CAN ROUNDABOUT CORRIDOR’S DESIGN IMPACT OPTIMAL CROSSWALK 1 LOCATION: A MULTI-OBJECTIVE ANALYSIS OF CAPACITY, DIFFERENT 2 POLLUTANTS AND SAFETY 3 4 5 6 7 8 9 Paulo Fernandes, MSc. 10 Graduate Student, Mechanical Engineering 11 University of Aveiro 12 Dept. Mechanical Engineering / Centre for Mechanical Technology and Automation 13 (TEMA) 14 Campus Universitário de Santiago, 3810-193 Aveiro - Portugal 15 Phone: (+351) 234 378 172, E-mail: [email protected]16 (Corresponding author) 17 18 Katayoun Salamati, PhD. 19 Adjunct Assistant Professor, Civil Engineering 20 Institute for Transportation Research and Education 21 North Carolina State University 22 NCSU Campus Box 8601, Raleigh, NC 27695-8601 23 Phone: (919) 515-1154, E-mail: [email protected]24 25 Nagui M. Rouphail, PhD. 26 Director, Institute for Transportation Research and Education 27 North Carolina State University 28 NCSU Campus Box 8601, Raleigh, NC 27695-8601 29 Phone: (919) 515-1154, E-mail: [email protected]30 31 Margarida C. Coelho, PhD. 32 Assistant Professor, Mechanical Engineering 33 University of Aveiro 34 Dept. Mechanical Engineering / Centre for Mechanical Technology and Automation 35 (TEMA) 36 Campus Universitário de Santiago, 3810-193 Aveiro - Portugal 37 Phone: (+351) 234 378 172, E-mail: [email protected]38 39 40 41 42 43 44 45 November 2015 46 Submitted for consideration for publication and presentation at the 95th Annual Meeting of 47 the Transportation Research Board, January 10-14, 2016. 48 49 Total number of words (excluding references): 4,998 (text) plus 2,000 for figures/tables 50 (8*250) = 6,998 words (Max 7000 words). 51
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CAN ROUNDABOUT CORRIDOR’S DESIGN IMPACT OPTIMAL CROSSWALK 1
LOCATION: A MULTI-OBJECTIVE ANALYSIS OF CAPACITY, DIFFERENT 2
POLLUTANTS AND SAFETY 3 4 5 6 7 8 9
Paulo Fernandes, MSc. 10
Graduate Student, Mechanical Engineering 11
University of Aveiro 12
Dept. Mechanical Engineering / Centre for Mechanical Technology and Automation 13
(TEMA) 14
Campus Universitário de Santiago, 3810-193 Aveiro - Portugal 15
a Peak period for pedestrian flow was depending on the sites location; 2 b Arterial traffic at the mid-block areas between roundabouts; 3 c There are only two crosswalks between downstream of RBT1 and the upstream of RBT5; 4 d Distance from the RBT2 exit section. 5
Fernandes, Salamati, Rouphail, Coelho 9
2.2. Microsimulation platform for traffic, emissions, and safety 1 2
2.2.1. Traffic modelling 3
VISSIM software package was selected to simulate traffic operations (17). Several reasons 4
support the use of this microscopic traffic model: 1) modelling reliable pedestrian-vehicle 5
interactions at roundabout corridors study sites (15); 2) defining parameters of driving 6
behavior for roundabouts such as critical gaps and car-following models (17); 3) calibrate 7
a wide range of parameters to set faithful representations of the traffic on a corridor level 8
for capacity and emissions’ purposes (9; 15); and 4) storing and exporting of both vehicle 9
and pedestrian trajectory files that can be used by external applications to assess emissions 10
and safety impacts. 11
The simulation experiments in each site were based on simulation runs of 75 12
minutes (4:45-6:00 p.m.). A fifteen minutes (4:45-5:00 p.m.) warm-up time was included 13
in each run to allow traffic to stabilize before collecting data for the remaining 60 minutes. 14
The coded network in VISSIM is depicted in FIGURE 2. Link speeds and flows (traffic 15
and pedestrians) were collected for all of these links. An average pedestrian walking speed 16
value of 1.34 m/s was adopted (6). 17
18
2.2.2. Model Calibration and Validation 19
Model calibration and validation procedure consisted of two steps. Data collected in all 20
sites were used to calibrate and validate the simulation models. About 80% of the data 21
were used for calibration to develop and calibrate the traffic model parameters, the 22
