## Highway Traffic Congestion Detection and Identification

The highway traffic conditions across the United States are in a grim situation caused by daily congestion and daily accidents. The current highway systems are used for daily commuting, transportation of goods and interstate travels. The motorist advocacy group AAA reports that accidents in the United States, cost $164.2 billion each year, with costs derived from medical care, emergency and police services, property damage, lost productivity and quality of life, while congestion costs the nation $67.6 billion each year. About 43,000 people die on the nation's roadway each year. It is then essential that we provide solutions to these problems or at least ways to alleviate the magnitude of their occurrences.

So, we first need to come up with ways to quantify traffic data and highway operations in order to channel a path to determine a solution. We then need to find ways to alleviate congestion that will also in turn help in reducing the number of accidents caused by congestion. In order to do that, we propose a method of detecting a congestion onset and its propagation along a highway segment. We have developed a stochastic linear hybrid system model that will be used to represent those congestion scenarios. Using a state-dependent-hybrid estimation algorithm, we estimate the states of the highway that will provide us with the traffic congestion information. The performance of the algorithm is analyzed using the correct detection and identification and false alarm rate indices, time-to-detection as well as the run time for each simulation.

We use a set of constructed data that will represent the congestion onset and propagation scenarios. The validation of the algorithm is done using real traffic data obtained from highway I-405 S in California.

With our SLHS model, we model the congestion onset of each cell using the triangular fundamental diagram as shown in Figure 1.

Figure 1 |

We divide our highway segment into four cells as shown in Figure 2, and the loop detectors that measure traffic flow or density are located at the upstream and downstream locations as well as the on- and off-ramp locations.

Figure 2

So, for each congestion onset mode (where the congestion onset takes place in a cell) we model a viable set of modes for congestion propagation. Instead of having g^{h} discrete modes (where g=2, (for the conditions F and C), and h=4, for the number of cells in our example), we only need 3 modes at each step. This makes the algorithm viable for online applications, since we only work with three discrete modes at each time step instead of 2^{2} discrete modes; see Figure 3 for congestion onset of mode FFFC. It is also important to note that as the number of discrete modes increases in a hybrid estimation algorithm, the accuracy in estimating the correct mode with certainty deteriorates. Hence, our algorithm is able to detect the discrete mode with much certainty, using a set of modes for the congestion propagation identification.

Figure 3

We present a scenario for a congestion onset and propagation. When a cell is congested, after a certain amount of time, the congestion will propagate upstream into the adjacent cell and eventually into the adjacent highway segment and so on. This is a realistic scenario of what takes place on the highways. A congested highway segment does not have to fully jammed or have zero velocity for it to be congested. The critical density for a highway means that there will be a decrease in traffic flow and that the highway system will be operating below its par capability. In this scenario, we will take a look at the detection, propagation and localization for a congestion taking place in cell 2. We address the congestion propagation scenario after a congestion onset. Since congestion propagates upstream, the scenario starts with an initially fully free-flow mode (FFFF), to the congestion onset in cell 2 (FCFF) and the congestion propagation into cell 1 as mode CCFF. Mode FCFF occurs at 20 minutes and mode CCFF occurs at 30 minutes. We assume that the entire scenario of interest takes place for 40 minutes. The maximum TTD delay for this scenario is 1.92 minutes, while the run time for this scenario is 1.3777sec. The density and mode probability plots are shown in Figures 4 and 5 respectively as well as their performance indices in Table I.

Figure 4

Figure 5

For validation of the proposed highway model and the traffic monitoring algorithm, we use real traffic data representing a highway segment in Los Angeles, California on November the 26th at 2400 to November the 27th at 0100, where there is usually a lot of traffic since it represents the day before Thanksgiving. The data was obtained from the Freeway Performance Measurement System (PEMS) in California, which is a collaboration of UC Berkeley, PATH and Caltrans. The data is obtained for a duration of 25 hours. Due to the huge amount of information, we will use a segment of the data for better visual presentation and analysis between 4:10am and 8:20am shown as between 50-100 5-minute time-steps in Figure 7. We show the cell densities for the entire 25 hours, but the mode plots are zoomed in to the times described above. The sampling time for the measurements is 5 minutes.

We compare the estimated modes and the real modes in Figure 6. This provides us with a way to determine the effectiveness of our algorithm. For this case the overall CDID and the FA are 88% and 12% respectively for the 4:10am through 8:20am duration. This takes into account for delays greater than 5 minutes, because the sampling time is done for every 5 minutes. The length of the highway segment is about 2 miles long and each cell has approximately 0.5 miles. The critical density here was 200 vehicles/mile. The number is high because we have 4 lanes on the highway, and also it was noticed that beyond this value the speed v was less than the speed limit of 70mph. The run time for this scenario is 12.22sec for the entire 25 hour duration with a mean TTD delay of 5min. This is reasonable for the performance in the detection and localization of modes. Other algorithms used for incident detection had a 17.4% FA rate and a mean time to detection of 5.5 minutes. In the PEMS system, the data fidelity for a 5-minute observation period is between 70% to 80% (Note that these are based on different scenarios). Therefore, we have demonstrated that the proposed model and algorithm accurately detect a traffic congestion and propagation as well as identifying its location.

Figure 6

Figure 7

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