=Paper=
{{Paper
|id=Vol-2247/poster2
|storemode=property
|title=Optimization of Urban Semaphore Times Turning into JSSP
|pdfUrl=https://ceur-ws.org/Vol-2247/poster2.pdf
|volume=Vol-2247
|authors=Antonio M.R. Almeida,Jose A.F. Macedo, Javam C. Machado
|dblpUrl=https://dblp.org/rec/conf/vldb/AlmeidaMM18
}}
==Optimization of Urban Semaphore Times Turning into JSSP ==
https://ceur-ws.org/Vol-2247/poster2.pdf
Optimization of urban semaphore times turning
into JSSP
Antonio M R Almeida1 , Jose A F Macedo1 , and Javam C Machado1
Federal University of Ceara, Fortaleza CE 60440-900, Brazil
manoel.ribeiro@lsbd.ufc.br, jose.macedo@dc.ufc.br,
javam.machado@dc.ufc.br http://www.lsbd.ufc.br
Abstract. The objective of this paper is to cover the research in the
area of adaptive traffic control with emphasis on applied optimization
methods. A distinction can be made between classical systems, which
operate with a common cycle time, and the more flexible ones, phase-
based approaches, which are shown to be more suitable for adaptive
traffic control. Classic optimization solutions for this problem result in a
model which is relatively easy to represent but may be difficult to fit into
the standard mixed-integer programming (MIP) scheme. We propose an
alternative approach to find an optimal global solution for the green
wave problem on hot routes, which consists of reducing it to a Job Shop
Scheduler problem using the Webster Model to adapt the cycles to road
characteristics and average traffic speed.
Keywords: Trajectory Pattern Mining, Green Wave, Traffic-Light Sched-
uler, Job Shop Scheduler
1 INTRODUCTION
In recent years, there has been a significant increase in the number of systems
with built-in GPS function. The proliferation of these devices allowed the col-
lection of a large number of GPS trajectories. Many applications, such as route
planners, route finders, and georeferenced social networks, began using GPS data
information to provide new services that were not previously available.
Traffic congestion is one of the leading causes of productivity loss and de-
crease of living standards in urban settings. The data generated by smartphones
with GPS provide rich datasets that can be mined to offer solutions to urban
traffic problems. Our problem creates an optimization method to program traffic
lights that encourages the creation of convoys of vehicles forming a green wave
of routes with greater flow, using as input the flow variation estimated by GPS
trajectories as input.
Traffic congestion causes delays that add significant costs to society and busi-
ness on a daily basis and also increases CO2 emissions and the risk of accidents.
The study [9] reports that in 2002, people who spent 100,000 hours in queues on
Greater Copenhagen’s road infrastructure, generated an economic loss of more
than 750 million euros.
Copyright held by the author(s)
2 Antonio M R Almeida et al.
In order to alleviate traffic congestion, there are basically two solutions: im-
proving public transportation or expanding road infrastructure. In urban areas,
the latter is often impossible due to residential areas adjacent to existing roads.
A more subtle way to improve network performance is to make better use of
existing roads, which can be achieved in part by proper configuration, optimiza-
tion of traffic signal parameters, increasing the overall flow efficiency of vehicles
and reducing losses.[19]
This paper is an extended version and clarify the novel scientific content
presented in the manuscript GPS2GR [3] of the same authors.
2 BACKGROUND
2.1 Green Wave Problem
Mobility is one of the most significant concerns in the world’s largest cities. Due
to the growth vehicle fleet levels and the limitation of urban roads, It can be
assumed that the vast majority of vehicles exceed the flowing capacity of large
cities. Paper [6] studied the optimization of urban traffic using an Automaton
cellular traffic model. This study demonstrates the effect of signal control strate-
gies on vehicle traffic. In addition, it has shown that traffic controlled by traffic
lights can be reduced to a simpler single-line problem.
