This paper presents the model and algorithms for traffic flow data monitoring and optimal traffic light control based on wireless sensor networks. Given the scenario that sensor nodes are sparsely deployed along the segments between signalized intersections, an analytical model is built using continuum traffic equation and develops the method to estimate traffic parameter with the scattered sensor data. Based on the traffic data and principle of traffic congestion formation, we introduce the congestion factor which can be used to evaluate the realtime traffic congestion status along the segment and to predict the subcritical state of traffic jams. The result is expected to support the timing phase optimization of traffic light control for the purpose of avoiding traffic congestion before its formation. We simulate the traffic monitoring based on the
The traffic crowds seen in intersection of urban road networks are highly influential in both developed and developing nations worldwide [
Nowadays, in an informationrich era, the traditional traffic surveillance and control methods are confronted with great challenges [
Traffic research currently still cannot fully express the intrinsic principle of traffic congestion formation and predict under which conditions traffic jam may suddenly occur. In the essentials, urban traffic is a typical selfdriven manyparticle huge system which is far from equilibrium state, where the traffic flow is a complicated nonlinear dynamic process, and the traffic congestion is the spatialtemporal conglomeration of traffic volume in finite time and space. In 2009, Flynn et al. have conducted some theoretical work to model traffic congestion with macroscope traffic flow theory and obtained some basic results in congestion prediction [
Traffic light control at urban intersection can be modeled as a multiobjective optimization problem (MOP). In UTCS (Urban Traffic Control System) such as SCOOT/SCATS/REHODES system, it always employs single loop sensor or double loops as vehicle detector deployed at upstream of the signalized intersections. Generally, in current traffic control strategies, optimization objectives include stop of vehicle, average delay, travel time, queuing length, traffic volume, vehicle speed, and even exhaust emission [
In this paper, we studied the intrinsic spacetime properties of actual traffic flow at the intersection and near segments and build an observation system to estimate and collect traffic parameters based on sparsely deployed wireless sensor networks. We are interested in understanding how to evaluate and express the degree of traffic congestion quantitatively and what the performance for traffic signal control would be if we take into account the traffic congestion factor as one of the objectives in timing optimization.
The rest of the paper is organized as follows. The current studies on traffic surveillance with wireless sensor networks are briefly reviewed in Section
Several research works on traffic monitoring with wireless sensor networks have been carried out in recent years. Most of them have focused on individual vehicle and point data detection, where the traffic spatialtemporal property is not an issue in these circumstances. Pravin et al. creatively applied the magnetic sensor networks to vehicle detection and classification in Berkeley PATH program from 2006 and obtained high precision beyond 95% [
The discipline of transportation science has expanded significantly in recent decades, and particularly traffic flow theory plays a great role in intelligent transportation systems [
The goal of this paper is to estimate traffic parameters based on sparsely deployed sensor networks, evaluate the degree of traffic congestion, and obtain a quantitative factor to express the spatiotemporal properties of traffic flow in real time. Based on this, introduce the congestion factor to the optimization model of traffic light control. In this paper we use
Deployment of wireless sensor networks for urban traffic surveillance.
The urban road network can be modeled as a directed graph consisting of vehicles
Nomenclature and symbols.

Location in road segment 

Traffic flow speed 

Vehicle trajectory 

Estimated traffic data 

Equilibrium speed 

Traffic pressure 

Sensor readings at time 

Time signals exceed threshold 

Temporalspatial scales 

Error from sensor 

Selfsimilar variable 

Min/max green time 

Cost function on lane 

Outflow in phase 

Demand flow in phase 

Saturation flow for green 

Existing phase state 

Observation time 

Traffic density 

Traffic data 

Maximum traffic density 

Free speed on empty road 

Flow production rate 

Vehicle detection threshold 

Detection flag 

Speed of vehicle 

Mean square error (MSE) 

