Traffic Forecasting using Vehicle-to-Vehicle Communication

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  Utilize a recently collected vehicle-to-vehicle communication dataset to generate high-resolution traffic forecasts.

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  Combine first principle models and deep learning to achieve better accuracy than either alone.

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  Investigate the generalizability of the method across different traffic conditions.

Describing and predicting the motion of vehicles in traffic has a long history, initially focusing on first principle models. These include, on one hand, car-following models such as the optimal velocity model (Bando et al., 1995), intelligent driver model (Treiber et al., 2000), and models with time delays (Igarashi et al., 2001; Orosz et al., 2010). These are often referred to as microscopic models as they aim to describe the behavior of individual vehicles. On the other hand, traffic flow models such as the LWR model (Lighthill and Whitham, 1955; Richards, 1956) and its novel formulations (Laval and Leclercq, 2013), the cell transmission model (Daganzo, 1994), and the ARZ model (Aw and Rascle, 2000; Zhang, 2002) aim for describing the aggregate traffic behavior. These are often called macroscopic models.

In what follows, we will use one of the most elementary car-following models introduced by Newell (2002). Newell’s model assumes that each vehicle copies the motion of its predecessor with a shift in time and space that is caused by the propagation of congestion waves in traffic. This can qualitatively capture an upcoming slowdown, and provide a rudimentary traffic preview for the ego vehicle. One can potentially improve prediction via more sophisticated first principle models, however, the uncertainty of human driver behavior makes it challenging to achieve low prediction errors. Alternatively, one may integrate these first principle models, which capture the essential features of traffic dynamics (like the propagation of congestion waves captured by Newell’s model), with data-driven approaches in order to improve the quality of predictions.

Recently, data-driven approaches such as deep learning have attracted considerable attention for modeling both aggregated (macroscopic) traffic behavior (Li et al., 2018; Yu et al., 2018) and individual (microscopic) driver behavior (Wang et al., 2018; Wu et al., 2018; Tang and Salakhutdinov, 2019; Ji et al., 2020). We refer readers to Veres and Moussa (2020) for a comprehensive survey on deep learning for intelligent transportation systems.

Using V2V communication to make traffic predictions with deep learning is a very new area. Wang et al. (2020) use V2V communication for perception around obstacles and for making short-term trajectory predictions in urban environments. Liang et al. (2020); Gao et al. (2020); Chang et al. (2019) similarly make short-term predictions on the order of 3 seconds for individual car trajectories in urban traffic using sensor data and not V2V data. Meanwhile, our work makes intermediate-term estimates (10-40 seconds) of connected vehicle trajectories on highways. These approaches consider individualized traffic forecasting for a given vehicle.

Alternatively, many works provide predictions for certain road locations rather than certain vehicles. Ma et al. (2017) uses 2D CNNs to make longer-term traffic predictions (10-20 minutes) on various road networks. Li et al. (2018) models traffic as a diffusion process using recurrent convolutional architecture. Alternatively, Cui et al. (2020) use recurrent graph convolutional networks, Loumiotis et al. (2018) consider general regression neural networks, and Yin et al. (2018) frame traffic prediction as a classification problem. Zhao et al. (2017) use a spatio-temporal LSTM to make traffic predictions on a similarly long timescale. More recently, attention mechanisms have been shown to be useful for forecasting on this time-scale (Do et al., 2019). These models all focus on road networks, so they cannot capture the behavior of individual vehicles in the flow. Their predictions are lower in spatial and temporal resolution than our model, since they rely on lower resolution road sensor data instead of V2V data. Nevertheless the widespread use of recurrent methods suggests their value in this domain.

The simplest first principle-based prediction algorithm is the constant speed prediction

which does not use data from the lead vehicle, but may work well for short term predictions.

