Transcript No Slide Title

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
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.
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.
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 Authority’s 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 model’s
travel times match with the existing conditions.
Automated 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
1
s
u  K p (Vv  K )  Ki (Vr  K )  Kd
(Vr  K )
s
s
1
N
Where
s is the Laplace operator,
K , K p , Ki , Kd and N are positive control parameters to be chosen,
Vr is the relative speed between the lead-following vehicle pair,
 is the spacing error between the two and
u 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
Sdes  S0  T (V )
Where,
S des= the desired spacing between the pair,
V = the speed of the following vehicle,
S0 = the spacing when the following vehicle is at rest and
T = 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.
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
Rutgers, The State University of New Jersey
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 (δ), and the desired speed ( ) as
follows.
  S  Sdes
Vdes  Vl  K
Where,
S = the current spacing,
K = 0.1s-1, a constant and
Vl = 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.
Acceleration equation
Controller Type
a  K p (Vdes V )
P Controller
a  K p (Vdes V )  Ki (Vdes V )
a  K p (Vdes  V )  K i  (Vdes  V )  K d
PI Controller
d (Vdes  V )
dt
PID Controller
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.
Condition
Control Decision
a > 2 ms-2
Set a = 2ms-2
Travel Times (Minutes)
20
18
16
14
12
10
FIG 3. Travel times obtained from simulation for various bus volumes
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.
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
a < -3.5 ms-2
Set a = -3.5ms-2
Vl + 2 ms-1 <= Vf and Vf <= Vl + 8
ms-1 and a > 0 ms-2
Set a = 0 ms-2
Vl - 2 ms-1
< Vf and Vf < + 2
ms-1
Set a = a ms-2
Vf <= Vl – 2 ms-1 and a < 0 ms-2
Set a = 0 ms-2
Vf > Vl + 8 ms-1 and gap < 16 m
Set a = -2.5 ms-2
Vf > Vl + 12 ms-1 and gap < 24m
set a = -3.5 ms-2
Vf > Vl + 16 ms-1 and gap < 32m
Set a = -4.5 ms-2
Vf > Vl + 20 ms-1 and gap < 40m
Set a = -5.5 ms-2
TABLE 5. Benefit-Cost ratios
Rate of Interest (Percentage)
Value of Time
(Dollars per Hour)
Normal Conditions (For
maintaining a smooth flow)
7.5
3%
1.50
5%
1.34
7%
1.22
10%
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
Conclusions and Future work
Emergency Conditions(For quick
stopping)
Controller
Jerk
13
P controller
0.113 ms-3
12
PI controller
0.942 ms-3
11
PID controller
0.742 ms-3
10
Human Model
0.448 ms-3
0
0:
-1
45 5
9: - 9:4
30 0
9: - 9:3
15 5
9: - 9:1
00 0
9: - 9:0
45 5
8: - 8:4
30 0
8: - 8:3
15 5
8: - 8:1
00 0
8: - 8:0
45 5
7: 7:4
30 0
7: - 7:3
15 5
7: - 7:1
00 0
7: - 7:0
45 5
6: - 6:4
30 0
6: - 6:3
15 5
6: - 6:1
00 0
6: - 6:0
45
5:
14
FIG 2. snapshot of the corridor from Google Maps and the Paramics model
22
Vehicle Following Conditions
TABLE 3. Comparison of Performance Measure (Jerk) for all the Controllers for
the Network.
FIG 1. Spacing errors for each of the controllers
24
TABLE 2. Non linear systems used for smooth control and emergency stopping
Existing travel times
17 Times obtained in the model
15
26
Existing Conditions
10% increase in volumes
20% increase in volumes
23% increase in volumes
30% increase in volumes
4. At the end of the next time cycle, repeat steps 1, 2 and 3.
18
16
28
TABLE 1. Acceleration Equations by Controller Type
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.
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.
Sensitivity Analysis
0
0:
-1
45 5
9: - 9:4
30 0
9: - 9:3
15 5
9: - 9:1
00 0
9: - 9:0
45 5
8: - 8:4
30 0
8: - 8:3
15 5
8: - 8:1
00 0
8: - 8:0
45 5
7: 7:4
30 0
7: - 7:3
15 5
7: - 7:1
00 0
7: - 7:0
45 5
6: - 6:4
30 0
6: - 6:3
15 5
6: - 6:1
00 0
6: - 6:0
45
5:
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 costbenefit analysis indicated that automation of the bus lane was
beneficial.
Kaan Ozbay, Ph.D., Teja Indrakanti and Ozlem Yanmaz-Tuzel, M.Sc.
Travel Times (Minutes)
Paper: 10-3495
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.