minimization of overall person delay at light rail transit crossings on
TRANSCRIPT
MINIMIZATION OF OVERALL PERSON DELAY AT LIGHT RAIL TRANSIT
CROSSINGS ON CONGESTED URBAN ARTERIALS
by
Nikola Mitrovic
A Thesis Submitted to the Faculty of
College of Engineering and Computer Science
in Partial Fulfillment of the Requirements for the Degree of
Master of Science
Florida Atlantic University
Boca Raton, Florida
May 2011
ii
Copyright by Nikola Mitrovic 2011
MINIMIZATIO OF OVERALL PERSO DELAY AT LIGHT RAIL TRANSIT
CROSSINGS 0 CO GESTED URBAN ARTERIALS
By
ikola Mitrovic
This thesis was prepared under the direction of the candidate' thesis advisor, Dr.Aleksandar Stevanovic, Department of Civi~ Environmenta~ and GeomaticsEngineering, and has been approved by the members ofhis supervisory committee. It wassubmitted to the faculty of the College of Engineering and Computer Science and wasaccepted in partial fulfillment of the requirements for the degree ofMaster of Science.
SUPERVISORY COMMITTEE:
IteetSewda/ 51eJ(;UA6V/CAleksandar tevanovic, Ph.D.Thesis or
~JiL~P.D. Scarlatos, Ph.D. :=Chair, Department of Civil, Environmentaland Geomatics Engineering
Karl . Steven ,Dean, College f ngineering and Computer Science
!7R:I~~Dean, Graduate College
111
~~Khaled Sobhan, Ph.D.
fJ!,.;)/5; U'I;Date r (
iv
ACKNOWLEDGEMENT
This research is the result of two years of hard work and a lot of determination.
Nonetheless, none of this would have been possible without the help, support and
encouragement of the faculty and student body of the Transportation Research Group at
Florida Atlantic University.
I would like to convey my gratitude to my advisor, Dr. Aleksandar Stevanovic. His
supervision, guidance and advice throughout the different stages of this paper were key to
the completion of my research. Dr. Stevanovic has inspired and enriched my growth as a
student, a researcher and a scientist.
A special thanks go to the Utah Transit Authority (UTA) and Utah Department of
Transportation (UDOT) for providing critical data used for this study, especially to Mrs.
Kerry Doene, Strategic Planner (UTA).
In addition, I would like to thank Dr. Evangelos Kaisar and Mrs Jarice Rodriguez for
their help and preparation of the thesis. And last but not least my transportation
colleagues, Ioannis Psarros, Dusan Jolovic, Claudia Olarte and Benazir Portal. Thank you
for your continuous support, motivation and encouragement
v
ABSTRACT
Author: Nikola Mitrovic
Title: Minimization of Overall Person Delay at Light Rail Transit
Crossings on Congested Urban Arterials
Institution: Florida Atlantic University
Thesis Advisor: Dr. Aleksandar Stevanovic
Degree: Master of Science
Year: 2011
This study describes analytical model as one innovative way to simulate Light Rail
Transit (LRT) operations and calculate vehicular, transit and person delays at LRT
crossings through Microsoft Excel. Analytical model emulates LRT trajectories from
field and use these trajectories to clearly define train and car phases through Visual Basic
for Applications (VBA) logic, which is part of analytical model. Simulation of train
trajectories and calculations of delays were done for different LRT strategies and
estimated roadway condition, Testing and validation of analytical model were performed
in one case study in Salt Lake City (UT). Results show that analytical model is capable of
emulating LRT trajectories and estimating delay at isolated LRT crossing. However,
analytical model is not capable of simulating different train strategies at two or more LRT
crossings, at the same time. Finally, extracted strategy provides savings from $100.000 to
$200.000 in study area, on annual basis for projected year.
vi
MINIMIZE PERSON DELAY AT RAILROAD CROSSING THROUGH SEARCH
BASED OPTIMIZATION TOOL
LIST OF TABLES ........................................................................................................... viii
LIST OF FIGURES ........................................................................................................... ix
1 INTRODUCTION ...................................................................................................... 1
1.1 Problem Statement ...............................................................................................2
1.2 Research Goals and Objectives ............................................................................3
1.3 Thesis Organization .............................................................................................3
2 LITERATURE REVIEW ........................................................................................... 5
2.1 Light Rail Operations ...........................................................................................5
2.2 Computation of Roadway Delay at Railroad Crossing ........................................8
3 NETWORK SIMULATION MODEL ..................................................................... 11
3.1 Case Study Area .................................................................................................11
3.2 Modeling process ...............................................................................................12
3.3 Calibration and Validation of VISSIM Model ...................................................15
3.3.1 Vehicular Data ............................................................................................ 15
3.3.2 Transit Data ................................................................................................. 17
3.4 Future Operations ...............................................................................................20
4 ANALYTICAL MODEL.......................................................................................... 21
4.1 Simulation of Train Trajectories ........................................................................21
vii
4.2 Calculation Vehicular, Transit and Person Delay ..............................................25
4.2.1 Vehicular Delay .......................................................................................... 26
4.2.2 Light Rail Transit Delay ............................................................................. 27
4.2.3 Person Delay ............................................................................................... 28
4.3 Validation of Analytical Model .........................................................................29
4.4 Simulation of Different Train Strategies ............................................................33
4.5 Limitations of Analytical Model ........................................................................35
5 RESULTS AND ANALYSIS ................................................................................... 37
5.1 Impact of Different Train Schedules on Overall Person Delay .........................38
5.2 Impact of Different LRT Priority Strategies ......................................................40
5.2.1 Different LRT Priorities at Crossing on 1300S SB .................................... 41
5.2.2 Different LRT Priorities at Crossing on 2100S NB .................................... 47
5.3 Person Delay Savings .........................................................................................52
6 DISCUSSION ........................................................................................................... 55
7 CONCLUSIONS AND FUTURE RECOMMENDATIONS ................................... 57
8 REFERENCES ......................................................................................................... 61
viii
LIST OF TABLES
Table 1: Recorded Parameters in VISSIM Simulation ..................................................... 26
Table 2: Overall Person Delay for Different Train Strategies .......................................... 38
Table 3: Overall Person Delay for Different LRT Strategies on 1300S ........................... 42
Table 4: Person Delay at Crossing on 1300S for Different Strategies on Same Crossing 43
Table 5: Significance of Results for Different Priority Strategies on 1300S .................... 45
Table 6: Overall Person Delay for Different LRT Strategies on 2100S ........................... 48
Table 7: Person Delay at Crossing on 2100S for Different Strategies on Same Crossing 49
Table 8: Significance of Results for Different Priority Strategies on 1300S .................... 50
Table 9: Person Demand at LRT Crossings ...................................................................... 53
Table 10: Saving Time at LRT Crossing .......................................................................... 53
Table 11: PM and Annual Overall Benefits ...................................................................... 54
ix
LIST OF FIGURES
Figure 1: Case Study Area ................................................................................................ 12
Figure 2: VISSIM Model of Study Area........................................................................... 13
Figure 3: Calibration of Roadway Traffic ........................................................................ 15
Figure 4: Validation of Roadway Travel Times ............................................................... 16
Figure 5: Validation of Transit Travel Times (Southbound) ............................................ 17
Figure 6: Validation of Transit Travel Times (Northbound) ............................................ 18
Figure 7: Distribution of Lateness and Early Arrivals (Southbound) ............................... 19
Figure 8: Distribution of Lateness and Early Arrivals (Northbound) ............................... 19
Figure 9: LRT Reference Points in Study Network .......................................................... 22
Figure 10: Simulation of LRT Trajectories in Analytical Model ..................................... 24
Figure 11: Duration of Blockage Event ............................................................................ 27
Figure 12: Validation of Search Based Optimization Tool for Dwell Time ..................... 31
Figure 13: Validation of Search Based Optimization Tool for Roadway Stopped Delay 32
Figure 14: Layout Of LRT References Point In Study Area ............................................ 34
Figure 15: Simulated LRT Strategies ............................................................................... 36
Figure 16: Overall Person Delay for Different Train Strategies on 1300S....................... 39
Figure 17: Overall Person Delay for Different Train Strategies on 2100S....................... 40
x
Figure 18: Person Delay at Crossing on 1300S for Different LRT Strategies on
Same Crossing .................................................................................................44
Figure 19: Impact of Priority Strategy on 1300S .............................................................. 46
Figure 20: Person Delay at Crossing on 2100S for Different LRT Strategies on
Same Crossing .................................................................................................50
Figure 21: Impact of Priority Strategy on 2100S .............................................................. 51
1
1 INTRODUCTION
According to the Transportation Research Board’s Committee on Light Rail Transit,
Light Rail Transit (LRT) is defined as “a metropolitan electric railway system
characterized by its ability to operate single cars or short trains along exclusive rights of
way at ground level, on aerial structures, in subways or, occasionally, in streets, and to
board and discharge passengers at track or car-floor level”. (1) With its lower
implementation cost than metro and comparable high-capacity LRT is often seen as an
affordable and efficient railway transit option which provides an alternative to the private
transportation. At the same time, LRT represents a competitive mode to private
transportation at conflict points in the network. At those points, train operations should be
defined in such a way to provide smooth most efficient operations for both LRT and
roadway traffic.
Several priority strategies can be implemented into the control plan for an at-grade
crossing. (2) These strategies can range from an unconditional priority (preemption) at all
times for LRT vehicles to a situation in which LRT vehicles must wait for an acceptable
gap in the traffic stream. From the perspective of transit services, preemption is a better
choice because it maximizes transit service reliability and quality of service by totally
eliminating transit delay (3). However, preemption causes additional delay to vehicular
traffic and pedestrians at LRT crossings. Analytical computations of these delays cannot
be normally encountered in traffic engineering analysis. Non-cyclical and directional
2
nature of LRT arrivals renders traditional intersections and network analysis technique
inappropriate. (4)
Regardless to the complexity of delay computations, literature and current practice
suggest person delay as a measure of effectiveness (MOE) which will provide a method
of associating a quantifiable user cost with the operation of an LRT system with at grade
crossings.