remaining 20% of data used for validation to assess the effectiveness of the model 23
calibration. 24
In the first step, calibration of VISSIM parameters was made by modifying driver 25
behavior and vehicle performance parameters, and by examining their effect on traffic 26
volumes and speeds for each link. The calibrated model parameters included car-following 27
parameters (average standstill distance, additive and multiple part of safety distance), lane-28
change parameters, gap acceptance parameters (minimal gap time and minimal headway), 29
desired speed distributions and simulation resolution (17). The above parameters were 30
optimized using a genetic algorithm (Simultaneous Perturbation Stochastic Approximation 31
– SPSA) in which the objective function was the minimization of Normalized Root Mean 32
Square (NRMS). The Geoffrey E. Havers (GEH), a modified chi-squared statistics that 33
incorporates both absolute and relative differences in comparison of estimated and 34
observed volumes, was used as calibration criteria. Fifteen simulation runs were then 35
carried out for each testing scenario (18). Further details about this procedure can be found 36
in (15). 37
In the second step, the model was validated by comparing estimated and observed 38
flows (traffic and pedestrians), speeds, and average travel time. GEH and Mean Absolute 39
Percent Error (MAPE) statistics were used to measure goodness of fit. 40
41
2.2.3. Emissions 42
Vehicular emissions were calculated using VSP methodology (19). VSP, an indicator of 43
engine load, accounts for engine power demand associated with changes in both vehicle 44
potential and kinetic energies, aerodynamic drag, and rolling resistance (19; 20). VSP 45
values estimated at 1 Hz are categorized in 14 modes, and an emission factor for each 46
mode is used to estimate vehicular CO2, CO, NOX and HC emissions from different 47
vehicle types. The main advantages of using VSP are: 1) it allows estimating instantaneous 48
emissions based on a second-by-second vehicle activity data, taking as input the trajectory 49
files given by VISSIM; 2) it includes the impact of different levels of accelerations and 50
Fernandes, Salamati, Rouphail, Coelho 10
speed changes on emissions (21); 3) and it is an useful explanatory variable for estimating 1
variability in emissions (22). In order to reflect the local car fleet compositions, the total 2
emissions were calculated considering the following distributions: 3
4
Portuguese Sites: 44% of Gasoline Passenger Vehicles (GPV) with engine size <1.4l, 5
35% of Diesel Passenger Vehicles (DPV) <1.6l, and 21% of Light Diesel Duty Trucks 6
(LDDT) <2.5l (23); 7
Spanish Site: 41% of Gasoline Passenger Vehicle (GPV) with engine size <1.2l, 51% 8
of Diesel Passenger Vehicle (DPV) <1.6l, and 8% of and Light Diesel Duty Trucks 9
(LDDT) <2.5l (24); 10
US Site: 39% of “Tier 1” Passenger Cars (T1 PCs) and 61% of “Tier 2” Passenger 11
Cars (T2 PCs) (25). 12
13
The average emission rates for pollutants CO2, CO, NOx and HC by VSP mode of the 14
above vehicles types are reported in the following studies: GPV (26), DPV and LDDT 15
(27), and T1 and T2 (PCs) (28). Both transit buses and heavy duty trucks were excluded 16
from this analysis because they represented less than 2% of sites traffic composition. 17
18
2.2.4. Safety 19
SSAM software application was developed by a research team in SIEMENS and 20
sponsored by the Federal Highway Administration (FHWA) (29). SSAM uses several 21
algorithms to identify conflicts from space-time vehicles trajectory files (*.trj file) 22
produced by microscopic simulation modes as VISSIM. For each vehicle-to-vehicle 23
interaction (or pedestrians) SSAM calculates surrogate measures of safety and determines 24
whether or not that interaction fulfils the criteria to be deemed a conflict. 25
This approach has all the common advantages of simulation such as safety 26
evaluation of new facilities before their implementation, or controlled testing 27
