TE-ITS 2016 Tuscolana Project work presentation.pptx

Calabrese Francesco 1722279
Di Blasi Roberta 1695211
Mainella Alessandra 1390447
Analysis of delays in
Via Tuscolana
Prof. Gaetano Fusco
Course of Traffic Engineering and ITS

20/07/2016Analysis of delays in Via Tuscolana Pagina 2
Flow Chart

Geography and Area Analysis
Study of the state of traffic of six signalized junctions in Via Tuscolana, one
of the most congested artery of Rome, in the VII District.
The total length of the artery is 1970 m from the first junction to the last one.
The satellite view of the analysed artery
The analysis was set on Monday, the 9th of May, from 8.30 AM to 11.00 AM,
evaluating the most congested period of analysis of 15 minutes.
The study area is crossed by the initial section of the
underground line A (Battistini-Anagnina), in particular
there are the stops of Cinecittà, Subaugusta, Giulio
Agricola and Lucio Sestio.

HCM Methodology
• Geometric characteristics of the roads
approaching the intersection.
• Traffic volumes for the intersection
must be specified for each movement on
each approach.
• This information includes a phase
diagram illustrating the phase plan, cycle
length, green times, and change-and-
clearance intervals.

Optimization:
It’s the art of maximize or minimize a real function by
systematically choosing input values from within an allowed set
and computing the value of the function. It includes finding "best
available" values of some objective function given a
defined domain (or a set of constraints).
Depending on the type of the Objective Function there are many
cases of study.
• Minimum Cycle and Optimum Cycle: input data (constraints).
Methods used:
• Frank Wolfe Algorithm;
• Enumerative Method;
• Gradient Method;
• Genetic Algorithms.

Minimum and Optimum Cycle

Frank-Wolfe Algorithm

Enumerative Method
Definition the
variables
domain
Definition of
the step
Analysis of the
all possible
combination of
variables
The enumerative method is based on research of the minimum.
with these input data:
• T = period of analysis;
• k = 0.50;
• Minimum Cycle;
• Lost Time;
• Saturation Flow;
Disadvantage:
A limit of this method is related to the precision through which to conduct the study,
because a good precision requests very long processing times.

Gradient Method
Gradient method is unconstrained multidimensional
optimization method.
Step,2.
Calculation of the
search direction:
Step.3
Mono-dimensional search:
Step.4
Calculation of the new point
through this equation:
Step.5
Stop test:
Step.1
Inizialization:
- Set stop parameter ε
- Set initial point

Genetic Algorithm
Genetic algorithm is a method used in order to solve constrained and unconstrained multidimensional non
linear optimization problems. This algorithm is based on Darwin’s natural selection principle.
In order to solve an optimization problem must follow 6 specific steps:
1. Random Generation of the first population of solution;
2. Application of fitness function to the solution belonging to current population;
3. Selection of the best individual;
4. Cross-over phase, reproduction and mutation;
5. Creation of new population,
6. New iteration.

Genetic Algorithm
After the selection it
is possible to apply
the following
operators:
• Cross-over;
• Reproduction;
• Mutation;
on the individuals, in
order to obtain the
new generation.
The selection criteria must ensure that an individual with a better
fitness is more likely to pass their genes to the next generation.
In particular the selection of individuals occurs through the Stochastic
Universal Sampling method. This method consist on to divide a
hypothetical wheel in parts with an amplitude proportional to the
physicality of each individual, the selection of individuals occurs by
rotating the roulette wheel.

Genetic Algorithm
In order to solve this problem, it is considered a penalty factor, element
through it is worsened the objective function of a value proportional to
the size of the violation of constraints.