1.1 Problem Statement
Person delay as a representative measure of effectiveness at light rail transit crossing
defines the average lost time per “user” while he/she is passing LRT crossing by either
private car or transit. Preemption defines no-delay for LRT passengers and causes extra
delay for private cars while the other priority strategies provide more green time for
private cars and introduce delay for LRT vehicles. Different train strategies bring the
different amount of delays for both private car and LRT. Therefore, person delay is also
different for different train strategies.
The other factor, which affects the person delay at LRT crossing, is train schedule.
Train schedules usually propose constant headway and unique offset time. Headway
represents amount of time between two consecutive departures from same station and
direction. Offset time defines the time between two consecutive train departures from
opposite directions. Train offset suggests the point in the network where trains from
opposite directions suppose to “meet”. If trains arrive at a crossing simultaneously, the
impact on private traffic (for same priority strategy) is much less than if they arrive at
different times. Furthermore, if one of LRT vehicles arrives immediately after another
3
(from opposite directions), the overall impact on private traffic may be much greater than
for separate arrivals.
The problem that needs to be addressed may be formulated as: What combinations
of train priority and train schedule for given traffic and transit volume is going to bring a
minimal overall person delay? In order to bring a minimal values, each possible
combinations of train priority and schedule has to be observed. This kind of problem can
not be efficiently addressed through micro-simulation. Building and analyzing of each
possible scenario in micro-simulation represent computationally intensive and expensive
process.
1.2 Research Goals and Objectives
This study searches for set of train priority and schedule, that brings a minimal
overall person delay in case study area. The goal of this study is to develop analytical
model, which will be able to extract combination of train priority and train schedule to
minimize overall person delay at three LRT crossings at case study area. The objective of
the study is to develop micro-simulation model of study area, which will provide a set of
input parameters for the analytical model, and through validation process defines strength
and weaknesses of analytical model. This was achieved through one case study example
in Salt Lake City, UT.
1.3 Thesis Organization
This thesis consists of seven chapters. The following chapter gives an overview of
light rail transit operations and analytical computations of vehicular delay at railroad
4
crossing. Chapter three describes the microsimulation model that is used in this study. It
includes the modeling process, calibration and validation of the model, and a description
of future basic scenario, which was built for the validation purpose of analytical model.
Chapter four describes analytical model. It defines analytical calculations of vehicular,
transit and person delay, validation of analytical model as well as some limitations which
were found during building process. Chapter five provides and analyses results obtained
using analytical model in case study area. Chapter six provide discusion about final
output and major limitations in analytical model. Chapter seven summarizes major
conclusions of study and identifies the areas for future research.
5
2 LITERATURE REVIEW
The primary goal of this research is to develop analytical model, which provides a
LRT strategy that minimizes person delay at LRT crossing. Simulation of Light Rail
operations and calculation of person delay without using any microsimulation traffic
software have represented challenging job. However, previous studies and research
significantly alleviated this duty. This chapter gives a brief overview of LRT impact on
private traffic as well as methodology for computational traffic delay at LRT crossing.
2.1 Light Rail Operations
Several studies were conducted in the past to quantify effects of LRT operations on
vehicular traffic. Chalander and Hoel, investigated the effects of light rail services on
average delays experienced by vehicular traffic. (1) They used the VISSIM computer
simulation model to test four scenarios with light rail crossings: isolated crossings of two-
lane and four-lane roads, a case in which light rail transit is located in the median of a
street, and a larger network that includes four crossings. For different variations of
vehicular and transit volumes, they investigated additional delay experienced by vehicles
due to LRT services. For isolated crossings of two/four lane roads they found that
average additional delays caused by LRT vehicle increased with the frequency of LRT
operations and the growth in vehicular volumes
6
James Cline, in his Master of Science Thesis, examined the delays of vehicular
traffic at LRT crossings caused by LRT service. (5) NETSIM computer simulation model
was used for testing four scenarios with light rail crossings: an isolated crossing, an
adjacent intersection crossing, a series of coordinated intersections with preemption, and
a case study based on a corridor in Houston. He found that the major factor in the
vehicular traffic delay, experienced by LRT service, was a volume to capacity (v/c) ratio.
Nelson and Bullock (6) examined the impact of emergency vehicle preemption on
closely spaced arterial traffic signals through seven preemption paths and three different
preemption times. They found that a single preemption call had a minimal effect on the
overall travel time and delay while multiple preemption call causes serious queuing and
delay problems. In addition, the impact of multiple preemption calls is more severe if
they are next to each other.
Bullock et al. (7) analyzed impact of emergency vehicle traffic signal preemption on
travel time and delay of traffic on a signalized corridor in Northern Virginia during the
morning rush hour. In their findings they emphasized impact of cycle transition
parameters on the controller’s ability to recover from preemption.
Gerken and Tracy (8) evaluated LRT impact on vehicular traffic through vehicular
delay and queue length at an existing isolated intersection in Union County, New Jersey.
They simulated and evaluated traffic operations at an intersection which is 254 feet away
from the railroad crossing. Their findings showed that frequent LRT service caused
additional delay for the tangent direction of tracks, while LRT service will have no
impact on the parallel direction of tracks.
7
Li et al. (9) described a concept and the implementation of LRT using an active
priority system for highway/rail grade crossing. The major part of active priority system
represents a priority request generator which adopts a three-scheme conditional priority
control strategy. Schemes are designed according to the train schedule adherence. The
concept was tested on a case study for a San Diego Trolley system and it showed
significant savings.
Ekeila et al. (10) compared conventional and dynamic Transit Signal Priority (TSP)
systems in two case studies - a hypothetical intersection and a proposed light rail
corridor. Simulations’ results showed that dynamic TSP system was better than the
conventional system.
Faran (11) provided an overview of innovative pedestrian and motor vehicle traffic
control designs and practices that had been applied to LRT in Barcelona, Spain. Tian et
al. (12) mathematically described a relationship between schedule-delay cost function
and in-vehicle congestion cost function. They found that concavity and convexity
characteristics of the in-vehicle congestion cost function and the schedule delay cost
function should be opposite.
Wadjas and Furth (13) used Vehicle Actuated Programming (VAP) logic in VISSIM
to develop a control strategy based on advanced prediction which provides passage with
near-zero delay for transit vehicles with negligible impact on the other traffic. They
conducted simulations on Massachusetts’ Huntington Avenue corridor in Boston, which
is served by a light rail line. Their results showed that 82% of the trains arrived during the
green phase which caused substantial improvements to transit travel time with little
impact on other traffic.
8
2.2 Computation of Roadway Delay at Railroad Crossing
Delays of vehicular traffic caused by train service at LRT crossing cannot be
normally encountered in traffic engineering analysis as a consequence of non-cyclical
LRT arrivals. In order to resolve this problem Walter Okitsu developed a model for free
LRT grade crossing delay. (14)
In order to provide quick and cheap estimation of traffic delay at LRT crossing,
caused by freight passage, commuter rail and Amtrak service Okitsu collected field data
and developed a model. During 24-hour video recording at 33 crossings in Los Angeles
County’s San Gabriel Valley, the behavior of traffic signals and the private traffic were
observed for each blockage event. Simple isolated crossings to complex crossings with
preempted traffic signals on one or both sides were observed in the study area. Frequency
of the train service occurs from 10 up to 80 times per day at the same locations while the
durations of crossing blockages ranged from a few seconds to 53 minutes.
By observing recorded field condition for each crossing and for each direction, Okitsu
defined a relationship between vehicular flow characteristics (arrival and saturation flow
rate, delay time) and total vehicular delay at LRT crossings, experienced by train service.
Okitcu’s formula [1] uses duration of each blockage event (B) and vehicular flow
characteristics at LRT crossing to estimate total vehicular delay (D) at railroad crossing
caused by LRT service. Vehicular flow characteristics such as arrival rate (AR),
saturation flow rate (S) and lost time (LT) have been quantified by observing field data.
9
2*( )
2*(1 )
AR B LTD
ARS
[1]
The total vehicular delay is calculated for each blockage event. The total daily
vehicular delay is the summation of these vehicular delays calculations throughout the
day. Authors didn’t have opportunity to calibrate and validate their calculation model.
Rymer at al. (15) tried to estimate vehicular delay as a function of crossing-volume to
capacity ratio (Xcr). Through NETSIM microsimulation software, they simulated LRT
grade crossing operations for different roadway cross section, vehicular and transit
volumes, and different clearance times. Cross-section varied from two to six lines.
Volume ranged from 250 vehicles to 1000 vehicles per hour per lane. LRT headway
varied from 2.5 to 12.5 min which corresponds tofive t o twenty-four LRT interruptions
during one hour. Crossing clearance times of 30, 40 and 50 seconds were tested.
They found that crossing-volume-to-capacity ratio (Xcr) is inversely proportional to
the time available for vehicular crossing time (g) and directly proportional to the
demand/saturation ratio (v/s) [2]. The vehicular crossing time (g) decreases as lost time
and LRT crossing time increase, which in turn penalizes the operational capacity of the
roadway segment.
1( ) ( )crvX
g s [2]
Vehicular crossing time (g) represents a portion of time available for the vehicular
traffic to cross the tracks. This time is calculated for known LRT headway (C), LRT
crossing clearance time (CCT) and lost time (L) [3].
10
( )C CCT Lg
C
[3]
During their research, they showed how clearance time and LRT headways have an
impact on vehicular delay. While either clearance time or LRT headways increases,
vehicular traffic delay tends to increase, too. As a final output, they defined a dependence
of vehicular delay (d) on crossing-volume to capacity ratio (Xcr) [4]
(sec/ ) 91.16 crd veh X [4]
In their estimation of vehicular delay, authors neglected the randomness in train
clearance time and train departure time.
Although some authors (14,15) developed a methodology for estimating vehicular
delay at LRT crossing, they didn’t have opportunity to test and validate their models.
Furthermore, they didn’t try to extract the most efficient LRT strategy. This study tried to
fill this gap. Analytical model was developed, validated and run to provide strategy that
minimizes person delay at LRT crossings in case study area.
11
3 NETWORK SIMULATION MODEL
This chapter describes a case study microsimulation model, which was built to
provide necessary data for building and validation of the analytical model. Case study
area is located in Salt Lake City and microsimulation model refers to projected 2015 year
when number of trains which traveling in study area will be significantly increased. Train
strategy for 2015 should be extracted through analytical model. .
