibrated so
that it replicates the existing traffic
conditions. Ten simulation runs were performed in
order to average out the stochasticities
associated with Paramics. Statistical tests were
conducted to make sure that the models travel
times match with the existing conditions. Automate
d Conditions Iaonnou and Zhang used a PID type
controller that is shown in the equation below.
We have implemented slightly modified feedback
based vehicle following controllers in Paramics
microscopic simulation tool Where s is the
Laplace operator, and N are
positive control parameters to be chosen, is
the relative speed between the lead-following
vehicle pair, is the spacing error between the
two and is the fuel input that needs to be fed
into the engine of the vehicle so that the
necessary acceleration/deceleration happens.
The Spacing policy The spacing between the two
vehicles varies linearly with the speed of the
following vehicle, which is written
mathematically as Where, the desired
spacing between the pair, the speed of the
following vehicle, the spacing when the
following vehicle is at rest and the time
headway. The value for used in the study is 4
meters. The speed here is expressed in meters per
second. The time headway is set at 2 seconds. It
might be argued that two second headway is high
for an automated system. But this value is chosen
to avoid crashes in the event of failure of the
system, thus making it more reliable during
emergency conditions.
.
Vehicle-Following Algorithm 1. For a
lead-following vehicle pair, obtain the existing
gap and the speeds of individual vehicles for the
current time cycle. 2. Calculate the spacing
error (d), and the desired speed ( ) as
follows. Where, the current spacing,
0.1s-1, a constant and the speed of the
leading vehicle. 3. Calculate the acceleration,
which is a function of error that is to be
applied for the next time cycle. The acceleration
is calculated by each of the controller using
the equations below. 4. At the end of the
next time cycle, repeat steps 1, 2 and
3. Emergency Control and Filters If the speed of
the leading vehicle fluctuates continuously, the
following vehicle, which always tries to get
closer to the speed of the lead-vehicle, will not
continue in a smooth state of motion. In
addition, the vehicles need to stop quickly in
case of emergency. For this purpose the following
set of conditions were used. As a
performance measure for the controllers, the rate
of change of acceleration (which is a measure of
comfort of ride) of each bus in the XBL has been
measured. The results obtained are shown in the
table below.
Sensitivity Analysis Cost Benefit
Analysis A Cost Benefit analysis was conducted
for a period of fifteen years starting from 2009.
The following tables show the costs incurred and
benefit cost ratios. Conclusions and
Future work In this study we have designed three
simple controllers to simulate automated control
of the buses at the XBL of the Lincoln Tunnel
corridor. For the whole period the automated
buses save 2.6 minutes of travel time for every
passenger. After automation, the capacity of the
roadway increased by 23. The cost-benefit
analysis indicates that the benefits exceed the
projected costs of the project. Studying the fuel
and emissions related benefits as a result of
automation in a micro-simulation software like
Paramics will be the next part of this study. We
intend to analyze the results from this study and
include fuel economy benefits in the cost
benefits analysis. Acknowledgements This project
was sponsored by a grant from the Rutgers
Transportation Coordinating Council/Federal
Transit Administration. The opinions and
conclusions presented are the sole responsibility
of the authors and do not reflect the views of
sponsors and other participating agencies.
FIG 3. Travel times obtained from simulation for
various bus volumes
TABLE 1. Acceleration Equations by Controller
Type
Acceleration equation Controller Type
P Controller
PI Controller
PID Controller
Introduction The Exclusive Bus Lane (XBL) is one
of the most successful and popular bus rapid
transit systems in the country. This lane has
already contributed in taking thousands of cars
off the road and saved precious time for
commuters. This popularity of the XBL attracted
more commuters to use this lane and eventually
resulted in reaching its capacity. Automation
reduces the reaction times and other headway
necessitated delays. The XBL is a single lane
roadway separated from the rest of the roadway by
temporary separators. It is possible that a human
driver will be more careful while passing through
such a lane, which increases the reaction time.
Such reaction times could be avoided in an
automated system and will yield better overall
travel times. There has been a lot of research
in the field of Automated Highway Systems (AHS).
Research was focused on several areas including
the understanding of platooning scenario,
handling the lateral position, longitudinal
control and studying the lane changing behaviour.
We used a longitudinal controller for the bus
lane that was developed by Ioannou and Zhang
(2006) and modified it slightly in order to
implement it in Paramics for the present
study. PARAMICS Simulation Model A calibrated
model was used to model the existing conditions.
Paramics provides certain features that modifying
changing the reaction times, safe headways for
accurate calibration.
TABLE 4. Total costs incurred by type of cost
Cost Type Total Amount (Dollars)
Incremental Cost in Materials 13,780.6
Incremental Cost in Fuel Consumption 561,827.4
Road Maintenance Costs 516,175.0
Bus Replacement Costs 30,925,129.0
Initial Automation Costs 61,650,000.0
Total 93,666,912.0
TABLE 2. Non linear systems used for smooth
control and emergency stopping
TABLE 5. Benefit-Cost ratios
Condition Control Decision Vehicle Following Conditions
a gt 2 ms-2 Set a 2ms-2 Normal Conditions (For maintaining a smooth flow)
a lt -3.5 ms-2 Set a -3.5ms-2 Normal Conditions (For maintaining a smooth flow)
Vl 2 ms-1 lt Vf and Vf lt Vl 8 ms-1 and a gt 0 ms-2 Set a 0 ms-2 Normal Conditions (For maintaining a smooth flow)
Vl - 2 ms-1 lt Vf and Vf lt 2 ms-1 Set a a ms-2 Normal Conditions (For maintaining a smooth flow)
Vf lt Vl 2 ms-1 and a lt 0 ms-2 Set a 0 ms-2 Normal Conditions (For maintaining a smooth flow)
Vf gt Vl 8 ms-1 and gap lt 16 m Set a -2.5 ms-2 Normal Conditions (For maintaining a smooth flow)
Vf gt Vl 12 ms-1 and gap lt 24m set a -3.5 ms-2 Emergency Conditions(For quick stopping)
Vf gt Vl 16 ms-1 and gap lt 32m Set a -4.5 ms-2 Emergency Conditions(For quick stopping)
Vf gt Vl 20 ms-1 and gap lt 40m Set a -5.5 ms-2 Emergency Conditions(For quick stopping)
Rate of Interest (Percentage) Rate of Interest (Percentage) Rate of Interest (Percentage) Rate of Interest (Percentage)
Value of Time (Dollars per Hour) 3 5 7 10
7.5 1.50 1.34 1.22 1.08
15 2.97 2.70 2.4 2.17
20 3.97 3.59 3.28 2.90
25 4.96 4.49 4.11 3.62
TABLE 3. Comparison of Performance Measure (Jerk)
for all the Controllers for the Network.
Controller Jerk
P controller 0.113 ms-3
PI controller 0.942 ms-3
PID controller 0.742 ms-3
Human Model 0.448 ms-3
FIG 2. snapshot of the corridor from Google Maps
and the Paramics model
FIG 1. Spacing errors for each of the
controllers