Fig. 1. Example of a Green Wave in the road
Another study [18] investigated traffic flow controlled by traffic lights on a
single track route using the ideal speed model. previous studies differ in the rela-
tionship between road capacity and the saturation limit. The [16] study described
Optimization of urban semaphore times turning into JSSP 3
vehicle traffic through a sequence of traffic lights on a highway and presented a
dynamic model in which a vehicle is prevented from passing other vehicles.
Figure 1 has an illustration with an example of a graph with a vehicle in the
space and time dimensions and the constraints for the green wave to occur. In
this the vehicle must be maintained between a minimum and maximum average
speed, thus maintaining the synchrony of displacement in the physical space of
the track and the elapsed time
The definition of the problem consider the flow of vehicles passing through
a finite series of traffic lights. Each vehicle moves at an average speed v, the
path is not blocked by other vehicles and there are no non-synchronized traffic
signals. We consider vehicle traffic in the one-dimensional network. It encourages
the formation of vehicle trains through the orchestration of traffic lights where
vehicles tend to travel together, all with the average speed of the v route. In
synchronized strategy, all traffic lights change simultaneously from red to green,
and vice versa over a fixed period of time. The sum of the times is called the
cycle time.
In the green-wave strategy, the traffic light changes with a certain time delay
t shifted between the semaphore phases of two successive intersections. The delay
time is called the travel time. The change of traffic lights spreads backwards, like
a green wave.
When a vehicle arrives at a traffic light and the light is red, the vehicle stops
there. Then, when the traffic light changes from red to green, the vehicle moves
on. On the other hand, when a vehicle reaches a traffic light and the light is green,
it does not stop and keep moving without changing the speed (green wave).
2.2 Systems for Offline Optimization
Definition 1 (Hot Route) It is used to reveal the common behavior of a set
of paths in a given time window. The hot route in this context is the sequence of
adjacent edges that share the certain amount of traffic (minTraffic) defined as a
parameter. [13]
Definition 2 (Convoy) Grouping of vehicles in space-time following a com-
mon flow at the average track speed held together in a green-wave window.
Definition 3 (Webster model) Study on semaphore times and formulas that
defines a simplified model of relation between the traffic lights times. [20]
Definition 4 (Green Route) Is a Green Wave over a Hot Route. Green Route
has the advantage of optimizing the flow independent of the path that the flow
follows in that time window.
A lot of research has been done since the 1960s on offline traffic optimization
systems. In order for the mathematical model to be solvable without an external
evaluation tool, such as TRANSYT, it must contain functional constraints that
relate, for example. the appropriate displacement for traffic lights along arte-
rial parameters for the specific flow, such as the saturation flow rate and the
4 Antonio M R Almeida et al.
vehicle convoy dispersion factor. Considering a typical optimization formulation
involving a common cycle time, divisions and green compensations, even con-
sidering a discretization of time, the search space of a solution is very broad,
especially when considering some form of simulation to obtain the target value.
Systems that operate in this way are best suited for off-line use, because trial
runs have resulted in very costly processes, typically of several hours, even for
small networks.
2.3 Adaptive & Cooperative Systems
The adaptive traffic control systems aim to coordinate the controlled intersec-
tions by signal, controlling a performance index that indicates an optimized
solution, but possibly not optimal. They do this by dynamically adjusting cycle
times, phase sequences, and green time according to both detected and predicted
traffic, thus reacting to dynamic aspects of traffic that cannot be captured by
the static optimization routines used to generate time-of-day plans. Here we
cite three adaptive operating systems: RHODES [15], Phase-by-Phase [14] and
DOGS [12]. These proposals offer solutions that converge at a time t to a mini-
mum that can be local. Simplifications commonly used as standard cycle times
may not be suitable for large networks.
2.4 Traffic density-based discovery of hot routes in road networks
This work [13] proposes a new density-based algorithm named FlowScan. In-
stead of clustering the moving objects, road segments are clustered based on the
density of common traffic they share.