3.1 Case Study Area
In order to satisfy estimated ridership in future years, Utah Transit Authority is going
to increase Light Rail Service in Salt Lake City. This extension in spatial coverage and
frequency will bring greater potential for operational conflicts with private cars. Segment
between crossings at 1300S and 2100S is chosen as the most critical part for projected
2015. Along this most-frequent LRT segment, expected number of trains will reach 26
trains per hour which represents a significant increase compared to the current 12 trains
per hour. LRT stations, which are located in vicinity the of LRT crossings, additionally
increase an impact on vehicular operations at crossing on 1300S and 2100S. Figure 1
shows the case study network as well as locations of LRT station.
12
Figure 1: Case Study Area
3.2 Modeling process
Microsimulation software VISSIM 5.2 (16) was an efficient and user-friendly tool in
modeling vehicular and transit operations in the case study network. Vehicle Actuated
Programming (VAP) platform within VISSIM significantly alleviates coding signal
timing preemption.
The study case network was modeled in a VISSIM simulation software, with the
existing network geometry, traffic volumes, turning movements at intersections, signal
timing data, and transit operations for the PM peak period from 4:00 PM to 6:00 PM.The
study area network was converted to the VISSIM’s link-connector model from the
VISUM UT State network model. Converted model was checked and corrected by
13
observing Google Earth. Figure 2 shows the modeled VISSIM geometry of case study
area.
Figure 2: VISSIM Model of Study Area
Modeled VISSIM geometry was loaded with traffic volumes provided from different
sources. Traffic volumes on arterial streets were estimated according to the Annual
Average Daily Traffic for 2008 and 2009 . Those data can be found on Utah Department
Of Transportation (UDOT) website. Traffic volumes on I15 ramps were found on UDOT
Performance Measurement System (PeMS) platform. Traffic counts for two intersections
(for 2008) were provided by UDOT while for the rest of the network, traffic counts were
estimated by using Excel balancing spreadsheet. Traffic signals were provided (as PDF
files) by UDOT. Those PDFs files were manually imported into the VISSIM’s NEMA
platforms for each individual controller.
14
LRT tracks in the study area with stations on 1300 South and 2100 South were coded
by observing Google maps and Google earth. Extensions of tracks on both side (south
and north) were modeled to accommodate dummy stations. Those stations emulate
lateness and early arrivals from the field. Additionally, future spatial extension of LRT
tracks was modeled according to arterial maps.
LRT segment was loaded with train departures according to the current Utah Transit
Authority (UTA) schedule. These departures were offset by certain intervals by creating
dummy stations right at the entering points. Dwell times on regular station, as well as
deviations in scheduled arrivals, were extracted from provided GPS train travel times
data. Those values were imported in VISSIM as empirical distributions. Each of those
empirical distributions is defined by its extreme value (min and max) and sets of
intermediate points with their belonging probability. Occupancy of LRT vehicle for each
line and direction was found in the current UTA ridership.
Preemption at railroad crossings was set-up according to UTA’ instructions.
Locations of check in and check-out detectors for each crossing as well as necessary
changing time from one stage to another (LRT to vehicular and vice versa) were given by
UTA. According to the UTA instruction:
“Once the train crosses the track circuit, the flashers on the gates begin and flash
for about 4 seconds, then the gates drop which takes about 3 seconds”
“The gates remain down until the last train vehicle passes a track circuit located
approximately 80 feet past the crossing. The gates then take about 7 seconds to
rise. Only then can auto traffic pass.”
15
3.3 Calibration and Validation of VISSIM Model
Calibration and validation of VISSIM model were performed for private and LRT
transit separately. This chapter provides analysis and results of this process.
3.3.1 Vehicular Data
Provided Traffic counts for signalized intersections and ramps were used to calibrate
traffic operations in the model. VISSIM was programmed to collect the same data
through 10 random seed simulations. Figure 2 shows high correlation between data sets
collected in the field and those from the simulation.
R² = 0.993
0
200
400
600
800
1000
1200
1400
1600
0 200 400 600 800 1000 1200 1400 1600
Model t
raff
ic c
ounts
[veh/h
]
Field traffic counts [veh/h]
Figure 3: Calibration of Roadway Traffic
16
Private traffic operations in the model were validated for travel times. Field travel
times were collected at four major intersections during PM peak hours during the week of
February 17th
,2010. Through floating-car technique, travel times were recorded using
GPS devices and laptops.
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Tra
vele
d d
ista
nce [ft
]
Time [s]
Travel Time Runs on 1700S WB
Field travel runs VISSIM travel runs
9%
2%
5%
Figure 4: Validation of Roadway Travel Times
Only trajectories of vehicles from simulation, whose routes are identical with those
of field vehicles were observed and included in validation process. Figure 3 (which refers
to 1700S WB travel time segment) shows such a travel time profile for one travel time
segment and percentage of vehicles (in microsimulation) whose travel time is similar
(within ± 10%) to the time of the vehicles in the field .The number (percentage) attached
to each activity shows how many percent of vehicles in the microsimulation (traveling on
17
the same segment and having the same origin and destination points) experience a very
similar activity.
3.3.2 Transit Data
GPS travel times of LRT vehicles were used to validate transit operations in the
study area. Travel times of the LRT vehicles were provided (by UTA) in a format that
included both travel times between two consecutive LRT stops and dwell time at the
arriving (second) LRT stop. VISSIM was programmed to collect the same data through
10 random seed simulations. Figures 4 and 5 show how accurately the VISSIM model
replicates travel times and dwell times at LRT stations near 1300S and 2100S.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
<135 135-145 145-155 155-165 165+
Rela
tive fre
quency
Travel time (including dwell time) [sec]
FIELD
VISSIM
Figure 5: Validation of Transit Travel Times (Southbound)
18
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
<135 135-145 145-155 155-165 165+
Rela
tive fre
quency
Travel time (including dwell time) [sec]
Field
VISSIM
Figure 6: Validation of Transit Travel Times (Northbound)
Furthermore, train schedule deviations from the field were validated. Train
deviations represent important part of LRT operations and through introducing dummy
stations at the entrance points in the network, those deviations were modeled. If early and
late arrivals in the microsimulation did not resemble those from the field this then the
evaluation of various schedule scenarios would not provide trustworthy results. Field and
simulation deviations from the scheduled train arrivals are shown in Figures 6 and 7.
These figures show that VISSIM can simulate lateness and early arrivals of LRT trains
from the field and emulate LRT schedule adherence from the field.
19
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
-120 - 0 0 - 120 120 - 240 240 - 360 360+
Re
lative
fre
que
ncy
Deviations from scheduled arrival [sec]
Field
VISSIM
Figure 7: Distribution of Lateness and Early Arrivals (Southbound)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
-80 - -20 -20 - 40 40 - 100 100 - 160 160 - 220 220 - 280 280+
Re
lative
fre
que
ncy
Deviations from scheduled arrival [sec]
Field
VISSIM
Figure 8: Distribution of Lateness and Early Arrivals (Northbound)
20
3.4 Future Operations
One future scenario was built in a properly calibrated and validated model according
to the future traffic and transit operations for projected 2015.
Traffic volumes were inflated according to the estimated volumes for 2015.
Future traffic data were estimated according to the traffic demand for 2030 which
was provided by Wasatch Front Regional Council from their long range
transportation plan.
Transit volumes for 2015 are defined according to the UTA long-term plan. In the
study area network, UTA proposes 26 trains per PM peak hour (14 in southbound
and 12 in northbound direction). In the future basic scenario, trains from the
opposite directions simultaneously enter the network.
New dwell times on regular stations were estimated according to the current and
future ridership. Ratio between the future and current ridership was multiplied by
a current dwell time in order to estimate future dwell time.
Current and future headways were used to estimate future train scheduled arrival
deviations. Future deviations will be smaller as a consequence of more frequent
LRT operations.
The purpose of this scenario is to alleviate building of analytical model and to provide
input parameters for the future validation process of the analytical model. Train logic of
this scenario invokes preemption at all LRT crossings and a train schedule which
proposes simultaneous train departures from the opposite directions (offset 0).
21
4 ANALYTICAL MODEL
The purpose of analytical model is to calculate vehicular and transit delay for
different combinations of train schedule and train priority in order to bring transit strategy
which minimizes overall person delay at three isolated LRT crossings in study area. Idea
behind this model is to build and simulate LRT trajectories which resemble those from
the field and for given traffic, transit and signal timing data calculate traffic, transit and
person delay. Through one automatic and iterative process, train schedules and priority
were changed and tested.
4.1 Simulation of Train Trajectories
Train trajectories were simulated in the MS Excel spreadsheet using a set of
normally distributed random numbers and time space diagrams of LRT vehicles. Train
trajectories define the sets of times when train arrives at, departures from, or just passes
reference points in the network. Reference points in train trajectories represent points on
the LRT tracks which are important for modeling transit and traffic signal operations at
LRT crossings. These points are shown on Figure 9 and they are:
Entrance point in the network
Dummy station which was built to simulate lateness and early arrivals of
trains
22
Regular station in the network
Check in and check-out detectors for LRT crossings.
Figure 9: LRT Reference Points in Study Network
Normally distributed random numbers are introduced to simulate different travel
time between each two reference points as well as different dwell times of LRT vehicles
on regular and dummy stations. Those deviations can be found in LRT time space
23
diagrams. Time-space diagram of LRT vehicles can be extracted from either Global
Positioning System (GPS) data of LRT vehicles or microsimulation model (if one exist)
which is able to provide LRT trajectories as an output.
In this study, analytical model was built to extracts a best LRT strategy for projected
2015.Only source, which can be used to extract train trajectories in this case, is VISSIM
model. Future scenario was built to alleviate building of analytical model by providing
necessary data. Ten simulation runs of VISSIM model provided sample data of 260 train
trajectories in south bound and 240 train trajectories in north bound.
Distributions of dwell time on regular/dummy stations as well as travel time
distributions between each pair of references points were extracted from VISSIM
trajectories files and transformed into normal distributions with parameters µi and δi.