environments. However, notwithstanding the simplicity of user interface, SSAM has 28
several drawbacks. First, current microscopic traffic models are not able to model a few of 29
crash types such as head-on, sideswipe or U-turn related collisions. Second, the probability 30
of each automated conflict turning into a crash cannot be determined by SSAM (29). 31
The research team used Time-to-Collision (TTC) as a threshold to establish 32
whether a vehicle-pedestrian interaction is a conflict and the relative vehicle-pedestrian 33
speed (DeltaS) as a proxy for the crash severity (29). TTC is the minimum time-to-34
collision value observed during the interaction of two vehicles (or pedestrians) on collision 35
route. If at any time the TTC drops below a given threshold [2 s, as suggested for vehicle-36
pedestrian events (30)] the interaction is tagged as a conflict. DeltaS is the difference in 37
vehicle (or pedestrian) speeds observed at the instant of the minimum TTC (29). 38
SSAM classifies resulting conflicts into three categories based on a conflict angle 39
(from -180° to +180°): rear end if 0º<conflict angle<30°, a crossing conflict if 40
85º<conflict angle<180°, or is otherwise a lane change conflict (29). To address the 41
problem associated with pedestrian-to-pedestrian conflicts (15; 31), the authors filtered out 42
any conflict where the maximum speed was lower than 2.2 m/s. 43
44
2.3. Scenarios 45 Baseline scenario is the calibrated model with the observed pedestrian and traffic demands. 46
For all crosswalks locations, the research team modeled the centroids where pedestrians 47
enter and leave in the coded network in the same place as the actual pedestrian location. 48
Also, pedestrians always walked to the crosswalk. 49
Fernandes, Salamati, Rouphail, Coelho 11
For each site, baseline scenario was applied, assuming several possible pedestrian 1
crosswalk locations along the mid-block section: 1) from the downstream RBT1 to the 2
upstream of RBT2 for corridors with 2 roundabouts; and 2) from the circulatory ring of the 3
RBT2 to the upstream of RBT3 and RBT1 on the remaining sites. In the first set of 4
corridors (US1, SP1, PT1, PT2 and PT3), crosswalks were moved in 5-m increments [each 5
increment allows an extra stocking capacity of 1 vehicle (5)]. In the second set of corridors 6
(PT4, PT5 and PT6), nearly 25 PC1 and PC2 combinations along the mid-block section 7
were explored by site applying 5-m increments relatively to the roundabout exit section. 8
Next, a relationship between pollutant emissions, delay and DeltaS, and different 9
crosswalk locations (PC1 – corridors with 2 roundabouts; PC2 – corridors with more than 10
2 roundabouts) was established (FIGURE 1). During this phase, various regression models 11
were tested to identify whether the predictive regressions models were a good fit for the 12
evaluated data (32). 13
14
2.4. Multi-objective optimization 15 16
Objective Functions 17 On the basis of the scenarios presented above, the following multi-objective model was 18
constructed to minimize pollutant emissions, average delay and the relative difference 19
between vehicles and pedestrians speed (DeltaS). 20
For a given midblock pedestrian crosswalk location and site, the first and second 21
objectives of the model mostly reveal the vehicle driver’s viewpoint, which is to minimize 22
CO2, CO, NOX and HC emissions per unit distance generated by vehicles (Equation 1) and 23
the average delay of each vehicle movement (Equation 2) along the overall network: 24
25
1min
mN
mj
m
D
F
T (1) 26
27
Where: m = Label for second of travel (s); j = Source pollutant; Fmj = Emission factor for 28
pollutant j in label for second of travel m (g/s); Nm = Number of seconds (s); TD = Total 29
distance travelled by vehicle (km). 30
31
min v
id (2) 32
33
Where: v
id = control delay by vehicle (s/veh). 34
35
The third objective function is devoted to the perspective of the pedestrian safety, with the 36