2.5 The Job-Shop Scheduling Problem (JSSP)
The problem Job-Shop Scheduling is classified in the literature as NP-Hard, that
is, it is a problem for which there are no algorithms that solve it at polynomial
time. It is a combinatorial optimization problem (Souza, 2001), which is an ex-
plicit or implicit enumeration of all possible alternatives to search for satisfactory
solutions or the search for the optimal solution, depending on the class of the
optimization algorithm used.
The optimization algorithms can be classified into two classes: mathematical
models (search for optimal solution) and heuristics (search for approximation).
Since the problem of optimizing green waves on public roads is of NP-Hard
complexity, the solutions have been adaptive methods [19] to find local solutions
through trial and fee-feedback, similar to the methods of signal processing. In
figure 2 it has a runtime Pi that corresponds in the original problem to the green
time of the traffic light and a time to start Ti that corresponds to the time that
the convoy will take to reach the traffic light.
Consider a set of n tasks (jobs) and a set of m machines, where each task
is composed by a set of operations whose execution order is defined. For each
Optimization of urban semaphore times turning into JSSP 5
Fig. 2. Job Scheduler problem for green wave
operation, we want to know in which machine it must be executed and the
necessary time for it to be completed. Each convoy becomes a task, which runs
on multiple machines (traffic lights) synchronously.
– A task cannot be assigned to the same machine twice.
– There is no order of execution in relation to different task operations.
– An operation cannot be interrupted.
– Each machine can process only one task (operation) at a time.
The purpose of JSSP is to distribute tasks among machines so that the processing
time necessary to finish executing all of them (also known as makespan) is as
small as possible. In other words, we want to determine the sequence of machines
that minimize the makespan.
In our approach, we made a reduction of the problem of the green wave to
a problem of Job Scheduler where the traffic lights are the processors and the
convoys of vehicles are the tasks.
2.6 Simulation of Urban MObility
Simulation of Urban MObility (SUMO)[4] is an urban traffic microsimulation
framework, including import modeling and demand generation components. SUMO
helps to investigate various research topics such as route selection algorithms and
traffic signal programming or vehicle communication simulation. Therefore, the
framework is used in different projects to simulate automatic driving or traffic
management strategies.
In our work, we use the SUMO traffic simulation mechanism to compare the
base-line with constant traffic times, but optimized against the traffic-light times
produced by the GR algorithm.
6 Antonio M R Almeida et al.
3 METHODOLOGY
Our approach provides a flow optimization solution on previously identified Hot
Routes. We propose a method to optimize convoys of vehicles on hot routes.
These clusters of vehicles will gain benefit from the green light exchange, when
they are approaching an intersection. However, these convoys of vehicles need to
have an average speed that matches the average speed of the hot route. We have
concluded our approach by offering an alternative way to solve the optimization
problem, reducing it to a job shop scheduler problem, and applying a branch &
bound method to solve it.
In short, the proposed GR algorithm produces a green wave over predefined
flows using combinatorial optimization approach to arrive at the best solution
for an urban context.
3.1 Webster model
Variable Definition
Td Drive reaction time
Ty Yellow time
Tgr Global Red time
Tr Red time
Tg Green time
Tc Cycle time
Tf Clearance time
Table 1. Webster model for Traffic Lights
According to the Webster model in the table 1 for urban semaphores [20] ,
the yellow time of an isolated semaphore is given by the equation 1. For usual
situations, we can consider the driver’s reaction time Td = 1s and an average
deceleration given by a = 2.8m/s. Therefore, the yellow time depends on the
velocity in the approaching pathway (V).
V
Ty = Td + (1)
2a
For simplicity the standard defined in the table 2 is adopted for Ty .
The general red time Tgr , see table 3, of an approximation is a function of
the following variables:
– Velocity V of this approximation;
– Width L of the track to be crossed (of the distance to be covered by the
Vehicle within approach);
– Vehicle c length;
Optimization of urban semaphore times turning into JSSP 7
Approaching pathway Ty
Street - 40Km/h 3s
Avenue - 60Km/h 4s
Expressway - 80Km/h 5s
Table 2. Yellow time
– Clearance time Tf (minimum time elapsed between the beginning of time of
the transverse track and the moment of entry of a vehicle into Speed).