Figures 10 shows parameters for SB directions which were found in VISSIM future
model. Furthermore, figure 10 gives the Y-coordinates of reference points on the LRT
tracks and explains the role of normally distributed random numbers in calculation of
time when train pass across reference point. Dwell time at station on 1300S (cell H7 –
cell H6) is defined as normally distributed value with mean of 46.56 seconds (cell B7)
and standard deviation of 15.1 seconds (cell C7). VISSIM output trajectories of LRT
vehicles also show that dwell time at station on 1300S doesn’t exceed 70 seconds and
doesn’t take values which are smaller than 7 seconds. The same restrictions were
simulated in analytical model (formula bar).
24
Figure 10: Simulation of LRT Trajectories in Analytical Model
In simulation traffic and transit operation at LRT crossings, very important role plays
activation of traffic signal on these crossings. Activation of traffic signal is defined by
time when train activates a check in detector and amount of delayed time (if any exists)
which is introduced to simulate different priority strategies. This amount of time
represents a delayed activation of traffic signal and it can range from 0 which correspond
to preemption strategy up to same maximum value. This maximum value is defined as a
maximum dwell time at corresponding LRT station.
. During the observation of the VISSIM simulation, simultaneous passing trains across
LRT crossing were recorded. During these situations, one train activates traffic signal
while the other deactivates traffic signal and finished train phase. Additionally, on the
LRT crossings near regular stations it was recorded that one train (which is dwelling)
activates and deactivates traffic signal while the train from the opposite direction is
served. Those situations were also found in an Excel simulation of train trajectories.
25
In order to extract and chronologically define times of activation and deactivation of
traffic signals, Visual Basic for Applications procedure was written. This procedure
simulates traffic signal operation from the field and clearly defines the starts and
terminations of train and car phases. Instruction from the field, regarded to traffic signal
and gate operations were included in this procedure.
As a final output of the this step, the time value for each reference point of each train
trajectories are defined. Furthermore, activation and deactivation of traffic signal were
calculated .Train trajectories are simulated for both directions during the whole
simulation period.
4.2 Calculation Vehicular, Transit and Person Delay
In previous step, LRT trajectories were simulated and exact activations and
deactivations of traffic signals were provided. Those times provided sets of durations of
vehicular and transit phases. Duration of those phases have an impact on vehicular,
transit and person delay.
The other parameters which are necessary for calculation of vehicular, transit and
person delay are shown in Table 1 and these parameters were provided from VISSIM
future scenario output.
26
Table 1: Recorded Parameters in VISSIM Simulation
Vehicular, Transit and
Signal Timing Characteristics
LRT Crossing
1300S 1700S 2100S
Veh
icula
r tr
affi
c Arrival rate (veh/hour) WB 1244 587 867
Arrival rate (veh/hour) EB 1289 569 755
Saturation flow rate (veh/hour) 3600 3600 3600
Average occupancy (per/car) 1.3 1.3 1.3
Lost time (s) 0 0 0
Amber - flash (s) 4 4 4
LR
T
Arrival rate (veh/PM period)SB 26 26 26
Arrival rate (veh/PM period)NB 24 24 24
Ave. occupancy (pax/train) SB 348 348 348
Ave. occupancy (pax/train) NB 320 320 320
Gates drop (s) 3 3 3
Gates rise (s) 7 7 7
4.2.1 Vehicular Delay
Vehicular delay at LRT crossing in analytical model was calculated using Okitcy
formula from literature.[5] Okitcu formula uses duration of each blockage event (B) and
vehicular flow characteristics at LRT crossing to estimate total vehicular delay (D) for
each crossing and direction caused by LRT services. Average vehicular delay was
calculated by dividing total vehicular delay (D) with corresponding arrival rate.
* *( )
2
AR Q B LTD
……
1 ( / )
B LTQ
AR S
… [5]
D - Total vehicular delay (hours) AR - Arrival flow rate (veh/hours)
LT - Lost Time (hours) S - Saturation flow rate (veh/hours)
B – Duration of blockage event
27
Arrival and saturation flow rate as well as lost time were extracted from VISSIM
future scenario (Table 1). Duration of each blockage event was calculated by known
activation and deactivation of traffic signals at LRT crossings, flashing time and time
which gates take to rise up. Flashing and rise up time were found in both field and
VISSIM future model while time of activation and deactivation traffic signals were
provided in LRT trajectories. Figure 11 shows how duration of blockage event was
calculated. Calculation of blockage event and vehicular delay were calculated for each
crossing and each direction separately.
Figure 11: Duration of Blockage Event
4.2.2 Light Rail Transit Delay
Light rail transit delay represents the average delay which LRT vehicle and its
passengers experience while they traverse across light rail crossing. Delay time doesn’t
include dwell time at regular and dummy station. In addition, in order to alleviate both
comparison of different transit strategies and calculation of transit delay, acceleration and
deceleration lost times were neglected. These constant times don’t have any impact on
final decision.
28
Analytical model defines a light rail transit delay as average amount of time which
LRT passenger spend waiting to get right of way. LRT trains and its passengers can
experience this delay on stations which are located between check-in detector and LRT
crossing. On these stations, it can be recorded that train finishes boarding and alighting
passengers but still doesn’t have right of way. Those situations are related to conditional
preemption which was codded by delayed activation of traffic signals on LRT crossing. If
preemption is deployed on the LRT crossing, there is no delay for LRT vehicles. Delay of
LRT vehicles for the cases when conditional preemption is deployed in the field is
calculated from LRT trajectories according formula:
( )LRT d tp fD T T T
Td - Time when train passes across check-out detector (sec)
Ttp - Travel time between station and check-out detector when preemption is
deployed (sec)
Tf - Time when train is ready to leave a station (sec)
Previous formula shows that LRT delay is calculated as a difference between times
when train leaves a station (Td-Ttp) and time when train is ready to leave (Tf). This delay
was calculated for each crossing and direction separately.
4.2.3 Person Delay
The major goal of analytical model is to provide strategy which minimizes overall
person delay in study area. Person delay can be calculated for known volumes,
occupancies and average delays for both transportation modes on LRT crossings. Traffic
29
and transit volumes as well as average occupancy per car/train were provided by future
VISSIM scenario, while previous steps provided calculations of vehicular and LRT
delay. Arrival rates for each arterial street and direction as well as average occupancy of
LRT and cars were found in output data of VISIM model for 2015 (Table 1). Person
delay on particular crossing and overall person delay in study area network are calculated
according following formulas [6] and [7]:
/ / / //
car EB EB car WB WB LRT SB SB LRT NB NBp cr
EB WB SB NB
D P D P D P D Pd
P P P P
[6]
/ / / /
1/
1
i i i i i i i i
i i i i
n
car EB EB car WB WB t SB SB t NB NB
ip area n
EB WB SB NB
i
D P D P D P D P
d
P P P P
[7]
Where:
dp/c - average person delay per crossing
dp/area - overall person delay for n crossing in study network
- Average delay for transportation mode x which traveling in YZ direction
(sec/person)
- Number of persons who traveling in YZ direction
4.3 Validation of Analytical Model
Analytical model of case study area was validated for LRT dwell times and vehicular
delay at LRT crossings. Dwell times on regular and dummy stations were chosen
because their stochasticity and it was important to show that analytical model is capable
30
of emulating randomness in train departures and train dwell time from the field or
VISSIM model.
Dwell times on regular and dummy stations were extracted from train trajectories
through quite simple computational process. Reference point which represent train
arrivals at dummy/regular station were subtracted from reference point marked as train
departures for same dummy/regular station on the same train trajectory.
Through iterative process, dwell times for each train trajectory were extracted and
sample of data was provided. Mean values and standard deviations from this sample data
were compared to corresponding VISSIM outputs. Figure 12 shows results of those
comparisons and prove that analytical model is capable of precisely simulating train
trajectories from the field and field randomness in these trajectories.
31
0
20
40
60
80
100
120
140
160
180
DummyStation SB
DummyStation NB
Station on1300S SB
Station on1300S NB
Station on2100 SB
Station on2100 NB
Dw
ell T
ime [
sec]
Station
Microsimulation Model
Analytical Model
Figure 12: Validation of Search Based Optimization Tool for Dwell Time
Another parameter which was validated is vehicular delay at LRT crossing.
Vehicular delay in analytical model was provided as a final output of Okitcy formula
while in microsimulation this parameter was extracted as one of the VISSIM output
results. Vehicular delay was provided for each crossing and direction. Comparison of
corresponding roadway delays at railroad crossings is shown on Figure 15.
32
0
5
10
15
20
25
30
35
1300S WB 1300S EB 1700S WB 1700S EB 2100S WB 2100S EB
Dela
y [
sec/v
eh
]
Crossing & Direction
Microsimulation Model
Analytical Model
Figure 13: Validation of Search Based Optimization Tool for Roadway Stopped Delay
Figure 13 shows that the only disagreement between analytical and microsimulation
simulation model can be found on crossing on 1300S for west bound direction. This
crossing cannot be observed as a fully isolated, because queued vehicles at downstream
traffic signal exceed LRT crossing. Mentioned traffic signal on intersection 1300S and
300W is the most critical signal in the network, with highest traffic volumes. Green time
over cycle length ratio for west bound and eastbound direction is 0.3. The ratio on traffic
signal, which precedes LRT grading on 1300S for westbound direction, is significantly
bigger - 0.7.
Slightly different directional vehicular volumes at LRT crossing on 1300S (Table 1)
and identical vehicular green time at LRT crossing should produce a similar delay for
33
eastbound and westbound direction. However, downstream traffic signal causes extra
delay for westbound direction at LRT crossing on 1300S. As figure 10 shows, analytical
model is capable of estimating delay on isolated LRT crossing while extra delay, caused
by nearby traffic signal, cannot be estimated using this tool.
4.4 Simulation of Different Train Strategies
Analytical model calculates overall person delay for different combinations of train
schedule and train priority at LRT crossing. Through one incremental and iterative
process, input parameters such as train schedule and train priority were offset and tested.
Different train schedules were tested by changing the departure times from one
direction with 15 seconds of incremental step. Projected headway for 2015 is five
minutes or 300 seconds what brings 20 different train schedules. Those train schedules
were combined with different priority strategies in study area.