aim of minimizing relative difference between vehicles and pedestrians speed (DeltaS) 37
which is computed from SSAM (Equation 3). They were obtained from crossing conflicts 38
at the candidate pedestrian crosswalk. 39
40
min = DeltaS (3) 41
42
Where: DeltaS = magnitude of the difference in vehicle and pedestrians speeds (km/h). 43
44
45
Fernandes, Salamati, Rouphail, Coelho 12
Decision Variables 1 The decision variables are PC1 and PC2. They were measured from the circulatory ring 2
delimitation of RBT2 to the limit of crosswalk (FIGURE 2). 3
4
Constraints 5 Equation 4 represents the available range of spacing between roundabouts (see TABLE 1 6
for those details) which constitutes the principal constraint for the multi-objective 7
optimization: 8
9
max5 S S (4) 10
11
Where: Smax = maximum spacing length of the analyzed site that allows a stocking 12
capacity of 1 vehicle before the upstream of exit lane of the adjacent roundabout (m). 13
14
Solution Approach 15 Three multi-objective tests were optimized for each site: 1) delay-CO2-DeltaS; 2) delay-16
CO-DeltaS; 3) delay-NOX-DeltaS and 4) delay-HC-DeltaS. The regression functions were 17
PC (PC1 or PC2 dependent on the site) versus delay, PC versus CO2 emissions, PC versus 18
CO emissions, PC versus NOX emissions, PC versus HC emissions, and PC versus DeltaS. 19
The solution of a multi-objective model is always located in its Pareto optimal 20
(non-dominated) set. The Fast Non-Dominated Sorting Genetic Algorithm (NSGA-II) was 21
adopted (33) in this research for six main reasons: 1) less computational complexity; 2) 22
elitist approach; 3) emphasis on the non-dominated solutions during the process; 4) 23
diversity preserving mechanism, 5) no requisite to consider a sharing parameter; and 6) 24
real number encoding (33). The standard flowchart of NSGA-II presented in (15) was 25
used. 26
Sensitivity analysis on the NSGA-II parameters (population size, maximum 27
number of generations, and mutation and crossover rates) was performed before 28
optimization to ensure the diversity in the solutions and the convergence to Pareto Optimal 29
Front (POF). 30
For the purpose of analysis, all objective variables are considered to have the same 31
weight during the optimization procedure. NSGA-II does not take into account the 32
different units and magnitudes of the measures involved during its procedure. This means 33
that the set of optimal values includes values that will minimize emissions, delay and 34
relative different between vehicles and pedestrians speed regardless of the magnitude or 35
units of the output measure. 36
37
3. RESULTS AND DISCUSSION 38 39
3.1. Model Calibration and Validation 40 Summary statistics of the VISSIM calibrated model at the selected sites are shown in 41
TABLE 2. The model uses 15 random seed runs (18) and is based on the validated datasets 42
for the paired estimated-observed flows and speeds in each link. The NRMS, the GEH and 43
MAPE goodness-of-fit measures, as well as average travel time for through movements are 44
also presented. It must be emphasized that lane-change parameters were marginally 45
unaffected by the calibration while a simulation resolution of 10 time steps per simulation 46
seconds was used in all sites. 47
The findings showed a good fit between estimated and observed data using a linear 48
regression analysis. Specifically, applying the site-calibrated values, R2 values higher than 49
0.90 and 0.75 were produced for estimated traffic flows and speeds, respectively, against 50
Fernandes, Salamati, Rouphail, Coelho 13
field data. This meant that the estimated data explained more than 75% variation in the 1
field measurements. Moreover, the calibrated critical gap times reflected countries driving 2
habits, as presented elsewhere (34). The outputs of TABLE 2 showed the improvement of 3
the GEH statistic with calibrated model parameters. More than 85% of the links achieved a 4
GEH statistic less than 4, thereby satisfying the calibration criteria (35), while MAPE 5
