# Exploiting Spatial Abstraction in Predictive Analytics of Vehicle Traffic

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Spatial Abstraction of a Transportation Network

_{1},t

_{2}] is computed as the mean of the mean speeds of all objects that moved from cell A to cell B during this time interval.

- Divide the value range of attribute A into intervals.
- For each value interval of A:
- Find all time steps in which the values of A fit in this interval.
- Collect all values of B occurring in these time steps.
- From the collected values of B, compute summary statistics: mean, quartiles, 9
^{th}decile (i.e., 90th percentile), and maximum. - For each statistical measure (i.e., mean, 9
^{th}decile, maximum, etc.), construct an ordered sequence of values corresponding to the value intervals of A arranged in the ascending order.

^{th}decile of the mean speed. We have taken the 9

^{th}decile because this statistical measure is less sensitive to outliers as the maximum. Outliers among the values of the mean speed often occur in time intervals of low traffic intensity, when a single or only a few vehicles traverse a link. The graph on the right shows for each link the dependency of the maximal relative traffic intensity on the mean speed. The horizontal axis corresponds to the mean speed and the vertical axis to the maximal relative traffic intensity.

**Figure 2.**The graphs represent the interdependencies between the traffic intensity and mean speed for the links of the abstracted transportation network of Milan shown in Figure 1.

**Figure 3.**The two-way dependencies between the traffic intensity and mean speed can be represented by polynomial regression models.

**Figure 4.**The maps show spatially abstracted transportation networks of Milan built with cell radii ≈ 2 km (top) and 4 km (bottom). The graphs to the right of each map represent the two-way dependencies between the relative traffic intensities and the mean speeds on the network links.

## 4. Advantages and Limitations of Spatial Abstraction

- The number of nodes and links in an abstracted network can be much smaller than in the underlying physical network. Hence, much less time and effort is needed for model building and calibration, and also simulations can be carried out much faster compared to the current practices. This enables, in particular, rapid approximate predictions and assessments of traffic dynamics in emergency situations, when time is very limited.
- Spatial abstraction compensates for the sparseness of real data on streets with low traffic. There may be not enough trajectory points on a given street segment for reconstructing the dependency between the mean speed and traffic intensity, but aggregation of several physical links into one abstract link alleviates this problem.
- It is possible to build an abstract network in which the level of spatial abstraction varies across a territory according to the variation of the data density. In areas with high traffic, abstracted links may very closely approximate physical links (i.e., street segments), whereas areas with low traffic can be represented by large cells. Hence, it is possible to have different levels of detail in traffic simulations and prediction in areas with high and low traffic, when fine details in low traffic areas are not important.

## 5. Deriving Traffic Models from Real Data

## 6. Use of Models for Traffic Prediction and Simulation

- For each link, determine how many vehicles need to move through it in the current minute.
- Using the dependency model from the traffic intensity to the mean speed, determine the mean speed that is possible for this link load.
- Using the dependency model from the mean speed to the traffic intensity, determine how many vehicles will actually be able to move through the link in this minute.
- Promote this number of vehicles to the end place of the link and suspend the remaining vehicles in the start place of the link.

**Figure 5.**Simulated trajectories of cars moving from the vicinity of the San Siro stadium to supposed home places after a soccer game are shown in a space-time cube.

**Figure 6.**The simulated trajectories are shown on a map. The red and green circles represent the trip origins and destinations, respectively.

## 7. Evaluation of Model Goodness

_{q}and a busy time interval t

_{b}and finds the difference ΔN between the total numbers of the vehicles N(t

_{b}) and N(t

_{q}) that were present in the network in these two intervals: ΔN = N(t

_{b}) − N(t

_{q}). Then the analyst simulates the scenario as if ΔN extra vehicles appeared in the network in the time interval t

_{q}in addition to the normal traffic for t

_{q}. The extra vehicles are distributed over the nodes of the network proportionally to the differences in the vehicle counts between the intervals t

_{b}and t

_{q}. After performing the simulation, the predicted traffic intensities combining the regular and extra traffic are compared with the real traffic intensities in the interval t

_{b}. The evaluation is repeated several times for different pairs of t

_{q}and t

_{b}. We applied this approach to the models built for Milan and for Tuscany and obtained very high correlations between the predicted and real values.

## 8. Conclusion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Andrienko, N.; Andrienko, G.; Rinzivillo, S.
Exploiting Spatial Abstraction in Predictive Analytics of Vehicle Traffic. *ISPRS Int. J. Geo-Inf.* **2015**, *4*, 591-606.
https://doi.org/10.3390/ijgi4020591

**AMA Style**

Andrienko N, Andrienko G, Rinzivillo S.
Exploiting Spatial Abstraction in Predictive Analytics of Vehicle Traffic. *ISPRS International Journal of Geo-Information*. 2015; 4(2):591-606.
https://doi.org/10.3390/ijgi4020591

**Chicago/Turabian Style**

Andrienko, Natalia, Gennady Andrienko, and Salvatore Rinzivillo.
2015. "Exploiting Spatial Abstraction in Predictive Analytics of Vehicle Traffic" *ISPRS International Journal of Geo-Information* 4, no. 2: 591-606.
https://doi.org/10.3390/ijgi4020591