- Research Article
- Open Access

# Traffic Flow Condition Classification for Short Sections Using Single Microwave Sensor

- Muhammed G. Cinsdikici
^{1}Email author and - Kemal Memiş
^{2}

**2010**:148303

https://doi.org/10.1155/2010/148303

© Muhammed G. Cinsdikici and Kemal Memiş. 2010

**Received:**19 October 2009**Accepted:**2 September 2010**Published:**19 September 2010

## Abstract

Daily observed traffic flow can show different characteristics varying with the times of the day. They are caused by traffic incidents such as accidents, disabled cars, construction activities and other unusual events. Three different major traffic conditions can be occurred: "Flow," "Dense" and "Congested". Objective of this research is to identify the current traffic condition by examining the traffic measurement parameters. The earlier researches have dealt only with speed and volume by ignoring occupancy. In our study, the occupancy is another important parameter of classification. The previous works have used multiple sensors to classify traffic condition whereas our work uses only single microwave sensor. We have extended Multiple Linear Regression classification with our new approach of Estimating with Error Prediction. We present novel algorithms of Multiclassification with One-Against-All Method and Multiclassification with Binary Comparison for multiple SVM architecture. Finaly, a non-linear model of backpropagation neural network is introduced for classification. This combination has not been reported on previous studies. Training data are obtained from the Corsim based microscopic traffic simulator TSIS 5.1. All performances are compared using this data set. Our methods are currently installed and running at traffic management center of 2.Ring Road in Istanbul.

## Keywords

- Support Vector Machine
- Traffic Flow
- Traffic Condition
- Ring Road
- Multi Class Problem

## 1. Introduction

Traffic flow characteristic shows dynamical change at different time periods of the day. Many traffic incidents such as accidents, disabled cars, construction activities, high demands on traffic, and other unusual events cause this change. For dealing with these unstable traffic problems, traffic conditions should be clarified. Mainly there exist three different major traffic conditions: "Flow Traffic," "Dense Traffic," and "Congested Traffic". Clarification of them requires careful/detailed examination of the flow parameters of *speed*, *volume, and occupancy (SVO)*.

Accurate interpretation of *SVO* supports traffic management centers to make proper decision on directing the traffic to the less intensive roads. Hence, the response time for intervention in an incident will be reduced.

*SVO*have changed for the last 60 years of the span (i.e., especially the last 40 years with the rapid rise in the number of freeways). Indeed, they are still changing [1]. Some of them are

- (i)
measurement at a point,

- (ii)
measurement over a short section (about 10?meters),

- (iii)
measurement over a length of road (at least 0.5?km),

- (iv)
measurement with mobile observer in the traffic stream,

- (v)
measurement with multiple simultaneous mobile vehicles, as part of ITS (Intelligent Transportation Systems).

Although all measurement methods above produce *speed* and *volume* of *SVO,* the only method producing *occupancy* (i.e., the percentage of unit time that the detection zone of the instrument is occupied by vehicles) is the measurement over a short section [1].

Detectors used for short section measurement can be based on inductive loop (IL), microwave, radar, photocell, ultrasonic, and analog/digital camera technologies [1]. Since the quick and effortless installation is possible only on IL technology, we have used Radio Transmissions Microwave Sensor-based (RTMS) IL detector. We have collected *SVO* parameter values at different times of day by using RTMS-IL.

The collected *SVO* data is analyzed through our three distinct novel approaches to classify traffic flow as "Flow", "Dense", or "Congested". These approaches are estimating error prediction for multiple linear regression analysis, two improved variants of support vector machines (SVM), and backpropagation neural network. First two methods are linear classifiers, whereas NN is non-linear.

In Section 2, the contributions of our paper will be given in the related works. Then, background is presented. In the Section 4, all details about the proposed study are going to be given. Section 5 summarizes experimental results. Finally, conclusion is given.