Priority strategies were defined by observing layout of LRT reference points in study
area network . According , LRT layout from the field it was found that:
Different priority strategies should be tested at LRT crossing on 1300S for
southbound direction and at LRT crossing on 2100S for northbound
direction. In these cases, regular station is located between check-in and
check-out detectors for corresponding crossing and dwell time on those
stations has impact on vehicular operations (Figure 12)
Dwell time on regular stations on 1300S for northbound direction and on
2100S for southbound direction doesn’t have impact on vehicular operations
on LRT crossing. These stations are located behind corresponding check-out
34
detectors (Figure 12) and as a consequence, LRT preemption is kept for these
approaches.
There is no regular station in vicinity of grading 1700S. (Figure 12)
Consequently, there is no sense to implement any other priority on this
crossing except currently deployed preemption logic, which provide more
efficient operation for both transportation modes.
Figure 14: Layout Of LRT References Point In Study Area
35
The impact of different LRT’ priority on overall person delay is simulated through
delayed activation of traffic signal on 1300S SB and 2100S NB. Delayed activation
varied from 0 to maximum dwell time with incremental step of 10 seconds. Maximum
dwell times at station on 1300S and 2100S NB are 70 sec and 50 seconds respectively.
4.5 Limitations of Analytical Model
Analytical model was built to test all possible combinations of train schedules and
train priorities and to provide a minimal overall delay in case study area. In this particular
study area there are two LRT crossings (1300S and 2100S) where different priority
strategies should be simultaneously tested. These priorities are simulated by introducing
delayed activation of traffic signals on LRT crossing. Ten seconds increment of delayed
activation of traffic signal for maximum dwell time of 70/50 seconds on station on 1300S
SB/2100S NB provide in total 48 different combinations. Furthermore, those 48 different
combinations should be tested for 20 different train schedules. This is going to bring a
960 combination of different LRT strategies.
Unfortunately, MS excel is not capable of simulating delayed activation of traffic
signals (conditional preemption) at two or more different LRT crossings, simultaneously.
Excel warns that formula refers to the cell in which it is contained, either directly or
indirectly and stops the further executions. In order to mitigate and partially resolve this
problem simulation of conditional preemptions at different crossings were modeled
separately for station 1300S SB and 2100S NB.
Figure 11 shows variety of train schedules and transit priority which were changed
and tested through analytical model. Two sub-scenarios were modeled in order to
36
separately perform simulations of different transit priorities at LRT crossings on 1300S
and 2100S in study area network.
Figure 15: Simulated LRT Strategies
.
37
5 RESULTS AND ANALYSIS
This chapter provides results obtained from analytical model. Analytical model
estimated a delay for different combinations of train schedules and delayed activation of
traffic signal on either 1300S SB or 2100S NB. Each combination of input parameters
was simulated for PM peak period through ten random seeds. Analytical model was set-
up to calculate and extract overall person delay for different combinations of train
schedule and train priority.
Analytical model is not able to simultaneously emulate conditional preemption
strategies on two or more LRT crossings. Because of mentioned limitation, two sub-
scenarios were modeled. In each of them, different delayed activation of traffic signal
were changed at only one LRT crossing while preemption was deployed at others LRT
crossings in the network. Results are organized on such a way to show impact of train
schedules and different priority strategies on overall person delay. Furthermore, impact of
train strategies on person delay were observed on that crossing where strategies were
changed and tested.
38
5.1 Impact of Different Train Schedules on Overall Person Delay
Different train schedules were tested through changing departure times for one
direction with constant incremental steps of 15 seconds. Extracted overall person delays
for different offsets in train schedule are shown in Table 2. Table 2 shows statistics (mean
and standard deviation) for overall person delay for each of the train schedules when
preemption was deployed at all crossings. Hypotheses that mean values of various
performance measures are equal was tested. T-test for means and paired samples were
used, with 95% confidence level. The results show that train schedule with offset of 270
seconds is significantly better than the other seventeen train schedules.
Table 2: Overall Person Delay for Different Train Strategies
Overall person delay
offset0 9.96 (0.91)
offset15 9.93 (0.59)
offset30 9.98 (0.38)
offset45 10.10 (0.79)
offset60 9.65 (0.43)
offset75 9.37 (0.33)
offset90 9.94 (0.65)
offset105 9.45 (0.38)
offset120 9.35 (0.45)
offset135 9.68 (0.44)
offset150 9.56 (0.43)
offset165 9.37 (0.40)
offset180 9.36 (0.50)
offset195 9.28 (0.58)
offset210 9.07 (0.47)^
offset225 9.80 (0.87)
offset240 9.27 (0.62)
offset255 9.39 (0.74)
offset270 8.78 (0.39)
offset285 8.93 (0.54)^
offset300 9.86 (0.49)
^ value is not significantly different from corresponding offset 270 value
39
Schedule of 270 seconds doesn’t represent a best solution only for the case when
preemption is deployed at all crossing. Figures 18 and 19 show overall person delay for
different train schedules and priority strategies on LRT crossing on 1300S (Figure 18)
and 2100S (Figure 19). Those figures show that there is no unique offset value which
generates the minimal overall person delay for each priority strategies on 1300S/2100S.
However, from those figures can be seen that values of minimal overall person delay for
different train strategies on 1300S or 2100S are clustered around offsets of 270 and 285
seconds.
4
5
6
7
8
9
10
11
12
13
14
0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300
Ove
rall
Pe
rso
n D
ela
y i
n S
tud
y A
rea
Train Schedule Offset (sec)
Preemtion at all crossings
Delayed activation of signal on 1300S for 10 sec
Delayed activation of signal on 1300S for 20 sec
Delayed activation of signal on 1300S for 30 sec
Delayed activation of signal on 1300S for 40 sec
Figure 16: Overall Person Delay for Different Train Strategies on 1300S
40
8
8.5
9
9.5
10
10.5
11
11.5
12
0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300
Ove
rall
Pe
rso
n D
ela
y i
n S
tud
y A
rea
Train Schedule Offset (sec)
Preemtion at all crossings
Delayed activation of signal on 2100S for 10 sec
Delayed activation of signal on 2100S for 20 sec
Delayed activation of signal on 2100S for 30 sec
Delayed activation of signal on 2100S for 40 sec
Figure 17: Overall Person Delay for Different Train Strategies on 2100S
5.2 Impact of Different LRT Priority Strategies
Different train priorities were simulated by changing delayed activation of traffic
signal on crossing 1300S and 2100S separately from zero to maximum dwell time for
corresponding station with 10 seconds incremental step. Impact of different priority
strategies was observed on overall person delay as well as on person delay on that
crossing where priority strategies where changed and tested. Furthermore, graph and
statistical interpretations of results was provided for person delay on particular crossings.
41
5.2.1 Different LRT Priorities at Crossing on 1300S SB
Impact of different LRT priorities on 1300S was observed on overall person delay in
study area and person delay on crossing at 1300S. Delayed activation of signal on 1300S
was changed from 0 to maximum dwell time with 10 seconds incremental steps while the
preemption was kept on crossings 1700S and 2100S. Maximum dwell time at station on
1300S is 70 seconds what brings eight different priority strategies on 1300S. Overall
person delay as well as person, vehicular and LRT person on crossing 1300S were
calculated.
Table 3 shows overall person delay for all combination of train schedules and train
priorities on 1300S SB. Results show that the minimal overall delay can extracted by
strategy which defines train schedule offset of 285 seconds and delayed activation of
traffic signal on 1300S of 30 seconds. Again, additional improvement is possible to
achieve by simultaneously changing priority strategy on 2100S which can not be model
in analytical model.
42
Table 3: Overall Person Delay for Different LRT Strategies on 1300S
Delayed Activation of Traffic Signal on 1300S SB 0 sec 10 sec 20 sec 30 sec 40 sec 50 sec 60 sec 70 sec
Offset 0 9.96
(0.91) 8.74
(0.55) 8.09
(0.40) 7.34
(0.57) 7.02
(0.55) 7.19
(0.36) 8.60
(1.26) 9.22
(0.17)
Offset 15 9.93
(0.59) 8.75
(0.47) 8.02
(0.29) 7.25
(0.32) 7.35
(0.86) 7.03
(0.43) 7.85
(0.49) 8.68
(0.71)
Offset 30 9.98
(0.38) 8.66
(0.62) 8.01
(0.47) 7.41
(0.36) 7.20
(0.44) 7.28
(0.52) 7.83
(0.35) 8.48
(0.56)
Offset 45 10.1
(0.79) 8.76
(0.51) 7.89
(0.38) 7.37
(0.49) 6.97
(0.36) 7.15
(0.54) 7.69
(0.65) 8.63
(0.45)
Offset 60 9.65
(0.43) 8.90
(0.53) 7.96
(0.38) 7.37
(0.52) 7.11
(0.36) 7.27
(0.38) 7.97
(0.82) 8.70
(0.77)
Offset 75 9.37
(0.33) 8.47
(0.39) 7.96
(0.45) 7.61
(0.33) 7.21
(0.37) 7.39
(0.51) 7.76
(0.53) 8.62
(0.85)
Offset 90 9.94
(0.65) 8.53
(0.50) 7.94
(0.40) 7.32
(0.40) 7.34
(0.46) 7.35
(0.54) 7.67
(0.55) 8.07
(0.57)
Offset 105 9.45
(0.38) 8.47
(0.27) 8.05
(0.26) 7.51
(0.34) 7.40
(0.53) 7.62
(0.50) 7.79
(0.67) 8.58
(0.54)
Offset 120 9.35
(0.45) 8.82
(0.57) 7.61
(0.36) 7.69
(0.45) 7.23
(0.44) 7.76
(0.58) 7.83
(0.75) 8.49
(0.65)
Offset 135 9.68
(0.44) 8.62
(0.46) 7.67
(0.60) 7.23
(0.35) 7.23
(0.39) 7.21
(0.77) 7.50
(0.54) 8.45
(1.03)
Offset 150 9.56
(0.43) 8.48
(0.41) 7.71
(0.53) 7.59
(0.53) 7.26
(0.54) 7.10
(0.35) 7.86
(0.48) 9.16
(0.41)
Offset 165 9.37
(0.40) 8.35
(0.59) 7.89
(0.62) 7.27
(0.71) 7.03
(0.59) 6.93
(0.56) 7.85
(0.42) 9.08
(0.62)
Offset 180 9.36 (0.50
8.31 (0.61)
7.46 (0.47)
7.06 (0.48)
7.08 (0.64)
7.00 (0.38)
7.76 (0.44)
9.05 (0.67)
Offset 195 9.28
(0.58) 8.58
(0.58) 7.68
(0.32) 7.19
(0.61) 6.87
(0.66) 7.06
(0.72) 7.90
(0.74) 8.98
(0.59)
Offset 210 9.07
(0.47) 8.27
(0.46) 7.64
(0.51) 6.80
(0.43) 7.06
(0.70) 7.07
(0.45) 8.26
(0.79) 9.29
(0.56)
Offset 225 9.80
(0.87) 8.21
(0.38) 7.20
(0.52) 7.10
(0.42) 6.66
(0.40) 6.85
(0.57) 7.80
(0.51) 9.09
(0.90)
Offset 240 9.27
(0.62) 7.88
(0.38) 7.48
(0.38) 7.14
(0.60) 6.64
(0.52) 7.11
(0.63) 7.90
(0.39) 9.01
(0.59)
Offset 255 9.39
(0.74) 8.06
(0.50) 7.19
(0.46) 6.97
(0.82) 6.57
(0.39) 6.95
(0.53) 7.54
(0.58) 8.63
(0.60)
Offset 270 8.78
(0.39) 8.00
(0.51) 7.45
(0.90) 6.54
(0.41) 6.43
(0.42) 6.77
(0.46) 7.76
(0.46) 8.94
(0.77)
Offset 285 8.93
(0.54) 8.03
(0.56) 7.14
(0.38) 6.42
(0.34) 6.52
(0.46) 6.87
(0.52) 7.46
(0.62) 8.88
(0.59)
Offset 300 9.86
(0.49) 8.97
(0.40) 7.94
(0.41) 7.19
(0.34) 7.36
(0.82) 7.15
(0.34) 8.34
(0.73) 9.24
(0.48)
Table 4 shows the person delay at crossing on 1300S for different combinations of
train schedule and delayed activation on traffic signal on 1300S. Table 4 shows that the
minimal person delay at 1300S can be achieved by train schedule of 270 seconds and
delayed activation of traffic signal on 1300S of 30 seconds. Graphical interpretation of
results from table 4 is given on Figure 18.