Considering the usual situations, the following parameters were adopted:
– Secondary roads (streets) with a maximum width of 9 m, and speed of 40
km / h
– Preferred routes (avenues) up to 30 m wide, and speed 60 km / h;
– Vehicle of 5 m;
– Clearance time Tf = 1.2s.
Approaching pathway Way to be crossed Tgr
Any Street 0s
Street Avenue 2s
Avenue Avenue 1s
Expressway Expressway or Avenue 0.4s → 1s
Table 3. General red time
According to Webster’s model, we must adopt sub-multiple cycles of time or
programming period, to enable any change of plans without cutting abruptly
the time of green current, never adopt Tc less than 30 s and only in special cases
accept Tc greater than 120 s
Tc = Tg + Ty + Tr + Tgr , 30 ≤ Tc ≤ 120 (2)
The concept of minimum green time Tg−min is associated with the concept
of time-wasted of the Webster model and must be respected under the penalty
of causing major traffic jams. In table 4, the usual values of Tg−min are shown:
To define the percentage of the cycle that corresponds to green, we adopted
a proportion of traffic volume between the approach path and the secondary
pathway, that is, where Fa is the approach path flow and Fb the secondary path
flow, then
Tg = Tc − Ty − Tgr ∗ Ta /(Ta + Tb ) (3)
Tc = Tr + Ty + Tgr + Tg (4)
8 Antonio M R Almeida et al.
Approaching pathway minimum green time Tg−min
Street - 40Km/h 12s
Avenue - 60Km/h 15s
Expressway - 80Km/h 17s
Table 4. Minimum green time
3.2 Implementation of Green Route
The classic problem of optimizing [19] the semaphore scheduler to produce a
green wave effect on a path is represented by the following mathematical model,
see notation in table 5:
L
X
min T T (Ψ, q ∗ (Ψ )) = ql · tj (Ψ, q ∗ (Ψ ))
l=1
subject to : Cmin,n ≤ Cn ≤ Cmax,n ,
0 ≤ θn ≤ Cn − 1 ∀n , (5)
φmin,np ≤ φnp ≤ φmax,np ∀n,p ,
Pn
X
Cn = (φnp + Inp ) ∀n
p=1
n ∈ {1, ..., N } Intersection indexes
p ∈ {1, ..., Pn } Indexes of phases at intersection n
Ψ A set of signal timing settins
Cn Cycle time for intersection n
θn Offset of intersection n
φnp Phase p green time for intersection n
Inp interstage (lost) time from the end of phase p until the next
l ∈ {1, ..., Pn } Link indexes
ql ∈ q ∗ (Ψ) User equilibrium link flow given signal timing parameters
tl (Ψ, q ∗ (Ψ)) Travel time on link l considering signal timings and user response
Table 5. Notation for the traffic signal and network model
We propose an optimized method that reduces the green-wave problem to
the Job-shop scheduler problem, allowing the use of Branch and Bound solver
[10] to find an optimal solution to the original problem.
We generate convoys on the hot routes and look for an optimal solution for
these convoys to travel on hot routes without colliding. Inspired by the work
[11] we propose the formation of virtual convoys of vehicles on a hot route,
Optimization of urban semaphore times turning into JSSP 9
optimizing the displacement of these convoys along the hot route. With this
model the sequence of block subsections traversed by a convoy are viewed as a
set of machines in a job shop scheduling problem, where convoys correspond to
jobs. The traversing of a block subsection by a convoy is called an operation oi ,
and requires a running time pi . [8]
3.3 Reduction of the green wave problem to Job-shop scheduler
Consider the following transformations from the original semaphore optimization
problem to a JSSP:
– Traffic lights are mapped to the processors
– Convoys are formed to replicate the Webster cycle on the Hot Route
– Convoys are mapped to the Jobs
– Green time is the job run time
– Webster model are problem constraints
– We will use the branch and bound method to find an optimal solution that
minimizes makespan
– The solution generates a set of Jobs that can execute without conflicts in
the processors, that is, a set of convoys of vehicles that travel at the average
speed of the route and are able to pass in all the open semaphores
In this way the JSSP variables are:
– Job-shop(Jm ): In a job shop with m machines (traffic lights), each job
represents a car convoy that has a particular and predetermined route to
follow (hot route)
– Processing time (pij ): The pij represents the processing time of the Job
j on machine i.