JUNCTIONS ANALYSIS
Junction 1: Via Tuscolana – Via delle Capannelle – Via di Torre Spaccata
Direction Number of
lane
Lane Width
(m)
Grade %
WB 3 3.5 0
EB 3 3.5 0
NB 2 3.5 0
SB 5 3.5 6
Geometry of the junction
SB
WB
EB
NB
LINE NUMBER LAST STOPS
213 Cinecittà (MA) - Largo Preneste
502 Comandini - Tribuni
654 Cinecittà (MA) - Lagonegro
789 America (MB) - Cinecittà (MA)
C11 Cinecittà (MA) - Cimitero Laurentino
N1 Battistini (MA) - Anagnina (MA)
Lines of bus

Junction 1: Via Tuscolana – Via delle Capannelle – Via di Torre Spaccata
Real Cycle
g1 (s) 74
g2 (s) 28
g3 (s) 17

Results:
Real Configuration Minimum Configuration Optimum Configuration Frank-Wolfe Algorithm
Cycle (s) 131 66 146 200
g1 (s) 74 28 60 114
g2 (s) 28 12 35 39
g3 (s) 17 10 35 35
Delay by EB (s/veh) 22,63 22,79 41,23 32,90
Delay by WB (s/veh) 24,86 34,23 54,56 35,83
Delay by SB (s/veh) 138,80 254,02 66,37 335,18
Delay by NB (s/veh) 125,37 493,49 241,24 485,65
LOS E F E F
Intersection delay
(s/veh)
56,85 125,38 74,65 143,12

Warning
In this project, Frank-Wolfe algorithm was applied by the student
team for illustrative purposes and only 4 iterations were carried out
manually.

Direction Number of
lane
Lane Width
(m)
Grade %
WB 3 3.5 0
EB 3 3.5 0
NB 5 3.5 0
SB 4 3.5 0
SB
EB
NB
WB
213 Cinecittà (MA) - Largo Preneste
451 Cinecittà (MA) - Ponte Mammolo (MB)
548 Cinecittà (MA) - Stazione Tiburtina (MB)
558 Gardenie - Torre Maura
559 Anagnina (MA) - Cinecittà (MA)
N27 Cinecittà (MA) - Policlinico/Tor Vergata
Lines of bus

Junction 2: Via Tuscolana – Circonvallazione Tuscolana – Viale Palmiro Togliatti
Real cycle
g1a (s) 63
g1b (s) 27
g2a (s) 47
g2b (s) 18

Results:
Real configuration
PHASE_1_A_WB PHASE_1_B_WB PHASE_1_A_EB PHASE_2_A_CIRCO_NB PHASE_2_A_TO_SB PHASE_2_B_TOGLIATTI
LT TH LT TH RT_P_1 TH LT TH RT_P_2 TH_2A RT_2A LT TH_2B RT_2B
UNIFORM DELAY d1 (s/veh) 41,67 43,26 63,61 63,72 68,00 39,90 42,88 45,20 50,83 43,65 43,69 73,50 66,34 66,33
INCREMENTAL DELAY d2
(s/veh)
4,69 3,31 9,59 4,75 378,54 1,15 0,10 0,23 4,73 0,19 0,42 466,57 0,51 1,01
DELAY d (s/veh) 46,36 46,58 73,20 68,46 446,54 41,05 42,97 45,43 55,56 43,85 44,11 540,07 66,86 67,34
LOS D D E E F D D D E D D F E E
APPROACH FLOW RATE [vph] 579 1272 248 545 557 1484 62 547 327 144 70 907 56 27
INTERSECTION DELAY (s/veh) 146,69 INTERSECTION LOS F

Results:
Enumerative
Method
(s/veh)
14,69 16,39 2,76 1,31 120,27 3,01 0,55 2,03 191,16 1,24 2,68 49,91 0,13 0,27
DELAY d (s/veh) 41,56 44,28 28,50 27,09 150,91 28,73 32,82 36,05 227,42 34,10 35,57 82,74 26,52 26,64
LOS D D C C F C C D F C D F C C
INTERSECTION DELAY (s/veh) 60.61 INTERSECTION LOS E
Genetic Algorithm
(s/veh)
14,69 16,39 2,76 1,31 120,27 3,01 0,55 2,03 191,16 1,24 2,68 49,91 0,13 0,27
DELAY d (s/veh) 41,56 44,28 28,50 27,09 150,91 28,73 32,82 36,05 227,42 34,10 35,57 82,74 26,52 26,64
LOS D D C C F C C D F C D F C C
INTERSECTION DELAY (s/veh) 60.61 INTERSECTION LOS E

