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Speed Transition Matrix: Novel road traffic data modeling technique

Explore a new way of visualizing and analysing road traffic data

Explore a new way of visualizing and analyzing road traffic data

Photo by Alexander Popov on Unsplash
Photo by Alexander Popov on Unsplash

There are lots of ways of modeling the road traffic data. Researchers mostly use some kind of time series that represents the changes in some traffic parameters in time, like speed, delay, or volume. Mostly, aggregation of a lot of data is needed to create this kind of time series. In this step, different problems arise, mostly related to large deviations. The Speed Transition Matrix (STM) is proposed to cope with this problem and provide a way to extract more from traffic data. With this story, I will explain some basic concepts and use cases for the STM. For more details, you can jump to the paper "Traffic State Estimation and Classification on Citywide Scale Using Speed Transition Matrices" published in the Sustainability journal.


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Basic concepts

Let’s first explain the basic parts of the STM:

1. Transition

In STM concept, the transition is defined as the movement of a single vehicle between two consecutive road segments (links). In one transition, we have two links, origin and destination. It is important to mention that link length depends on the map that you use. For example, OpenStreetMap uses very short links (a few meters), while other map providers define one link as all road segments between two junctions.

Examples of two transitions on the road network (Image by: Author)
Examples of two transitions on the road network (Image by: Author)

2. Speed

The second step is the speed calculation. To construct an STM, we compute the speed of every vehicle that travels through the transition. It is important to compute speed on the origin and destination link. We used a harmonic speed because it favors the lower values to extract a better representation of the congestions, but one can experiment with other speed computation methods, like the average or median speed. Here are examples for the GNSS data, but other data sources can be used.

Speed calculation on the transition (Image by: Author)
Speed calculation on the transition (Image by: Author)

3. Matrix

The first iteration of the matrix is used to represent the counts of the speeds in one transition. Here is an example of five vehicle routes that pass through a green transition in the picture below. It can be seen that observation time is a very important parameter when computing the STM. If more time passes, the counts will be higher, because more cars will travel through the observed transition.

STM computation (1st part - counting the speed transitions) (Image by: Author)
STM computation (1st part – counting the speed transitions) (Image by: Author)

Here are two most common examples of the STMs for one transition observed in two intervals: 1) from 08:30 h to 15:30 h, and 2) from 15:30 h to 17:30 h:

Examples of the STMs: 1) non rush hour, 2) evening rush hour (Image by: Author)
Examples of the STMs: 1) non rush hour, 2) evening rush hour (Image by: Author)

Now we can work with this! On the first image, origin and destination speeds are placed at the middle with high origin and destination speeds, which can indicate normal traffic with no congestion. On the second image, we can observe that most of the counts are located in the upper left corner with low origin and destination speeds, which can indicate congestion. With this, we have extracted some useful traffic patterns.

You can also observe that origin and destination speeds are represented with the absolute values expressed in km/h. To make the STM more comparable on the city-wide scale, it is important to represent the speeds in their relative form within the range of 0–100 %. We chose to represent the speed relative to the speed limit, but you can represent it relative to the highest speed or average night speed. Also, we have transformed the counts into probabilities by dividing every value in the matrix by the sum of the matrix values. With this, the results are more interpretable and easier to explain.

Final form of the STM: relative values, probabilities (Image by: Author)
Final form of the STM: relative values, probabilities (Image by: Author)

Pros and cons

Here some most important advantages and disadvantages to consider when using the STMs. Advantages:

  • easy to interpret
  • more informative
  • does not suffer from the aggregation issues Disadvantages:
  • more complex than time-series Data
  • higher computation time
  • cannot be used with very sparse data

STM use cases

Traffic State Classification Using the Speed Transition Matrices

Novel Road Traffic Anomaly Metric Based on Speed Transition Matrices

Using Fuzzy Logic for Road Traffic Congestion Index Estimation

Conclusion

The STM is the novel Traffic data modeling technique that shows great potential in traffic data representation and analysis. In the recently published paper, we show the possibility of applying the STM for the traffic state estimation, but it can be used for anomaly detection, visualization, and similar.

Alongside its advantages, is have some disadvantages that must be considered before the implementation. Currently, this method is in "work in progress" status and will be a major part of my Ph.D. thesis.

If you are interested in similar, traffic-related topics follow my Medium profile, or check the published research at Research Gate 🙂

If you have any questions or suggestions, feel free to comment or contact me! https://www.linkedin.com/in/leo-tisljaric-28a56b123/

Published papers

Here is a list of published papers that show the usage of the STMs.

  1. L. Tišljarić, T. Carić, B. Abramović, and T. Fratrović, "Traffic State Estimation and Classification on Citywide Scale Using Speed Transition Matrices," Sustainability, vol. 12, no. 18, p. 7278, 2020.
  2. L. Tišljarić, S. Fernandes, T. Carić, and J. Gama, "Spatiotemporal Traffic Anomaly Detection on Urban Road Network Using Tensor Decomposition Method," in Discovery Science. Lecture Notes in Computer Science, vol. 12323, A. Appice, G. Tsoumakas, Y. Manolopoulos, and S. Matwin, Eds. Cham: Springer, 2020, pp. 674–688.
  3. L. Tišljarić, Ž. Majstorović, T. Erdelić, and T. Carić, "Measure for Traffic Anomaly Detection on the Urban Roads Using Speed Transition Matrices," in Proceedings of International Convention on Information and Communication Technology, Electronics and Microelectronics, 2020, pp. 268–275.

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