43
Table 4: Person Delay at Crossing on 1300S for Different Strategies on Same Crossing Delayed Activation of Traffic Signal on 1300S SB
0 sec 10 sec 20 sec 30 sec 40 sec 50 sec 60 sec 70 sec
Offset 0 9.88
(1.21) 8.15
(0.84) 7.23
(0.60) 6.05
(0.88) 5.60
(0.74) 5.87
(0.49) 7.92
(1.79) 8.91
(0.34)
Offset 15 9.92
(0.87) 8.21
(0.65) 7.01
(0.55) 5.96
(0.50) 6.06
(1.04) 5.77
(0.73) 6.87
(0.55) 8.23
(1.03)
Offset 30 10.02 (0.62)
7.98 (0.94)
7.05 (0.73)
6.37 (0.59)
5.84 (0.57)
5.97 (0.78)
6.94 (0.49)
7.99 (0.85)
Offset 45 10.33 (1.25)
8.27 (0.77)
7.13 (0.52)
6.15 (0.63)
5.51 (0.69)
6.07 (0.82)
6.78 (1.02)
8.03 (0.67)
Offset 60 9.84
(0.64) 8.54
(0.84) 7.30
(0.50) 6.34
(0.60) 6.00
(0.39) 6.12
(0.62) 7.27
(1.34) 8.27
(1.16)
Offset 75 9.36
(0.49) 7.94 (0.5)
7.30 (0.68)
6.78 (0.54)
6.07 (0.43)
6.55 (0.59)
7.11 (0.76)
8.28 (1.14)
Offset 90 10.22 (0.90)
8.27 (0.62)
7.30 (0.58)
6.36 (0.56)
6.44 (0.69)
6.48 (0.8)
7.00 (0.74)
7.65 (0.75)
Offset 105 9.72
(0.58) 8.09
(0.36) 7.63
(0.42) 6.66
(0.47) 6.41
(0.63) 6.98
(0.50) 7.18
(0.94) 8.42
(0.67)
Offset 120 9.54
(0.49) 8.63
(0.57) 7.15
(0.55) 7.03
(0.57) 6.43
(0.59) 7.10
(0.86) 7.20
(1.07) 8.37
(0.93)
Offset 135 10.03 (0.51)
8.49 (0.46)
7.23 (0.66)
6.37 (0.50)
6.34 (0.66)
6.43 (0.99)
6.98 (0.84)
8.10 (1.47)
Offset 150 9.73
(0.58) 8.20
(0.62) 7.26
(0.62) 7.03
(0.88) 6.62
(0.62) 6.29
(0.40) 7.37
(0.67) 9.20
(0.60)
Offset 165 9.49
(0.36) 8.15
(0.64) 7.34
(0.81) 6.42
(0.97) 6.1
(0.87) 6.05
(0.87) 7.42
(0.51) 9.04
(0.77)
Offset 180 9.59
(0.64) 7.86
(0.74) 6.65
(0.51) 6.25
(0.45) 6.14
(0.95) 6.25
(0.62) 7.32
(0.59) 9.01
(0.98)
Offset 195 9.5
(0.79) 8.54
(0.75) 7.00
(0.56) 6.06
(1.00) 5.9
(0.78) 6.3
(0.99) 7.33
(1.22) 8.78
(0.88)
Offset 210 8.94
(0.51) 7.78
(0.61) 6.83
(0.60) 5.93
(0.55) 5.71
(0.74) 6.3
(0.38) 7.95
(1.00) 9.15
(0.73)
Offset 225 9.48
(0.86) 7.75
(0.61) 6.4
(0.91) 5.94
(0.58) 5.49
(0.49) 5.9
(0.69) 7.06
(0.76) 9.01
(1.03)
Offset 240 9.19
(0.78) 7.34
(0.64) 6.47
(0.64) 6.03
(0.57) 5.36
(0.66) 6.02
(0.88) 7.33
(0.39) 8.72
(0.79)
Offset 255 9.08
(0.68) 7.21
(0.49) 6.19 (0.5)
5.40 (0.29)
5.21 (0.52)
5.83 (0.58)
6.77 (0.65)
8.34 (0.93)
Offset 270 8.38
(0.63) 7.31
(0.38) 6.23
(0.56) 5.02
(0.40) 5.20
(0.50) 5.43
(0.58) 6.71
(0.52) 8.84
(1.08)
Offset 285 8.64
(0.77) 7.04
(0.31) 5.92
(0.42) 5.08
(0.29) 5.08
(0.57) 5.34
(0.46) 6.63
(0.83) 8.28
(0.79)
Offset 300 9.75
(0.67) 8.39
(0.62) 7.02
(0.54) 5.89
(0.44) 6.02
(1.02) 5.75
(0.59) 7.55
(0.99) 8.78
(0.71)
44
Figure 18: Person Delay at Crossing on 1300S for Different LRT Strategies on Same Crossing
Strategies in blue area generate better results than those in any other colored area.
One of these strategies should be deployed in the field. Strategies from red zones
generate the worst results and according figures these strategies refer to preemption.
Statistical analysis was performed for person delay on 1300S. Train priorities were
changed on 1300S and it is very important to show how these changes impacted a person
delay on same crossing. Table 5 shows a significance of results from Table 4 where
symbol “X” refers to strategies which extract significantly different person delay on
1300S than the best strategy. Symbol “O” belongs to strategy which extracts not
significantly different person delay on 1300S than the best strategy. Bolded “O”
represents best strategy and it can be found for delayed activation of traffic signal of 30
seconds and train schedule with offset of 270 seconds. Table 5 shows that 7 train
strategies provide results which are not significantly different from those which are
generated by best train strategy.
45
Table 5: Significance of Results for Different Priority Strategies on 1300S Delayed Activation of Check-in Detector on 1300S SB
0 sec 10 sec 20 sec 30 sec 40 sec 50 sec 60 sec 70 sec
Offset 0 X X X X X X X X Offset 15 X X X X X X X X Offset 30 X X X X X X X X Offset 45 X X X X X X X X Offset 60 X X X X X X X X Offset 75 X X X X X X X X Offset 90 X X X X X X X X
Offset 105 X X X X X X X X Offset 120 X X X X X X X X
Offset 135 X X X X X X X X Offset 150 X X X X X X X X
Offset 165 X X X X X X X X Offset 180 X X X X X X X X Offset 195 X X X X X X X X Offset 210 X X X X X X X X Offset 225 X X X X X X X X
Offset 240 X X X X O X X X Offset 255 X X X X O X X X
Offset 270 X X X O O O X X
Offset 285 X X X O O O X X
Offset 300 X X X X X X X X
The impact of different train strategies on 1300S on person delay at same crossing
can be easily seen on Figure 18. This figure shows vehicular, transit and person delay at
crossing on 1300S for different priority strategies and train schedule offset of 270
seconds. By increasing delayed activation of traffic signal, vehicular delay is going to
decrease because of smaller amount of red time, while at the same time LRT delay tends
to increase. Person delay at crossing on 1300S decreases simultaneously with increasing
activation delayed time up to 30 seconds. After this point, with further increasing delayed
46
activation, person delay tends to increase. Minimal person delay are achieved for 30
seconds of delayed activation.
LRT delay represents average delay for LRT trains ant their passengers. LRT trains,
which traverse in northbound direction, always have a full preemption at crossing on
1300S and their passengers travel without any delay on this crossing. However, LRT
passengers who traverse in southbound direction are faced with delay because of
conditional preemption at LRT crossing on 1300S and this delay is greater than average
LRT delay.
0
5
10
15
20
25
0 10 20 30 40 50 60 70
Dela
y a
t C
rossin
g o
n 1
300S
Delayed Activation of signal on 1300S SB
Vehicular
Person
Light Rail Transit
Figure 19: Impact of Priority Strategy on 1300S
47
5.2.2 Different LRT Priorities at Crossing on 2100S NB
Impact of train’s priority at crossing on 2100S was done on identical way as for
crossing on 1300S. Delayed activation of traffic signals on 2100S was changed from zero
up to maximum dwell time (50 sec) with incremental 10 seconds steps. Six different
priority strategies on 2100S were combined with different train schedules in order to
estimate vehicular, transit and person delay in study area and at LRT crossing on 2100S.