– Makespan (Cmax ): The makespan (manufacturing time), defined as Max
(C1 , ..., Cn ), the end time of the last job leaves the system. A minimum
manufacturing time usually implies maximum use of the machine (s).
3.4 Implementation details
The whole implementation was done in C# language, because some of the base-
line algorithms were originally written in this language. The implemented code
is available in the GitHub repository. [2]. The input of GR algorithm are Route
Routes and Map (OSM) and the output is the traffic light scheduller (XML).
4 SIMULATION RESULTS
4.1 Input data
For testing purposes, we used real trajectory data extracted from Taxi Simples,
a taxi company based in Fortaleza, Brazil. [5] This dataset had a very high
10 Antonio M R Almeida et al.
ALGORITHM 1: GR - Green Way over Hot Route
Input: R[] set of trajectories with flow annotation
Output: S set of scheduler for all traffic light
1 P rocessors ← {};
2 Jobs ← {};
3 w ←WebsterModel(R[]);
4 w.greentime ← w.mingreentime;
5 (w.greentime++ <= w.maxgreentime) P rocessors ← DTL(R[], w);
6 Jobs ← MC(R[], w);
7 s ←JSSP.Solver(Processors, Jobs);
8 if s!= null then
9 break;
10 end
/* repeats by increasing the green time, in search of a solution */
11 return s;
/* s variable contains an optimal solution */
ALGORITHM 2: MC-MakeConvoys
Input: R[] set of trajectories with flow annotation
Input: w Webster model variables
Output: Jobs list of tasks (convoys)
1 Convoys ← {};
2 ConvoysSize ← w.getT otalT imeRoute() / w.CycleT ime;
3 while n 6= ConvoysSize do
4 c ← new Convoy();
5 c.hotRoute ← this;
6 c.processingT ime ← w.GreenT ime;
7 c.timeInHotRoute ← w.CycleT ime;
8 Convoys.add(c);
9 end
10 return Convoys;
Optimization of urban semaphore times turning into JSSP 11
ALGORITHM 3: DTL-DiscoveryTrafficLights
Input: R[] set of trajectories with flow annotation
Input: w Webster model variables
Output: Jobs list of processors (traffic lights)
1 P rocessors ← {};
2 foreach s ← R.Segments do
3 foreach n ← s.N odes do
4 F ound ← T rue;
5 if n.TrafficSignal == True then
6 t ← new P rocessor(n.Id);
7 foreach p ← P rocessors do
8 Result ←checkIfProcessorCloser(p, t);
9 if t.Id 6= p.Id ∧ Result > 30 then
10 F ound ← F alse;
11 end
12 end
13 if !Found then
14 p ← new P rocessor();
15 P rocessors ← p;
16 end
17 end
18 end
19 end
frequency sampling rate, but was filtered down to reflect one with a low-sampling
character. Maps in OSM XML format were obtained from OpenStreetMap and
then parsed into a road network-like graph data structure using an XML parser
written in C# [22, 1] . The dataset used has collected data paths in the period
between 11/14/2015 and 09/05/2016, containing 22,791,003 GPS points.
4.2 Experiments Setup
For the experiments, we used a Intel (R) Core (TM) i7-4770S CPU @ 3.10GHz
with 16GB RAM memory, 256KB Cache L1, 1.0 MB Cache L2 and 8.0 MB
Cache L3.