values for the speeds ranged from 6% to 14% between the PT4 and PT3 sites, respectively. 6
The maximum average travel time difference [using 150 floating car runs (35) by each 7
through movement] was reached in the PT3 site for South-North movement (~10%). 8
Fernandes, Salamati, Rouphail, Coelho 14
TABLE 2 Summary of calibration for the traffic model with adjusted parameters 1
Site ID Parameter Value NRMS GEH R2a MAPE Travel time [sec]b
US1
Average standstill distance
(m)
0.9
0.549 < 4 for 93 %
of the links
Flows: 0.95
Speeds: 0.85
Flows: 3.3%
Speeds:11.1%
Observed NS: 51.1±10.6
Estimated NS: 54.0±3.3
Observed SN: 41.6±7.0
Estimated SN: 44.4±2.5
Additive part of safety
distance
1.0
Multiple part of safety
distance
1.1
Minimal gap time (s) 4.3
SP1
Average standstill distance
(m)
1.0
0.307 < 4 for 96 %
of the links
Flows: 0.94
Speeds: 0.81
Flows: 2.9%
Speeds:10.2%
Observed WE: 50.5±5.2
Additive part of safety
distance 1.2 Estimated WE: 52.6±2.0
Multiple part of safety
distance 1.4 Observed EW: 55.1±9.3
Minimal gap time (s) 3.4 Estimated EW: 50.9±1.5
PT1
Average standstill distance
(m)
1.1
0.479
< 4 for 91%
of the links
Flows: 0.92
Speeds: 0.76
Flows: 6.0%
Speeds:12.8%
Observed WE: 51.9±3.6
Estimated WE: 51.2±1.6
Observed EW: 47.1±5.0
Estimated EW: 48.6±2.6
Additive part of safety
distance 0.9
Multiple part of safety
distance 1.8
Minimal gap time (s) 2.9
PT2
Average standstill distance
(m)
1.1
0.174
< 4 for 96 %
of the links
Flows: 0.91
Speeds: 0.88
Flows: 7.0%
Speeds:9.4%
Observed WE: 50.1±3.8
Estimated WE: 52.3±1.5
Observed EW: 52.0±1.7
Estimated EW: 49.0±2.2
Additive part of safety
distance 1.3
Multiple part of safety
distance 1.8
Minimal gap time (s) 3.1
PT3
Average standstill distance
(m)
1.0
0.355 < 4 for 95 %
of the links
Flows: 0.93
Speeds: 0.80
Flows: 3.4%
Speeds:13.7%
Observed NS: 61.9±6.0
Estimated NS: 58.1±3.4
Observed SN: 59.9±5.6
Estimated SN: 53.6±2.0
Additive part of safety
distance 1.0
Multiple part of safety
distance 1.2
Minimal gap time (s) 3.1
PT4
Average standstill distance
(m)
1.0
0.247 < 4 for 92 %
of the links
Flows: 0.92
Speeds: 0.86
Flows: 5.0%
Speeds:6.4%
Observed WE: 87.5±6.7
Estimated WE: 89.9±1.3
Observed EW: 83.9±7.5
Estimated EW: 89.1±1.9
Additive part of safety
distance
0.9
Multiple part of safety
distance
1.3
Minimal gap time (s) 3.3
PT5
Average standstill distance
(m)
1.1
0.232 < 4 for 92 %
of the links
Flows: 0.93
Speeds: 0.85
Flows: 2.8%
Speeds:8.6%
Observed NS: 90.2±3.0
Estimated NS: 92.3±2.2
Observed SN: 89.9±5.2
Estimated SN: 87.7±1.0
Additive part of safety
distance
1.0
Multiple part of safety
distance
1.3
Minimal gap time (s) 3.2
PT6
Average standstill distance
(m)
1.0
0.410 < 4 for 100 %
of the links
Flows: 0.95
Speeds: 0.88
Flows: 4.6%
Speeds:10.4%
Observed WE: 82.6±9.3
Estimated WE: 85.6±2.1
Observed EW: 91.3±6.5
Estimated EW: 86.9±1.7
Additive part of safety
distance
1.2
Multiple part of safety
distance
2.2
Minimal gap time (s) 3.2
a Linear regression analysis between the estimated and the observed flows and speeds on each coded link; 2 b The relative difference between estimated and observed travel time was computed using the following equation: 100× (Estimated Travel Time – Observed Travel Time) / Observed Travel Time. 3
Notes: WE – West to East movement: EW – East to West movement: NS – North to South movement; SN – South to North movement 4
Fernandes, Salamati, Rouphail, Coelho 15
3.2. Sites traffic operations analysis 1 This section evaluated and compared average delay, pollutant emissions (CO2, CO, NOX 2
and HC) per unit distance and DeltaS measures by site and with existing crosswalk 3
locations. Delay and vehicle activity data as speed, acceleration-deceleration and slope on 4
a second-by-second basis were given from the vehicle record evaluation of the VISSIM 5
model while DeltaS was computed in SSAM. 6
Specific-site operational, emissions and safety outputs are summarized in TABLE 7
3. Several conclusions about the effect of crosswalk location can be drawn. (i) As 8