Table 6 shows overall person delay for all combination of train schedules and train
priorities on 2100S SB. During those simulations, preemption was kept on 1300S and
1700S.If preemption is deployed on 1300S and 1700S then minimal overall delay in
study area can extracted by strategy which defines train schedule offset of 285 seconds
and delayed activation of traffic signal on 2100S of 20 seconds. It is interesting to
conclude that identical train schedule offset (285 seconds) generates best results in two
subscenarios.
48
Table 6: Overall Person Delay for Different LRT Strategies on 2100S
Delayed Activation of traffic signal on 2100S
0 sec 10 sec 20 sec 30 sec 40 sec 50 sec
Offset 0 9.96 (0.91) 9.60 (0.62) 9.69 (1.40) 9.70 (0.40) 11.04 (0.90) 11.97 (1.12)
Offset 15 9.93 (0.59) 9.66 (0.59) 9.54 (0.56) 9.70 (0.53) 10.30 (0.37) 12.60 (1.14)
Offset 30 9.98 (0.38) 9.66 (0.50) 9.58 (0.78) 9.53 (0.50) 10.58 (0.42) 12.12 (0.71)
Offset 45 10.10 (0.79) 9.34 (0.28) 9.42 (0.35) 9.88 (0.65) 10.70 (0.59) 11.88 (0.97)
Offset 60 9.65 (0.43) 9.46 (0.50) 9.43 (0.52) 9.61 (0.39) 10.40 (0.43) 11.88 (0.75)
Offset 75 9.37 (0.33) 8.99 (0.70) 9.15 (0.51) 9.68 (0.82) 10.19 (0.64) 11.66 (0.91)
Offset 90 9.94 (0.65) 9.66 (0.65) 9.62 (0.6) 9.63 (0.75) 10.29 (0.61) 11.62 (0.74)
Offset 105 9.45 (0.38) 9.29 (0.48) 9.29 (0.46) 9.47 (0.51) 10.47 (0.68) 11.48 (0.42)
Offset 120 9.35 (0.45) 9.24 (0.55) 9.21 (0.41) 9.3 (0.38) 10.37 (0.59) 11.35 (0.74)
Offset 135 9.68 (0.44) 9.00 (0.66) 9.04 (0.45) 9.21 (0.50) 10.26 (0.74) 11.03 (0.69)
Offset 150 9.56 (0.43) 9.16 (0.58) 9.27 (0.64) 9.21 (0.74) 10.07 (0.44) 11.25 (0.55)
Offset 165 9.37 (0.40) 9.30 (0.68) 9.01 (0.66) 9.28 (0.48) 10.06 (0.6) 10.67 (0.59)
Offset 180 9.36 (0.50 9.48 (0.75) 8.95 (0.60) 9.34 (0.53) 9.95 (0.51) 10.44 (0.72)
Offset 195 9.28 (0.58) 8.90 (0.61) 8.94 (0.52) 9.36 (0.42) 9.80 (0.76) 10.77 (0.70)
Offset 210 9.07 (0.47) 9.08 (0.67) 8.71 (0.40) 9.14 (0.81) 9.61 (0.53) 10.87 (0.83)
Offset 225 9.80 (0.87) 8.97 (0.52) 8.53 (0.50) 8.75 (0.47) 9.83 (0.74) 10.82 (0.76)
Offset 240 9.27 (0.62) 8.64 (0.38) 8.29 (0.44) 8.67 (0.59) 9.54 (0.8) 10.97 (0.95)
Offset 255 9.39 (0.74) 9.00 (0.85) 8.68 (0.64) 8.97 (0.68) 9.80 (0.49) 10.69 (0.61)
Offset 270 8.78 (0.39) 8.52 (0.53) 8.54 (0.58) 8.90 (0.79) 10.01 (0.52) 10.42 (0.46)
Offset 285 8.93 (0.54) 8.46 (0.41) 8.27 (0.45) 8.73 (0.47) 9.96 (0.44) 10.83 (0.64)
Offset 300 9.86 (0.49) 9.81 (0.80) 9.45 (0.70) 9.71 (0.47) 10.53 (0.37) 11.98 (0.56)
Table 7 shows the person delay at crossing on 2100S for different combinations of
train schedule and delayed activation on traffic signal on 2100S. Train schedule offset of
180 seconds and delayed activation of traffic signal on 2100s of 20 seconds brings the
minimal person delay at LRT crossing on 2100S if preemption is deployed at other LRT
crossings. Figure 19 shows graphical interpretation of results from table while table 8
shows a significance of results in table 7.
49
Table 7: Person Delay at Crossing on 2100S for Different Strategies on Same Crossing
Delayed Activation of traffic signal on 2100S
0 sec 10 sec 20 sec 30 sec 40 sec 50 sec
Offset 0 4.46 (0.36) 3.54 (0.23) 3.32 (0.21) 3.81 (0.37) 5.58 (0.55) 7.65 (0.76)
Offset 15 4.41 (0.38) 3.51 (0.23) 3.42 (0.27) 3.97 (0.3) 5.40 (0.68) 7.99 (0.58)
Offset 30 4.24 (0.27) 3.4 (0.22) 3.31 (0.25) 3.96 (0.42) 5.40 (0.62) 7.76 (0.53)
Offset 45 4.29 (0.21) 3.4 (0.16) 3.19 (0.12) 3.8 (0.4) 5.42 (0.44) 7.68 (0.89)
Offset 60 4.07 (0.22) 3.44 (0.19) 3.05 (0.17) 3.77 (0.41) 5.22 (0.72) 7.76 (0.62)
Offset 75 3.94 (0.24) 3.32 (0.17) 3.12 (0.2) 3.74 (0.35) 5.05 (0.54) 7.19 (0.73)
Offset 90 4.00 (0.38) 3.30 (0.26) 3.01 (0.13) 3.72 (0.38) 5.08 (0.42) 6.8 (1.43)
Offset 105 3.76 (0.22) 3.16 (0.34) 3.01 (0.29) 3.57 (0.48) 5.14 (0.68) 6.99 (0.99)
Offset 120 3.68 (0.24) 3.35 (0.27) 3.05 (0.30) 3.75 (0.62) 5.00 (0.58) 7.02 (0.94)
Offset 135 3.94 (0.50) 3.09 (0.18) 3.07 (0.47) 3.58 (0.53) 4.81 (0.84) 6.41 (0.86)
Offset 150 3.78 (0.4) 3.38 (0.67) 3.24 (0.57) 3.39 (0.43) 4.73 (0.45) 6.45 (0.73)
Offset 165 3.85 (0.75) 3.49 (0.79) 3.13 (0.68) 3.74 (0.58) 4.82 (0.88) 6.52 (1.23)
Offset 180 4.07 (0.56) 3.66 (0.91) 2.88 (0.62) 3.51 (0.56) 4.61 (0.57) 5.72 (1.16)
Offset 195 3.63 (0.26) 3.40 (0.53) 3.21 (0.67) 3.59 (0.8) 4.51 (0.94) 6.26 (0.67)
Offset 210 3.83 (0.47) 3.33 (0.64) 3.01 (0.32) 3.82 (0.87) 4.56 (0.50) 6.52 (1.65)
Offset 225 4.05 (0.48) 3.48 (0.70) 3.01 (0.49) 3.49 (0.46) 5.08 (0.88) 6.27 (0.99)
Offset 240 3.94 (0.52) 3.21 (0.34) 2.95 (0.32) 3.32 (0.56) 4.88 (0.88) 6.95 (1.22)
Offset 255 3.88 (0.43) 3.79 (0.99) 3.16 (0.71) 3.79 (0.38) 5.07 (0.81) 6.91 (0.99)
Offset 270 3.89 (0.21) 3.21 (0.14) 3.04 (0.44) 3.96 (0.74) 5.02 (0.6) 6.88 (0.81)
Offset 285 3.82 (0.24) 3.38 (0.54) 2.99 (0.5) 3.67 (0.67) 5.60 (0.62) 7.32 (0.84)
Offset 300 4.45 (0.20) 3.50 (0.20) 3.27 (0.29) 4.00 (0.43) 5.67 (0.35) 7.90 (0.66)
50
0 5 10 15 20 25 30 35 40 45 500
100
200
300
2
3
4
5
6
7
8
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
Delay Activation on Signal on 2100S NB (sec)
Train
Schedule Offset
(sec)
Per
son D
elay
(se
c)
Figure 20: Person Delay at Crossing on 2100S for Different LRT Strategies on Same Crossing
Table 8: Significance of Results for Different Priority Strategies on 1300S Delayed Activation of traffic signal on 2100S 0 sec 10 sec 20 sec 30 sec 40 sec 50 sec
Offset 0 X X X X X X
Offset 15 X X X X X X
Offset 30 X X O X X X
Offset 45 X X O X X X
Offset 60 X X O X X X
Offset 75 X X O X X X
Offset 90 X X O X X X
Offset 105 X O O X X X
Offset 120 X O O X X X
Offset 135 X O O X X X
Offset 150 X O O X X X
Offset 165 X O O X X X
Offset 180 X X O X X X
Offset 195 X O O X X X
Offset 210 X O O X X X
Offset 225 X X O X X X
Offset 240 X X O X X X
Offset 255 X X O X X X
Offset 270 X O O X X X
Offset 285 X O O X X X
Offset 300 X X O X X X
51
Same as in previous case, impact of different priority strategies can be clearly seen at
Figure 21. This figure shows vehicular, transit and person delay at crossing on 2100S for
different priority strategies and train schedule offset of 270 seconds. By 20 seconds of
delayed activation of traffic signal on 2100S, minimal person delay can be provided on
this crossing.
0
2
4
6
8
10
12
14
0 5 10 15 20 25 30 35 40 45 50
Dela
y a
t C
rossin
g o
n 2
100S
Delayed Activation of Signal on 2100S NB
Vehicular
Person
Light Rail Transit
Figure 21: Impact of Priority Strategy on 2100S
52
5.3 Person Delay Savings
Analytical model tests different train strategies in order to find which one brings the
minimal overall person delay. Previous results shows that minimal person delay is
possible to achieve by introducing some amount of delay time on check-in detectors.