The trajectory data of the Taxi [5] were downloaded and unzipped, and the
day 6/5/2016 was randomly chosen to perform the experiments of this article,
which alone contains 749,049 GPS trajectory points. The format of the files was
converted from CSV to GPX, and the city map of Fortaleza was downloaded
from the website Open Street Map [17].
To demonstrate the effectiveness of our algorithms, we perform the sequence
of the following steps on the raw data of GPS trajectories in the city of Fortaleza.
12 Antonio M R Almeida et al.
4.3 Experimental Results
To evaluate the GR algorithm we used frequent routes obtained from the data
set of taxi trajectories mentioned above, using routes that contained traffic lights
in their route and where there were intersections. To extract the Hot routes we
use the Flowscan algorithm[13], we use the minTraffic = 1 parameters to ensure
that the Hot Routes have the greatest possible coverage of the trajectories of
the city. We used the Webster Model to calculate cycle times based on highway
type parameters and average track speed.
All the approaches used in this study showed very promising results and
high applicability. Based on real-time trajectories of raw data we can obtain the
city traffic behavior at each time slice where the behavior is linear. The query
visualization can be used as a tool to discover the higher density flow (hot routes)
and influence the creation of public policies for urban traffic.
In our experiments, we used the Simulation of Urban Mobility (SUMO) [7]
software (version 0.29.0). That tool is open source, and has a tremendous ef-
ficiency on large sets of data routes. Moreover, to show the effectiveness of
the Green Route algorithm, three simulations were performed on a Intel(R)
Core(TM) i7-4770S CPU @ 3.10GHz.
In each simulation, we isolated a fixed number of hot routes, using one in the
first experiment, two in the second, and finally three on the third. In addition, for
each hot route, we extracted its respective traffic lights, latitude and longitude
positions. Furthermore, in order to execute the experiments, we had to calculate
the rate of cars passing on each hot routes. For that, each hot route has an
attribute called traffic segment, which tells us the number of vehicles in that
specific segment. Therefore, by summing up all the traffic segments (on each hot
route), we get the rate of cars.
On SUMO, for each simulation, we measured the average trip length (s), the
average trip duration (s), and the average waiting time (s). For each simulation,
we first performed it using the default traffic lights of the SUMO software, which
are generated based on the common traffic of the route. Only after, we performed
it again but then using our traffic lights configuration, in which we get it from
our GR algorithm.
In Table 6, we present the results of the simulations for the first, second, and
third scenarios. In the first line, we show the amount of vehicles loaded, then
in the second line the number of hot routes, and finally on the third line the
is show lane length (km). The remaining ones are the measures that we used
throughout the simulation.
Listing 1.1. Part of scheduler file from GR
< t r a f f i c −l i g h t i d ="0">
Optimization of urban semaphore times turning into JSSP 13
Simulation First scenario Second scenario
SUMO GPS2GR % SUMO GPS2GR %
loaded vehicles # 791 791 6291 6291
rot houtes # 1 1 3 3
total lane length (km) 84,94 84,94 653,26 653,26
Average time
Trip1 waiting time (s) 11,6 11,32 -2,41 28,49 28,11 -1,33
Trip duration (s) 110,95 110,53 -0,38 247,5 246,74 -0,31
Trip time loss (s) 34,2 33,8 -1,17 77,71 77 -0,91
Table 6. Simulation results
...
5 DISCUSSION AND CONCLUSIONS
We were able to complete an implementation and tests of the GR algorithms.
This algorithm converged and generated optimized solutions of the opening and
closing times of the traffic lights along the hot routes [21].
We prove by simulation that the solution obtained by the GR algorithm
is optimal since its optimal solution is always better than the good solutions
generated by heuristic methods. Optimization on rot route can solve classic
vehicle containment problems at the end of a green wave, as it takes into account
flow optimization, that is, green wave overflow, no matter what its path is.
As future work we can consider the application of GR algorithm on real time
information streaming in order to reflect real time aspects of the flow such as
accidents, road maintenance, etc.
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