Direction Number of
lane
Lane Width
(m)
Grade %
WB 3 3.5 0
EB 3 3.5 0
NB 3 3.5 0
SB 3 3.5 0
EB
SB
NB WB
451 Cinecittà (MA) - Ponte Mammolo (MB)
502 Comandini - Tribuni
557 Piazza Cardinali - Vignali/Scintu
559 Anagnina (MA) - Cinecittà (MA)
N27 Cinecittà (MA) - Policlinico/Tor Vergata
Lines of bus

Junction 3: Via Tuscolana – Via Tito Labieno – Via Orazio Pulvillo
Real Cycle
g1 (s) 44
g2 (s) 24

Results:
Real
Configuration
Minimum
Configuration
Optimum
Configuration
Frank-Wolfe
Algorithm
Enumerative
method
Cycle (s) 96 21 66 146 35
g1 (s) 44 8 31 90 18
g2 (s) 24 4 26 37 8
g1/g2 1,83 2,00 1,25 2,43 2,25
Delay by EB (s/veh) 6,35 12.92 9,11 5,58 2,08
Delay by WB (s/veh) 10,80 3,06 4,77 4,36 3,51
Delay by SB (s/veh) 12.23 20,75 5,19 16,31 3,88
Delay by NB (s/veh) 8.43 3,53 4,08 12,32 9,03
LOS A A A A A
Intersection delay
(s/veh)
9,30 9,93 6,61 7,36 3,88

Direction Number of
lane
Lane Width
(m)
Grade %
WB 2 3.5 0
EB 2 3.5 0
NB 1 3.0 0
SB 1 3.0 0
EB
SB
WB
NB
590 Cinecittà (MA) - Risorgimento
650 Cinecittà (MA) - Piazza San Giovanni in Laterano
Lines of bus

Junction 4: Via Tuscolana – Viale Giulio Agricola – Viale Marco Fulvio Nobiliore
Real Cycle
g1 (s) 51
g2 (s) 31

Results:
Real
Configuration
Minimum
Configuration
Optimum
Configuration
Frank-Wolfe
Algorithm
Enumerative
method
Cycle (s) 96 22 47 32 41
g1 (s) 51 3 17 15 22
g2 (s) 31 10 21 10 10
g1/g2 1,64 0,30 0,80 1,50 2,20
Delay by EB (s/veh) 16,20 7,91 13,53 13,00 7,98
Delay by WB (s/veh) 19,68 15,80 21,57 33,91 10,52
Delay by SB (s/veh) 32,42 74,66 14,06 12,68 23,38
Delay by NB (s/veh) 32,43 74,62 14,06 12,68 23,40
LOS C C B C B
Intersection delay
(s/veh)
20,85 24,04 17,31 22,50 12,04

Direction Number of
lane
Lane Width
(m)
Grade %
WB 2 3.5 0
EB 2 3.5 0
NB 1 3.0 0
SB 1 3.0 0
EB
SB
NB
WB
Lines of bus

Junction 5: Via Tuscolana – Via Valerio Publicola – Via Calpurnio Fiamma
Real Cycle
g1 (s) 52
g2 (s) 36

Results:
Real
Configuration
Minimum
Configuration
Optimum
Configuration
Frank-Wolfe
Algorithm
Enumerative
method
Cycle (s) 96 24 51 24 50
g1 (s) 52 6 21 12 28
g2 (s) 36 12 23 6 14
g1/g2 (s) 1,44 0,5 0,91 2,00 2,00
Delay by EB (s/veh) 18,73 11,89 18,94 8,71 11,23
Delay by WB (s/veh) 24,32 34,64 46,14 16,98 15,76
Delay by SB (s/veh) 42,03 9,20 12,99 46,82 18,36
Delay by NB (s/veh) 29,18 17,53 18,07 261,35 33,55
LOS C C C D B
Intersection delay
(s/veh)
24,46 22,69 30,85 42,04 16,15