Those amounts of times are 30 seconds and 20 seconds for check-in detectors on 1300S
SB and 2100S NB, respectively for schedule offset of 270 seconds. Benefits of this
strategy can be quantified through monetary savings on annual basis.
As a consequence of tool’ incapability of simulating delays at check-in detectors on
different grading simultaneously, monetary savings were performed for each crossing
separately. Person savings are observed separately for LRT crossings on 1300S and
2100S by comparing minimal person delay per crossing for non-preemption and
preemption strategy. The best non-preemption strategy proposes a schedule offset of 270
seconds and delayed activation of 30 and 20 seconds on LRT crossings on 1300S and
2100S respectively. This strategy produces person delay of 5.02 seconds at crossing
1300S (Table 4) and 3.04 seconds of person delay at crossing on 2100S. (Table 7) The
best preemption strategy is achieved for train schedule offset of 270 seconds and this
strategy generates a person delays of 8.38 and 3.89 seconds at LRT crossing on 1300S
and 2100S, separately.
In first step, total number of persons who travel across LRT crossing by either
private car or light rail transit was calculated. Table 9 shows number of persons per
approach, transportation mode as well as total number of persons.
53
Table 9: Person Demand at LRT Crossings
Vehicular Traffic Light Rail Transit
EB WB SB NB
1300S
PM peak volumes 2576 2488 26 24
Ave. occupancy (person/car) 1.3 1.3 348 320
Persons 3349 3234 9048 7680
Persons (per mode) 6583 16728
Persons (Total) 23311
2100S
PM peak volumes 1610 1734 26 24
Ave. occupancy (person/car) 1.3 1.3 348 320
Persons 2093 2254 9048 7680
Persons (per mode) 4347 16728
Persons (Total) 21075
Table 10 shows person delay for strategy which is currently deployed in the field
(full preemption) as well for strategy extracted from analytical model. Furthermore,
Table 5 shows time savings per person and total savings per LRT crossing for PM peak
period. Finally, total savings at LRT crossings in network is equal to 27.17 person*hours
per PM peak period. It is important to repeat that these savings were estimated according
person delays at particular crossing, which were simulated in two separated sub scenarios
and obviously this way doesn’t represent best way of compering different strategies for
overall person delay in study area.
Table 10: Saving Time at LRT Crossing
Grading Volumes
(persons/PM)
Person Stopped Delay
(sec/per) Savings
(second)
Total savings
(person*hour) Preemption
Proposed
scenario
1300S 23311 8.38 5.02 3.36 21.76
2100S 21075 3.89 3.04 0.85 4.98
Total NA NA NA 26.74
54
Monetary savings are calculated by multiplication saved person hours with average
cost of time. Those savings refer to PM peak period for workday. Table 11 shows that
these values ranged between ~ $400.00 and ~$800.00 (forth row) for three different
values of times obtained from various US DOT and Urban Mobility studies. Table 6 also
show that annual overall benefits are ranged between ~$100,000 and ~$200,000.
Table 11: PM and Annual Overall Benefits
Urban Mobility and US DOT Values of Time
Cost per hour $14.60 $20.00 $30.00
Hours of delay
time 26.74 26.74 26.74
Dollars of time
in delay $390.40 $534.80 $802.20
Number of work
days per year 250 250 250
TOTAL $97,601.00 $133,700.00 $200,550.00
Time savings are quantified for LRT crossings during PM peak period. Impact of
different train strategies on roadway operation at nearby traffic signals cannot be
observed and further quantified. Quantifying time savings during off PM peak period
wasn’t possible to achieve because of unavailability of vehicular and transit delay.
55
6 DISCUSSION
Analytical model was built to extract a strategy which minimizes overall person
delay in study area. Some limitations, which still can’t be resolved, restricted the
performance of this task. Analytical model defines a strategy which brings a minimal
person delay at particular crossing if preemption is deployed on others LRT crossing.
Furthermore, analytical model show that minimal person delay at LRT crossing is
possible to achieve by introducing delayed activation of traffic signal (on that side where
station precedes to LRT crossing). This amount of delay depends of estimated vehicular
and transit volumes as well as dwell time on station which precedes to LRT crossing. The
major benefit of this model should be its capability of re-running for different sets of
traffic and transit volumes and different dwell time parameters on regular and dummy
station. On that way, potential wrong estimation of traffic and transit data for 2015 can be
easily corrected.
Traffic and transit volumes can be collected in field. Dwell time at regular station as
well as deviations in train schedule can be found in future GPS data. Train technical
characteristics as well as safety requirements at LRT crossing can be changed in future
years. Any of these changes (if any happens) can be on fast and cheap way addressed in
analytical model. Furthermore, impact of this wrong estimation can be seen and
analytical model can be re-run to extract a best strategy for new data on each LRT
56
crossing, separately. Although analytical model can not simulate different train strategies
on two or more LRT crossings at same time, this model shows impact of different LRT
strategies on vehicular and transit operations on particular crossing. By simulating a wide
range of possible combination, analytical model give as a wide picture of potential future
operation and shows how LRT operations should be codded to provide the highest
benefit.
Person delay savings were done to estimate future savings for given vehicular and
transit data. Although, best strategy can not be simulated through analytical model, with
high level of confidence we can claim that proposed strategy will bring significantly
better results in field then currently deployed preemption strategy. This strategy could be
provided without using any microsimulation software. Again, VISSIM model provided
necessary data only for validation of analytical model.
57
7 CONCLUSIONS AND FUTURE RECOMMENDATIONS
The goal of this study was to develop analytical model which will be able to estimate
person delay for different LRT schedules and priorities, and extract strategy to minimize
overall person delay at LRT crossings. Building and validation of analytical model was
done and explained through one case study example. In this case study, trains which
traverse in north-south direction disrupt vehicular operations at three LRT crossings.
Location of transit station in study area additionally affects vehicular operations on
particular crossing. Dwell times of southbound trains at station on 1300S and northbound
trains on 2100S affect duration of “gate-down” time on corresponding crossing. Impact
of LRT dwell time on vehicular traffic accompanied with different train schedule was
estimated for projected 2015 when transit volumes will significantly increase. This was
done through one analytical model, which was adopted for case study in Salt Lake City.
Analytical model simulated train operations for different combinations of train
schedule and priority strategies on those crossing where station’ dwell time affects
vehicular operations. Furthermore, this model estimates person delay at LRT crossing for
each transit strategy. Finally, this model, through one searching process, extracts strategy
which brings minimal person delay on particular crossing if preemption is deployed on
other crossings. Person or user delay was chosen as a representative measures of
effectiveness (MOE) because at the same time invokes a vehicular and transit delay.
58
The following conclusions were reached in this study during building and validation
analytical model.
Analytical model is capable of simulating train trajectories from the field.
Randomness in station dwell time and deviations in train schedule and train travel
times are simulated using normally distributed random numbers. Distributions
behind those random numbers were provided from VISSIM model which
simulated train and vehicular operations for 2015.
Analytical model can estimate vehicular delay at isolated LRT crossings.
Through automatized calculation process, based on Okitcy formula, analytical
model calculates a vehicular delay at isolated crossing. Traffic characteristics data
such as vehicular volumes and crossing signal parameters have to be known.
Analytical model brings a strategy, which minimize person delay on
particular crossing. Although this model was purposely made to find a strategy,
which minimizes an overall person delay, some limitations during building
process restrict this intense. However, analytical model can extracts strategy
which minimize person delay at particular LRT crossing. Through one
incremental-iterative process, different transit strategies were simulated and
tested. Results were compared and the best of simulated strategy was provided.
Impact of near traffic signal cannot be observed by analytical model.
Analytical model simulates train operations. Vehicular operations are defined by
vehicular volumes and LRT crossing signal parameters. Different patterns in
vehicular arrivals as well as vehicular operations at nearby traffic signals can not
be simulated using this model.
59
This model is not capable of simultaneously simulating different train
strategies at two or more LRT crossings. MS Excel cannot perform a logic
behind simultaneously simulation priority strategies on two or more LRT
crossings. In this case study, problem was partially overcome by separately
simulation priority strategies on two LRT crossings.
Analytical model was run for particular case study in Salt Lake City (UT). Additional
conclusions were reached for this study.
Train schedule with offset of 270 seconds provide best results for currently
deployed preemption at all LRT crossings. Results show that schedule offset of
270 seconds provides significantly better results than other 17 out of 19 train
schedules, if preemption is deployed at all crossings.
By increasing delayed activation of traffic signal, vehicular delay is going to
decrease while LRT delay is going to increase. Delayed activation of traffic
signal assigns more green time for vehicular traffic while at the same time
introduce potential delay for transit vehicles and their passengers. Solution, which
provides minimal sum of total vehicular and transit delay was searched by
analytical model.
It is estimated that between $100,000.00 and $200,000.00 can be saved per
year if best scenario (generated from analytical model) is used instead of the
currently deployed preemption. These savings do not represent real money but
are monetary equivalents of (reduced) delays experienced by all users of the
system during PM period. These savings reflect only PM peak period operations
60
and further analysis is necessary to investigate if off-peak operations offset or
further increase these savings.
Analytical model represents one innovative approach in simulation transit operations
without using any simulation traffic software. Although described VISSIM model was
used in building and validation search based tool, this source of data can be replaced by
GPS LRT data and field observation. The benefit of this model is providing cheap and
fast answer on question what is going to happened in future years if particular train
strategy would be deployed in the field. Broad ranges of transit strategy which can be
simulated through this tool at the same time represent the major advantage in compare to
simulation traffic softwares. However, this model can not provide wide range of
measures of effectiveness. This model was intentionally made as an additional tool to
alleviate set-up particular input parameters in microsimulation software. In order to avoid
tuning of some VISSIM input parameters this tool was run. Final output of analytical
model show values for mentioned input parameters.
Limited performance of analytical model should be investigated and improved in the
future. Simulation impact of nearby traffic signals as well as simultaneously simulations
of different train priority at two or more railroad grading should be addressed in the
future years.
61
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