## 2. Related Works

Flow theory has been tried to analyze traffic through the *speed*, *volume,* and the *vehicular concentration* parameters.

Temporal vehicular concentration named as *occupancy* can be measured only over a short section (i.e., shorter than the minimum vehicle length). So, this parameter becomes unmeaning for long section measurements.

*Density* as an alternative vehicular concentration has been a part of traffic measurement since 1930's. It depicts the number of vehicles over a long section (i.e., one mile or kilometer) in contrast to occupancy.

Although vehicular concentration encompasses both *density* and*occupancy* parameters, indeed, it would be fair to say that the majority opinion is in favor of using *density* during the evolution of traffic flow theory.

However, a minority view has intended to use *occupancy* in theoretical works. Although there are well-defined facts put forward by the majority for the continued use of *density*, the minority also propounds major reasons for making more use of *occupancy*. The most crucial reason among them can be given as *density* (i.e., vehicles per length of road) ignores the effects of vehicle length and traffic composition. *Occupancy*, on the other hand, is directly affected by both of these variables and therefore gives a more reliable indicator of the amount of a road being used by vehicles.

First mathematical model-based on *speed*, *volume,* and *density* variables had been developed by Greenshild in mid 1930s [2] using the aerial photographs. In his work, relationship between *speed* and *density* is introduced relying on simple linear regression approach.

After World War II, with the tremendous increase in use of automobiles and the expansion of the highway system, there was also a surge in the study of traffic characteristics and the development of traffic flow theories. In 1950's, theoretical developments based on a variety of approaches, such as car-following, traffic wave theory (hydrodynamic analogy), and queuing theory has emerged. Some of the seminal works of that period include the works by Reuschel (1950) [3–5], Wardrop (1952) [6], Pipes (1953) [7], Lighthill and Whitham (1955) [8], Newell (1955) [9], Webster (1957) [10], Edie and Foote (1958) [11], Chandler et al. (1958) [12], and other papers by Herman et al.

Reuschel and Pipes offered a microscopic traffic model that identifies the linear dependency between the *speed* of a vehicle and the *distance between the vehicles in* a single lane. The models described by Reuschel and Pipes were reasonable in concept, but no experimental verification of their conclusions was pursued for many years [13].

Wardrop's theory was based on two major principles. The first one was stating that travel times between the same origin and destination pairs for any used routes are less than or equal to the travel times for all unused routes. This is referenced as Dynamic User Equilibrium (DUE) in the literature and used for large-scale networks. Diverting traffic with DUE is inefficient and difficult-to-implement system optimum (i.e., min. average travel time) [14]. The second one aims at minimizing both the total travel times and average travel times for all assigned routes for all drivers on the whole network. However, individual choice of drivers was by no means guaranteed to satisfy this principle and in most cases did not [13].

A few years later, Lighthill and Whitham (L-W) together set out the first comprehensive theory of kinematic waves. In L-W traffic model, there exists correlation between traffic flow (cars/hour) and traffic density (cars/mile) [8]. Propagation of shock waves, generated by traffic transitions from one steady state to another, was also determined by L-W model. Nevertheless, this model was viable only for describing the density changes. Unfortunately, the model produces larger densities exceeding the possible maximum vehicle density.

Greenberg improved the existing mathematical models by adding the nonlinearity into the model structure [15]. He treats the traffic stream as a continuous fluid and derives the relations between *speed*, *density*, and *flow* by fluid dynamics.

The distinction of free (i.e., non-congested) and congested flow on the *speed*-*density* model was carried out by Eddie [16] and Underwood [17] and was investigated in an important empirical test by Drake et al. [18].

Athol [19] suggested using the *occupancy* rather than the density for the flow-concentration works, however his suggestion became popular one decade later.