20/07/2016Anlysis of delays in Via Tuscolana Pagina 35
Direction Number of
lane
Lane Width
(m)
Grade %
WB 2 3.5 0
EB 2 3.5 0
NB 1 3.0 0
SB 1 3.0 0
NB
SB
WB
EB
590 Cinecittà (MA) - Risorgimento
Lines of bus

Junction 6: Via Tuscolana – Via Lucio Sestio – Via Ponzio Cominio
Real Cycle
g1 (s) 53
g2 (s) 34

Results:
Real
configuration
Minimum
Configuration
Optimum
Configuration
Frank-Wolfe
algorithm
Enumerative
Method
Gradient
Method
Genetic
Algorithm
Cycle (s) 96 19 42 70 37 37 37
g1 (s) 53 5 12 30 15 15 15
g2 (s) 34 6 13 31 13 13 13
Delay by WB
(s/veh)
16,21 33,65 41,78 22,58 10,55 10,55 10,55
Delay by EB
(s/veh)
15,93 25,66 33,7 23,57 10,23 10,23 10,23
Delay by NB
(s/veh)
78,82 54,82 62,61 51,93 29,02 29,02 29,02
LOS C C D C B B B
Intersection
Delay (s/veh)
24,51 33,1 41,14 26,96 12,9 12,9 12,9

Junction 6: Gradient decreasing: contour map and 3D plot

Formulation of bandwidth problem
Synchronization of the traffic lights on the major artery (Via Tuscolana) in order to guarantee the
green wave.
1°
2°
3°

From the first junction to the third one
JUNCTION
DISTANCE FROM
PREVIOUS POINT [m]
PROGRESSIVE
DISTANCE [m]
CYCLE
LENGTH [s]
GREEN [s] g/C RED [s]
1 0 0 200 116 0.58 84
2 660 660 149 93 0.465 56
3 210 870 146 91 0.455 55
TOT 870 CYCLE MIN
200
CRITICAL
SPEED
[m/s]
10
A 1000
A/2 500
3A/2 1500
INC 1-2
Dx 660 th=0.5
u 0.66
b 0.3525 70.5
x0 -227.5
INC 1-2-3
Dx 1097.5 th=0
MANTISSA
u 1.0975 0.0975
b 0.355 71
x0 767.5

From the third junction to the sixth one
JUNCTION
DISTANCE FROM
PREVIOUS POINT [m]
PROGRESSIVE
DISTANCE [m]
CYCLE
LENGTH [s]
GREEN [s] g/C RED [s]
1 0 0 146 91 0.623288 55
2 520 520 32 15 0.10274 17
3 380 900 24 12 0.082192 12
4 200 1100 70 30 0.205479 40
TOT 1390 CYCLE MIN
146
CRITICAL
SPEED [m/s]
7
A 511
A/2 256
3A/2 766.5
INC 1-2
Dx 520 th=0.5
MANTISSA
u 1.017612524
b 0.371819961 54.28571429
x0 -128.5
INC 1-2-3
Dx 1028.5 th=0
MANTISSA
u 2.012720157 0.012720157
b 0.220645793 32.21428571
x0 970.75
INC 1-2-3-4
Dx 129.25 th=0.5
MANTISSA
u 0.252935421 0.252935421
b 0.086594912 12.64285714
x0 1160.75

Conclusions
- We have to give importance to Via Tuscolana rather then the other approaches;
- It has to be found a way to reduce pedestrian interference from the third junction to the
last one;
- It’s observed that the drivers don’t respect Traffic Laws where the road markings are
ruined or absent;
- Drivers perform manouvers not allowed.

Thank you for
your attention

TE-ITS 2016 Tuscolana Project work presentation.pptx

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