To leverage the data from V2V connectivity, we consider Newell’s car-following model (Newell, 2002) as another baseline. According to this model, the position $X_{\rm E}$ of the ego vehicle is the same as the position $X_{\rm L}$ of the lead vehicle with a shift $T$ in time and a shift $wT$ in space:

where $w$ is the speed of the backward propagating congestion waves in traffic. Newell’s model allows one to predict the ego vehicle’s future motion, which is illustrated graphically in Figure 2(c,d). Given the data about the lead and ego vehicles’ past motion (shown by black and blue curves) up to the time $t$ of prediction (see vertical line), one can identify the time shift $T(t)$ between the trajectories by numerically solving (2) for $T(t)$. Then, the ego’s future motion at $t+\theta$, ${\theta\in[0,T(t)]}$ (shown by green curve) is predicted by translating the lead vehicle’s past velocity (see red curve) according to:

where we use tilde $\tilde{v}_{\rm E}(t,\theta)$ to distinguish Newell’s prediction from other methods. Figure 2(c,d) illustrate that such a simple prediction (with wave speed ${w=5\,{\rm m/s}}$) can qualitatively capture an upcoming slowdown, although there are quantitative errors in the ego’s speed preview.

Practically, predictions are made in discrete time, using data at time steps ${t_{i}=i\Delta t}$, ${\theta_{j}=j\Delta t}$, ${i,j\in\mathbb{Z}}$, where the sampling time is ${\Delta t=0.1\,{\rm s}}$ in our dataset. For example, when predicting $l$ time steps of future motion, the constant (1) and Newell (3) predictions in discrete time are

respectively, where $\hat{v}_{\rm E}(i,j)$ is used as a short notation for $\hat{v}_{\rm E}(t_{i},\theta_{j})$. Here ${\sigma=T(t)/\Delta t}$ is the maximum achievable horizon, thus ${l\leq\sigma}$ must hold. We consider ${l=400}$, that is, 40 seconds of prediction horizon in what follows.

Apart from Newell’s model predictions, one may directly use deep learning to achieve more accurate results. As a baseline, we consider an algorithm which does not use data from V2V connectivity but relies solely on the ego vehicle’s data. This method, called Ego-only LSTM-FC, predicts $l$ time steps of future motion using $k$ time steps of past data according to

where we used ${k=600}$, ${l=400}$, while $M_{1}$ is the map underlying the deep learning architecture outlined below. Note that constant prediction is a special case where $M_{1}$ outputs values of $v_{\rm E}(i)$.

We propose a hybrid method which uses deep learning to improve the prediction $\tilde{v}_{\rm E}(t,\theta)$ output by Newell’s model. We thus leverage the insights of the first principle-based model and focus on learning higher order fluctuations in the signal. We explore two configurations: (i) using the Newell’s model prediction as an additional input feature and (ii) outputting the residual between the Newell’s model prediction and the truth.

In configuration (i), the input consists of two time series: $k$ time steps of the ego’s past velocity and $l$ time steps of the Newell prediction. The output is $l$ time steps of the ego’s predicted future velocity. The input-output relationship is given by a map $M_{2}$ as summarized by

where we used ${k=600}$, ${l=400}$. We implemented this configuration on two architectures: a fully-connected feed-forward neural network, called Vel-FC, and an LSTM network, called VelLSTM-FC; see details about the model architecture below.

For configuration (ii), the input also contains the residual error $R(i,j)=v_{\rm E}(i+j)-\tilde{v}_{\rm E}(i,j)$ of Newell’s model over the past. The output is the next $l$ time steps of the predicted residual $\hat{R}(i,j)$. Then $\hat{v}_{\rm E}$ can be reconstructed as $\hat{v}_{\rm E}(i,j)=\hat{R}(i,j)+\tilde{v}_{\rm E}(i,j)$. This can be written formally as

where we used ${k=600}$, ${\underline{k}=300}$, ${l=400}$. Here $M_{3}$ denotes the map underlying the deep learning architecture, which is an LSTM network called ResLSTM-FC.

We implement the functions $M_{1},M_{2}$ and $M_{3}$ using the same encoder-decoder architecture. We use a two-layer LSTM encoder (Hochreiter and Schmidhuber, 1997) with ReLU and $\mathrm{tanh}$ activation functions to encode the input into a hidden state vector $h=\texttt{LSTM-Enc}(\mathbf{x})$ where we initialize the hidden state vector randomly. In each case the input vectors are concatenated into a single long sequence. For VelLSTM-FC, $\mathbf{x}=[v_{E}(i-k+1:i)\ \ \tilde{v}_{E}(i,1:l)]$ and for ResLSTM-FC, $\mathbf{x}=[v_{E}(i-k+1:i)\ \ \tilde{v}_{E}(i,-\underline{k}+1:l)\ \ R(i,-{k}+1:0)]$. This structure accommodates different numbers of time steps for different inputs. The hidden state vector $h$ is then passed to a linear decoder layer which predicts $l$ future time steps in one shot $\mathbf{y}=\texttt{Dec}(h)$.