expected, the crosswalks that are located closest to the exit section of roundabout (US1, 9
PT3 and PT6) generate the highest CO2 emissions per unit distance and the lowest DeltaS 10
values, which agrees with the previous study conducted by Fernandes et al. (15); (ii) The 11
PT3 and PT6 sites result in weak traffic performance and high emission levels among 12
Portuguese sites, mostly because of the high pedestrian flows; (iii) Mid-block crosswalks 13
from the PT1 and PT2 sites cause the highest speeds differences between vehicles and 14
pedestrians when compared with others sites; (iv) The arterial where crosswalk is located 15
at the SP1 site has 10% and 65% less traffic and pedestrians flows, respectively than the 16
equivalent arterial at the PT1, but vehicles generate higher emissions per unit distance for 17
local pollutants (more than 15%). 18
19
TABLE 3 Specific-site output measures with existing crosswalk locations 20
Site ID
Capacity Emissions Safety
Delay
[s/veh]
CO2
[g/km]
CO
[mg/km]
NOX
[mg/km]
HC
[mg/km]
DeltaS
[km/h]
US1 7.8 170 478 121 32.79 22.0
SP1 7.9 129 189 414 7.21 23.0
PT1 8.3 122 153 340 6.19 27.0
PT2 3.8 105 130 277 4.61 26.1
PT3 10.1 140 185 415 6.61 21.4
PT4 10.7 114 146 320 5.74 22.8
PT5 12.5 120 155 340 6.11 24.0
PT6 11.2 174 194 419 7.82 22.8
21
Next section describes the optimization of current crosswalk locations to assess their 22
performance. The main purpose of this step is to improve the aforementioned outputs 23
(delay, pollutant emissions, and DeltaS). The results will then be compared with the 24
existing crosswalk locations. 25
26
3.3. Multi-objective optimization 27 This section presents the main results of the multi-objective optimization of crosswalk 28
locations. The parameters used in NSGA-II are summarized below: 29
30
The population size (set of optimal solutions) is 10; 31
The maximum number of generations is 1000; 32
The crossover rate is 90%; 33
The mutation rate is 10%. 34
35
These values were found appropriate to ensure the diversity in solutions and convergence 36
to POF. TABLE 4 summarizes the optimal crosswalk locations (PC1) for corridors with 37
two roundabouts by pollutant criteria from the POF involved through the course of 38
Fernandes, Salamati, Rouphail, Coelho 16
optimizations (1000 generations). The findings confirmed the trade-off between delay and 1
emissions, and DeltaS from the minimal to the maximum extremes values in the set of 2
optimal solutions. 3
Most of solutions were located at the mid-block sub-segments and near the 4
circulatory ring of the roundabout (PC1<15meters). If one adopts the solution that 5
minimizes global pollutant emissions of each site, then one could save between 1% and 6
6% in average CO2 emissions at the SP1 and PT3 sites, respectively when compared with 7
the existing crosswalk location. 8
The improvements in average delay at the PT3 site were particularly impressive. 9
This site initially presented the closest crosswalk to the exit section and high pedestrian 10
flows. For a chosen PC1 value of 96 m, 15% less delay could be reached compared with 11
current location (PC1 = 7 m). As expected, crosswalks near by the roundabouts exit 12
section recorded the lowest differences between vehicles and pedestrians speeds. The lack 13
of optimal PC1 values higher than 36 m at the SP1 site is possible due to right-turn bypass 14
lane at RBT2. Accordingly, vehicles drive at low speeds along the mid-block section. 15
An intriguing result was detected at the PT1 and PT2 sites. In spite of having 16
similar spacing between roundabouts, the optimal PC1 set for some pollutants is quite 17
different. While in the PT1 site the solutions in the approximate POFs are mostly found at 18
the mid-block area, in the PT2 site some are located at 6 to 17 m away from the 19
roundabout exit section. The explanations for this fact may be in the differences between 20
sites’ arterial traffic flow (PT2~235 vph/lane; PT1~590 vph/lane) in addition to site’s 21