*Speed*, *flow,* and *occupancy (SFO)* relationships have been studied at the free flow level by Hurdle and Datta [20], Persaud and Hurdle [21], F. L. Hall and L. M. Hall [22], Banks [23], Smith et al. [24], Hall et al. [25], and Wemple et al. [26]. Also, *SFO* have been studied at congested flow level and by Hall and Montgomery [27], Zhou and Hall [28], and Banks [29, 30].

SVMs are usually employed for incident detection algorithms identifying the anomalies of traffic flow model using single or two sensors [31]. The process for determining the presence of an incident is twofold. The first is a determination of congestion (exits/not-exists), one of the states we also want to identify. Next is the binary analysis of type of congestion (incident occurred/not-occurred). Past researches and applications usually tend to use the traffic descriptors of two traffic sensors as their input parameters for incident detection with SVM methods.

In ITS, neural networks can be found on the areas like vehicle detection, road detection, and single loop vehicle type classification [32, 33]. Rarely some work related with traffic flow control can be found and they are also not well defined [34].

All retrospective researches so far show the binary relationships between the traffic parameters such as *flow rate* and *occupancy (FR-O)*, *flow rate* and *speed (FR-S)*, *speed* and *occupancy (S-O)* at congested or flow levels. Traffic status is assessed according to these binary relationships or by inspecting only one parameter (like *speed*) rather than examining all of them.

The first contribution of this paper to the traffic studies is focusing on another major traffic flow level ignored in earlier researches called *dense flow* level. All the previous works studies congested and flow traffic levels.

The second contribution of the paper is that no one in the earlier works is based on "single sensor" (i.e., all of them used double sensor placed within some distance) with using *SVO* triplets (i.e., triple relations of traffic parameters).

The third one is our new approach of "estimation with error prediction" for multiple-linear regression.

The fourth and most important one is our novel algorithms of "Multiclassification with One-Against-All" and "Multiclassification with Binary Comparison" as variants for support vector machine (SVM) classifier for the traffic flow model.

The final contribution is that none of the earlier works uses neural network model to classify the traffic control by short section with single ILD.

## 3. Background

- (i)
Volume shows the count of total vehicles passed through this short section for one period.

- (ii)
Speed shows the average speed of total cars passed through this short section for one period.

- (iii)
Occupancy shows the sum of the time; vehicles occupy the short section divided by one period time.

### 3.1. Linear Multiple Regression Analysis Method as a Classifier

*E*for each data point, defined by LMS as in (2). The parameters and are obtained from solving the partial derivatives of

for given data.

### 3.2. Support Vector Machine as a Classifier

Another innovative supervised pattern classifier technique SVM was first proposed by Vapnik in 1995 [36]. The formulation applied by SVM embodies the Structural Risk Minimization (SRM) principle, which has been shown to be superior to traditional Empirical Risk Minimization (ERM) principle [37]. While SRM minimizes an upper bound on the expected risk, ERM minimizes the error on the training data [38]. It is the difference which equips SVM with a greater ability to generalize, which is the goal in statistical learning. SVMs were developed to solve the classification problem (i.e., data must belong to either Class 1(+1) or Class 2( )) but recently they have been extended to the domain of regression problems [39].

*margin*" (i.e., smallest distance between decision boundary and any of the samples) should be found through [controlling the separability] [41]:

The dominating approach for solving multiclass problems using SVM has been based on reducing single multi class problem into multiple binary problems. For instance, a common method is to build a set of binary classifiers where each classifier distinguishes between one of the labels to the rest. This approach is a special case of using output codes for solving multi class problems [42]. However, while multi class learning using output codes provides a simple and powerful framework it cannot capture correlations between the different classes since it breaks a multi class problem into multiple independent binary problems [43].

The idea of casting multi class problems as a single constrained optimization with a quadratic objective function was introduced by Vapnik [44] and Watkins [45]. These attempts to extend the binary case are achieved by adding constraints for every class and thus the size of the quadratic optimization is proportional to the number of categories in the classification problems. The result is often a homogeneous quadratic problem which is hard to solve and difficult to store. The idea of breaking constrained optimization problem into smaller problems was extended by Joachims [46]. Multiple class problems were then discussed by Schölkopf [47]. Today's panorama of SVM is well summarized by Cristianini [48] and more completely by Schölkopf and Smola [49].