We constructed samples from the data using rolling windows with 600 input time steps (representing 60 seconds of data) and 400 output time steps (40 seconds of data) for two vehicle pairs. We used 50 second buffers between train, validation, and test sets in order to ensure the test data is not partially seen during training. We created two train-validation-test splits shown in Figure 3(a,c) and Figure 3(b,d) corresponding to sample sizes 7200/2400/2400 and 7800/2600/2600, respectively. Our primary split, shown in panels (a) and (c), has the test set during a traffic jam with slower speed and varying traffic conditions. These are the conditions under which Newell’s model applies and thus the target domain for our method. To test robustness, we also use an alternative split as shown in panels (b) and (d) where the test set falls in a regime with higher speed and less speed variation. The data was normalized by subtracting the sample mean and dividing by the standard deviation of the train set, and we denormalized our results using the inverse formulation.

We use the absolute prediction error (PE)

to compute two performance metrics called velocity error (VE) and average velocity error (AVE):

The velocity error at horizon $j$ is the average of the absolute prediction error amongst the samples in a certain dataset (e.g., training, validation or test set) denoted by $\mathcal{I}$ with $|\mathcal{I}|$ number of elements. The average velocity error, on the other hand, averages results over the prediction horizon $l$ as well.

The results for our primary data split are detailed in Table 1 and visualized in Figure 4. The velocity error decreases over the prediction horizon with different rates for different methods. The constant velocity metric gives the smallest velocity error for short horizon, but the error grows quickly. Conversely, the error for the Newell prediction starts somewhat higher but remains constant over time. These baselines are outperformed by our best performing model RelLSTM-FC, whose error is close to or better than the baselines across the forecasting window. In particular, it blends the positive characteristics of both baselines: having small error for small $\theta$ and low error growth for higher $\theta$. RelLSTM-FC has slightly higher error than constant prediction for small $\theta$, it has lower error than both baselines over $15\leq\theta\leq 30$, while it is surpassed by Newell’s model for larger $\theta$. Note that it is not possible to predict beyond $\theta>T(t)$ since at this point the traffic conditions of the ego vehicle have not yet been encountered by the lead vehicle.

Meanwhile, the Ego-only LSTM-FC architecture, which takes only the ego car’s velocity as input, has worse performance than both first principle-based methods and RelLSTM-FC. This justifies that using data from V2V connectivity has significant benefits and also validates our hybrid approach. Lastly, we compare to a monolithic fully connected network Vel-FC which has the same input and output as VelLSTM-FC (see Appendix B). These networks have similar performance, and they are both outperformed by ResLSTM-FC that gives the overall best average velocity error. These suggest that the most significant parts of our method are integrating deep learning with the first principle-based Newell prediction and predicting the residual from Newell’s model as output.

Figure 5(a,b,c) provide further visualization of the prediction accuracy by showing the absolute prediction error for the constant prediction, Newell’s model and ResLSTM-FC. Figure 5(d) shows their comparison for a selected horizon, while Figure 5(e) indicates the physically achievable maximum horizon $T(t)$. Sample predictions are visualized in Figure 6. For each network architecture, training was repeated five times. In all figures purple line shows the mean and shading indicates plus minus one standard deviation over five trained networks.

To investigate the robustness of our method, we also test using our alternative data split where training and validation data are in the middle of the traffic jam characterized by variable and slower speeds. However, the test set is from a period of faster and more free flowing traffic. Results are shown in Table 2. Velocity errors are smaller across all methods for this test set since cars have little variability in speed. The performance of the deep learning methods is worse relative to constant velocity and Newell baselines since small variations in the speed are hard to predict. However, we do see that our methods generalize reasonably well over the distributional shift as their overall error goes down despite the higher magnitude of the velocity outputs.