geometry. More precisely, a great portion of the vehicles is likely to be more retained by a 22
crosswalk near the exit section under high traffic flows. Moreover, vehicles attain 23
moderate speeds close to the RBT1 east exit of the PT1 site (caused by small deflection 24
angle in RBT1 east entry). 25
In corridors with more than 2 roundabouts, the final Pareto set of PC1 and PC2 26
dictated optimal solutions at the mid-block segment and near the RBT2 exit section, as 27
presented in TABLE 5. Among these, the PT6 site generated the highest emissions 28
reductions (2-9% depending on the pollutant) by adopting the solution 7. The findings 29
pointed out small differences among pollutants in the optimal data set points. However, 30
there were some aspects on the final POF that must be emphasized. In the PT4 site few 31
solutions were found near RBT1 circulatory carriageway (high PC1 values). This is 32
explained by the fact that vehicles from the West leg to the south leg at RBT1 drive at 33
moderate speeds, and still the South RBT1 exit leg is a downhill road (slope >5%) which 34
has a positive influence on the vehicle’s speed. Several solutions at the PT4 and PT5 sites 35
were located near to exit section. This can be explained by the differences of traffic and 36
pedestrian flows between RBT1/RBT2 and RBT2/RBT3, in which in turns allows traffic 37
to be less affected by crosswalks installed close to the roundabout exit section. 38
Three general points were outlined from above findings. First, optimal crosswalk 39
locations were mostly found at 5 to 20 m from the downstream roundabout exit section and 40
along the mid-block segment. Second, the set of optimal crosswalk locations did not vary 41
for both global and local pollutants. Third, crosswalks in a same corridor (e.g. PC1 and 42
PC2) presented different optimal locations along the respective mid-block segment. This 43
suggested that the spacing between roundabouts could have an important effect on the 44
optimal crosswalk location along the mid-block section. This subject is addressed and 45
discussed in the following section.46
Fernandes, Salamati, Rouphail, Coelho 17
TABLE 4 Optimal crosswalk locations (PC1) of each site considering the pollutant function criteria 1
Shadow cells indicate the minimal objective value for a specific crosswalk location 3
N/A: Not Applicable 4
Fernandes, Salamati, Rouphail, Coelho 19
3.4. Relationship between optimal crosswalk locations and corridor’s features 1 To complement the analysis, the optimal crosswalk locations which minimize respective 2
pollutant value at each site were plotted against spacing. The data points of crosswalk 3
locations were normalized in relation to the spacing between roundabouts by scaling 4
between 0 and 1. Specifically, 0 is the location at the (yield lane of) circulatory roadway of 5
the RBT1 (RBT2 for corridors with more than 2 roundabouts) while 1 is at the yield lane 6
of the upstream roundabout. 7
The estimated regression models for each case confirm prior predictions, as 8
displayed in FIGURE 3. There was a good regression between relative optimized locations 9
for CO2, CO, NOX and HC and spacing between roundabouts (R2 > 0.72 using exponential 10
models). Analysis of R2 (F-test) and the analysis of coefficients for the model (T-test) 11
resulted in p-values lower than 0.001 for each. For these models, the analysis of R2 (F-test) 12
and the analysis of coefficients for the model (T-test) resulted in p-values lower than 0.001 13
(32). 14
The scattered graphs show that for values lower than 100 m for the spacing, the 15
relative location of the optimal crosswalk is approximately in 20%-30% of the spacing 16
length. After that, the crosswalks are located near the midway position (value of 0.5), 17
between 140 and 200 m of spacing. 18
19
a) b)
c) d)
FIGURE 3 Relative location of the optimal crosswalk: (a) minimum CO2 versus 20
spacing; (b) minimum CO versus spacing; (c) minimum NOX versus spacing and (d) 21