### 3.3. Backpropagation Neural Network as a Classifier

In our paper work, we used alternative learning methods for comparing the performances. They are Gradient Descent with Momentum (gdm), Conjugate Gradient Descent (cgd), Scaled Conjugate Gradient (scg), and Levenberg-Marquardt Gradient Descent with momentum and Scaled Conjugate Gradient. In [52], you can find algorithms and related details about the formulation and theory about these learning methods.

## 4. Proposed Method

### 4.1. Data

For each traffic condition, different values and types of data can be acquired through the FHWA's (Federal Highway Agency) TSIS 5.1 software (i.e., a CORSIM-based microscopic traffic simulation tool). Differentiation of data is supplied by configuring simulation tool parameters such as distribution function of generated traffic, lane speeds, car distances, and incident creation intervals.

Each ILD sensors generates *speed*, *volume,* and *occupancy* parameters values for configurable one period of time (i.e., 60 seconds) for each lane on the freeway.

#### 4.1.1. Congested Condition

*speed*and

*volume*reach the minimum values.

#### 4.1.2. Flow Condition

*speed*is high and

*volume*is low, the

*occupancy*approximately reaches to zero. Under the low

*speed*and high volume conditions, occupancy rises but never reaches to the maximum value.

#### 4.1.3. Dense Condition

*speed*values, short-term incidents, and decreased distances between the cars in traffic. This condition is observed between the flow and congested conditions. As seen in Figure 6 the

*occupancy*never reaches to min or max values.

### 4.2. Multiple Regression Analysis

There exist two significant facts through the basis of this method. The prior one says it is obvious that *occupancy* approximates to zero whether the average *speed* of vehicles approximates to infinity in flow traffic condition or not. On the contrary, *occupancy* goes to maximum value when *speed* approximates to zero in congested traffic flow condition.

It is also obvious that, until the *volume* reaches its maximum, *occupancy* is also increasing. After the maximum, the *volume* is going to be monotonically decreasing whereas *occupancy* is still increasing.

Under these circumstances, in flow traffic condition more *volume* leads to more *occupancy*. However, in congested traffic flow, the less *volume* observed leads to more *occupancy*.

*speed,*and

*volume*can show the zero, although

*occupancy*approaches to maximum. Unless the vehicles exist along the freeway (i.e., flow condition),

*speed*,

*volume,*and also the

*occupancy*indicate zero. A linear dependency of

*SVO*for each traffic condition with respect to the discrepancy are modified from (6) as in (7). For each flow condition

*a*, and

*β*

_{ 2 }parameters are different,

#### 4.2.1. Regression Planes

Using the CORSIM data, , , and values for each traffic condition are calculated using LMS (Least Mean Squares) method. The obtained results can be tracked through following subtitles.

*occupancy*reaches max (98.2) when the

*speed*and

*volume*are marked as zero. This verifies the expectations of the real traffic condition.

*occupancy*as 0 whereas

*speed*and

*volume*also share the same value. Through the crosschecking (9), it can easily be seen that

*occupancy*reaches min (0.05) when the

*speed*and

*volume*are marked as zero. This verifies the expectations of the real traffic condition.

(d) Combined Data and Regression Planes. Data and regression planes of all traffic conditions are shown in Figure 10.

(1) Using Analytic geometry (AG). From the CORSIM simulation, regression planes are defined for each traffic conditions. AG calculates the distances between all data points and each plane. The result (i.e., nearest plane) supplies us to infer the class (status) of current traffic.