Congestion factor of lane 

Effective green time 

Inflow in phase 

Arrival traffic flow at stop line 

Exit flow in phase 

Saturation flow for yellow 

Queue length in phase 
In this section, we firstly describe the intrinsic characteristic of traffic flow and then propose a method to estimate traffic parameters based on scattered data collected by sparsely deployed sensor networks.
The continuum model is excellent to describe the macroscopic traffic properties such as traffic congestion state. In 1955, Lighthill and Whitham introduced the continuum model (LWR model) [
In (
Based on the exact LWR solver developed by Berkeley [
In this paper, we employ high sensitive magnetic sensor, as shown in Figure
(a) Magnetic sensor node and gateway. (b) Presentence and velocity detection based on ATDA.
Where
In actual applications, for sake of cost, the sensor node number is expected as few as possible [
The detection grid in
For sensor reading
The sensor network is sparsely deployed, and the total number of sensor node is
Assume that we have trajectories of a certain number of vehicles
With the scattered measurements as boundary initial values, the traffic data can be estimated by numerical interpolation based on the approximated traffic equations, as shown in Figure
Scattered data fitting with proximity points.
There are many evaluation criteria for error optimization; we use the same objective function as that in [
Assume
The velocity change in real traffic flow
The traffic data estimation can be transformed to a twodimensional data fitting problem with timespace constraints based on scattered measurements. To solve the conditional extremum problem based on (
In this section, we focus on traffic congestion evaluation and signal optimization. Based on traffic flow theory, the traffic flow near signalized intersections and connecting links can be modeled as entrance and exit ramps. The traffic light control algorithm will generate a shock wave at the stop line of the lanes, from the beginning of red signal phase, which will affect the traffic state in future. We introduce congestion factor to evaluate the degree of traffic congestion, and cost function to represent the influence of current timing phase on next phase. The result is helpful to optimize signal control.
The traffic congestion without external disturbance is an unsolved mystery. Knowing that traffic on a certain road is congested is actually not very helpful to traffic control system, and the information about how congested it is and the process it formed is more useful. There is much novel research about traffic congestion prediction and evaluation in last decades [
Applying this assumption to (
The subcritical condition is therefore denoted as (
The road can be regarded as share resource for vehicle and traffic flow link, and according to Jain’s fairness index for shared computer systems, the quantitative congestion factor can be defined based on the traffic congestion model, as (
Considering an intersection with four phases numbered
Four phases of traffic control.
Under the scenario of traffic flow stops by red signal, for instance of lane
With the Matlab implementation of an exact LWR solver [
Traffic congestion factor at observation point
Density factor
Congestion factor
The problem of traffic timing optimization for an urban intersection in a crowded city has been previously approached in much research [
Urban intersection and road link model for traffic signal control.
Based on the dynamics of traffic flow, the control objective of the dynamic model is to minimize the total delay and traffic congestion factor. To minimize,
With constraints subject to
For a given time window
Based on the above model and computational method, the overall block diagram of traffic data detection and control algorithm is shown in Figure
Flow diagram of traffic flow detection and adaptive control model based on sensor network.
The traffic congestion state can be evaluated based on (
The model and algorithms are simulated based on VISSIM platform. The traffic flow data is generated with the Mobile Century field test dataset [
With the DLL and COM interfaces, we designed a software/hardware in the loop simulation platform based on VISSIM, as shown in Figure
Software/hardware in the loop simulation based on VISSIM.
The traffic data for simulation is based on Mobile Century dataset. Traffic data near three intersections is used to simulate traffic data collection and timing phase optimization. The traffic network is shown in Figure
Traffic networks for timing optimization simulation.
We select a fixed coordinate without sensor and try to estimate traffic parameters with the method proposed in this paper based on proximity sensor readings. The estimation precision under different smooth factor
Performance of traffic data estimation based on traffic equations.
In the control simulation, we analyzed the performance by two scenarios: control with delay constraint only and combining delay with traffic congestion factor together as the optimization objective, and compare the performance with fixed time control. On the same traffic flow dataset, the performance is illustrated in Figure
Performance analysis of traffic control based on congestion factor.
Average delay
The maximum queue length
In this paper we study the traffic flow congestion evaluation and congestion factor based control method using sparsely deployed wireless sensor network. Taking into consideration the traffic flow intrinsic properties and traffic congestion model, try to obtain optimal phase timing with as few sensor node as possible. The main idea is to study the congestion and its influence on future traffic flow, combine traffic equations with the optimization function, to obtain the numerical solution of the traffic equations via approximate method, and finally to refine traffic sensor data based on data fitting. The model and algorithms are simulated based on VISSIM platform and
Current research is limited to single intersection and simple segments with continuous traffic flow. Future research should focus on complex segments and even road network, such as ramp, long road with multiintersections. And the traffic control strategy, road capability, and dynamics caused by incidents need to be taken into consideration in actual applications. Furthermore, complex traffic flow pattern simulation and traffic control strategies on a networked scale among multiintersections and arbitrary connecting segments in road network are also an important aspect in next step.
This work was supported in part by the National High Technology Research and Development 863 Program of China under Grant no. 2012AA111902, the National Key Technology R&D Program of China under Grant no. 2011BAK02B02, the National Natural Science Foundation of China under Grant no. 60873256, and the Fundamental Research Funds for the Central Universities under Grant no. DUT12JS01.