minimum HC versus spacing. 22
23
y = 0.149e0.009x
R² = 0.85
Adjusted R² = 0.820.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250
Rel
ati
ve
lo
cati
on
of
the
cro
ssw
alk
Spacing [m]
y = 0.172e0.007x
R² = 0.73
Adjusted R² = 0.710.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250
Rel
ati
ve
lo
cati
on
of
the
cro
ssw
alk
Spacing [m]
y = 0.175e0.007x
R² = 0.79
Adjusted R² = 0.76
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250
Rel
ati
ve
lo
cati
on
of
the
cro
ssw
alk
Spacing [m]
y = 0.155e0.008x
R² = 0.83
Adjusted R² = 0.81
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250
Rel
ati
ve
lo
cati
on
of
the
cro
ssw
alk
Spacing [m]
Fernandes, Salamati, Rouphail, Coelho 20
4. CONCLUSIONS 1 This study examined the impact that different pedestrian crosswalk locations have on 2
average delay, CO2, CO, NOX and HC vehicular emissions, and on the relative speed 3
between vehicles and pedestrians. The study covered eight roundabout corridors in three 4
different countries. A multi-objective analysis of crosswalks placed at different locations 5
along the mid-block section was conducted. The paper also analyzed the impact of the 6
spacing between intersections on the optimal location of the crosswalks along the mid-7
block section. The methodology used was executed using a microsimulation traffic model 8
connected to emission and safety models. 9
The main findings indicated that the implementation of crosswalks near the 10
circulating roadway, which represents the current state of practice, offered advantages 11
strictly from a pedestrian’s safety point of view (low speeds). Crosswalks located near the 12
mid-block section, however, tended to be associated with reduced delay and pollutant 13
emissions, a finding that applied to all eight study corridors. No relevant differences in the 14
optimal crosswalk location were noted when a specific pollutant was considered in the 15
optimization. In spite of modeling different vehicle fleets across the three countries, the 16
fleet effect on the optimal crosswalk locations was minimal (optimal solutions for US1 and 17
SP1 sites included crosswalks located 10 to 15 m from the circulatory road). 18
The analysis of the relative crosswalk location for different values of spacing, 19
confirmed the greater impact of spacing (R2 > 0.72) on optimized crosswalk locations 20
along mid-block section. Specifically, if the spacing is lower than 100 m, optimal 21
crosswalk location is approximately in 20%-30% of the spacing length. Otherwise, if the 22
spacing is between 140 and 200 m, crosswalk can be located at the midway position. 23
Notwithstanding the small improvements on delay, emissions or safety in the 24
majority of the sites after the optimization procedure, this study contributed to the current 25
literature in four aspects: 1) to assess the spacing between roundabouts as an influencing 26
factor in determining the optimal crosswalk location; 2) to include a local pollutant criteria 27
to account location-specific environmental concerns (e.g. CO or NOX emissions); 3) to 28
identify trade-offs between environmental/energy/delay, and pedestrian safety fields; and 29
4) to supply basic design principles that help local authorities and transportation engineers 30
about pedestrian crosswalk location to accommodate location-specific needs and 31
vulnerabilities. 32
Although the present study provides information on how best to balance among 33
competing objectives in placing the crosswalk, it should be cautioned that neither 34
pedestrian delays nor illegal maneuvers (crossing outside the crosswalk) were considered 35
in the analysis. Hence, future work will focus to include these outputs on multi-objective 36
optimization. 37
38
ACKOWLEDGEMENTS 39 P. Fernandes acknowledges the support of the Portuguese Science and Technology 40
Foundation (FCT) – Scholarship SFRH/BD/87402/2012. 41
42
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