(2) Estimating Occupancy without Error Prediction (EO). In EO, linear regression (6) is used and error is assumed as zero. Using this assumption *occupancy* estimator can be calculated for each simulated traffic condition (8), (9), (10) using the real *speed* and real *volume*. After acquiring these estimators, they are compared with the real *occupancy*. The one nearest to real *occupancy* becomes the result of our traffic flow condition.

(3) Estimating Occupancy with Error Prediction (EOwEP): Another method for finding the traffic flow class is extended version of EO. This method calculates *occupancy* estimators by adding the predicted error values.

*occupancy*estimator for that condition can be determined. So the obtained equation as

### 4.3. Support Vector Machines

As mentioned in background, SVM is generally applied to binary classification problems. Since the addressed problem is mapping the input data into one of three flow conditions, SVM can be seen inapplicable at first. However, without changing its calculation style, SVM can also be used in multiclassification problems. The idea lays behind multi classification is just using more than one SVM and classifing the data according to the outputs of multiple SVMs. We use our two novel approaches for Multiple SVM.

Multiclassification with One-Against-All Method (OAAM). The designated architecture (our novel approach) for this method is composed of three SVMs. Each SVM represents one of the traffic flow conditions. Detector values can be fed into each SVM, respectively. The bipolar output ["+1" (Class 1), " " (Class 2)] indicates if the input data belongs to this SVM or not.

**Algorithm 1**

- (i)
Initialize weights (

*v*_{ i,j }*, w*_{ j,k }) with small random values - (ii)
Broadcast the input data to the input layer

*x*_{ i }

- (i)
Calculate the hidden layer unit signals

("

*f*" is sigmoid function in our work) - (ii)
Calculate the output unit signal

- (i)
Calculate the residual. By using expected value for output signal (

*t*_{ k }).where

*a*is learning rate. In the learning phase, is updated according to learning rule. - (ii)
Then calculate reflectance of the residuals and propagate it to the input weights.

- (iii)
All weights are updated with learning rule (i.e., gdm/scg).

- (iv)
Test the stopping condition (i.e., reaching to "goal"; predefined Mse —mean square error- of the total residuals)

After training is done, each member of Multiple-SVMs has its own linear planes for OAAM. In order to get the correct class of the queried data is just easy as to look at the responses of each SVMs. The "+1" response of the SVM clarifies the class of the data. For instance if F-SVM's response is "+1" (i.e., the others are expected as " ") then the class of the data belongs to flow traffic.

- (i)
If at least two SVMs produce output "+1", then the one with the longest L2 distance from data point to its own SVM plane can be picked out. Since the furthest distance from the data point to plane exposes the stricter and more accurate data for current traffic flow condition, we choose the furthest one.

- (ii)
If all SVMs produce output " ", the one with the shortest L2 distance to SVM plane must be chosen. Producing output "–1" implies that the data does not belong to the current SVM's traffic condition. Since, the shortest distance from data point to SVM plane is the nearest one to "+1" (Class 1), we can pick this SVM out as our desired class.

Multiclassification with Binary Comparison (BC)

Our other novel approach applied to classify our data is again composed of three SVMs. However, it can be distinguished from the OAAM method by its architecture. In BC method, each SVM is responsible for the following binary combinations, respectively; (Congested, Dense), (Congested, Flow), and (Flow, Dense). This multi classification method depends on basic voting principle. There exist three candidates (i.e., Congested, Flow, and Dense traffic conditions) and three voters (each SVM). The one among the candidates wins the election if it gets the most votes from voters.

Backpropagation Neural Network Architecture*s*

In the learning phase, we have used the algorithms of only Gdm, Levenberg-Maquardt with Gdm and Scaled Conjugate Gradient with Gdm [52]. Matlab 7.6.0 (Rev.2008a) Neural Network Toolbox where our related work algorithms and learning rules are ready is used.

Backpropagation Neural Net Performances.

GDM | LM | SCG | |||||
---|---|---|---|---|---|---|---|

LogSig-PurLin | PurLin-PurLin | LogSig-PurLin | PurLin-PurLin | LogSig-PurLin | PurLin-PurLin | ||

BackPrp 3-10-3 | Cong | 100 | 100 | 0.9604 | 0.9472 | 100 | 0.4073 |

Dense | 0.5733 | 0.5612 | 0.5134 | 0.5671 | 0 | 0 | |

Flow | 0.9502 | 0.9189 | 0.9210 | 0.9470 | 0 | 0.062 | |

Total (Rate/Iteration) | 0.9678/1000 | 0.9258/1000 | 0.9352/360 | 0.9170/5 | 0.0068/156 | 0.0615/15 | |

BackPrp 3-20-3 | Cong | 0.6227 | 0.9472 | 100 | 0.9393 | 100 | 0.9393 |

Dense | 0.6914 | 0.6878 | 0.4677 | 0.6778 | 0.8531 | 0.6725 | |

Flow | 0.9804 | 0.8950 | 0.7492 | 0.8967 | 0.9914 | 0.9468 | |

Total (Rate/Iteration) | 0.8785/1000 | 0.9192/1000 | 0.7367/168 | 0.9102/4 | 0.9794/301 | 0.9512/23 | |

BackPrp 3-50-3 | Cong | 0.9721 | 0.9393 | 0.9732 | 0.9893 | 0.9789 | 0.9472 |

Dense | 0.4552 | 0.6686 | 0.1256 | 0.6800 | 0.6318 | 0.6711 | |

Flow | 0.9571 | 0.9869 | 0.9899 | 0.9907 | 0.9879 | 0.9867 | |

Total (Rate/Iteration) | 0.9120/1000 | 0.9265/1000 | 0.9058/35 | 0.9803/3 | 0.9595/136 | 0.9512/16 |

## 5. Experimental Work

Turkey General Directorate of Highways has carried out works in managing traffic in Istanbul hence traffic management center is planned to be opened at the end of December 2007. The system is installed by Turkey's leading electronics company ASELSAN Inc. In Istanbul traffic management system, microwave radar type detectors are used for occupancy, speed, and traffic volume measurements. There exist almost 30 radio transmission microwave sensors along the 2.Ring Road. The measurements recorded at critical points on the road are transmitted periodically to the management center [53].

Occupancy, speed, and traffic volume measurements are both recorded in the database, and the traffic status according to these measurements is mapped to color codes and displayed on a large screen. Whenever any congested state or dense state occurs along the road, alarms with severity levels are generated and the operators are informed. Information regarding the traffic status is also displayed on LED-based Variable Message Signs (VMS) on the road.

*SVO values*]. These data sets are used to for the Table 2.

Estimation Performance of Our Model for Each Traffic condition.

Method | Flow | Dense | Congested |
---|---|---|---|

Analytic Geometry | 99% | 84% | 70% |

| 100% | 78% | 35% |

| 99% | 24% | 46% |

| 100% | 46% | 97% |

| 100% | 74% | 100% |

| 99.14% | 85.31% | 100% |

| 99.07% | 68% | 98.93% |

| 95.02% | 57.33% | 100% |

## 6. Conclusion

Eight methods discussed above have applied the one day data captured from 7 sensors on 2.Ring Road in Istanbul. Their performance for each traffic condition can be seen in Table 2.

Although our novel approaches OAAM and BC for Multiple SVM have good performances, our BPNN architecture of 3-20-3 with SCG (3-20-3) is better than all other seven methods. As a result of this comparison, this method has chosen and installed for the evaluation of traffic condition in Istanbul traffic management center (at Istanbul 2.Ring road).

According to the result it calculates, our algorithm colors the road map for each status changes on GIS projection screens. Once congested level is detected, it produces an alarm with high severity to inform the operators. Nevertheless, dense level also creates alarm with lower severity. After verification of this assessment by operator, VMS can be supplied by messages to inform drivers about the road flow condition.

## Authors’ Affiliations

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