# Weather-Aware Long-Range Traffic Forecast Using Multi-Module Deep Neural Network
## 3 New Traffic Forecasting Model Using Multi-Module Deep Neural Networks  
The TW-DNN, which precisely forecasts the speeds of highway networks, is introduced in this section. Before describing the system, we first introduce the major variables that will be used, as well as their formats. Traffic data consists of data regarding the speeds and single-lane flows of each predefined road section (i.e., _links_), and time. The set of links constructs the highway graph, where edges and vertices correspond to links and the intersections, respectively. The specific information of a link such as the number of lanes, length, highway route number, direction, and _link shift_ (the distance of the current link from the origin of the highway) is stored in the corresponding edge. Because traffic varies with time, the temporal information such as the date, time, and holiday information is included. In addition, weather data is included; from these, we consider hourly weather as well as daily weather information. The hourly weather information represents the local weather of the link, whereas daily weather covers the weather of nine major cities of South Korea, measured and forecasted by the Korea Meteorological Administration [24]. Although hourly weather is not available, we estimate it by linear interpolation. Now, the traffic forecasting system updates the weather every hour. Table 1 shows an example of inputs for one link. Date, time, and weather data are renewed at the corresponding update time. All numerical data are normalized to be within \([0,1.0]\). TW-DNN forecasts all traffic values for a given time range \([t_{\text{start}},t_{\text{end}}]\) with a resolution of a time interval (or window) \(\Delta t\). As shown in Figure 1, there are two parts functioning together depending on the prediction periods, as explained below. 1. **The initial traffic predictor** predicts the _initial_ speeds and single-lane flows for the first \(R\)-time intervals, \([t_{\text{start}},t_{\text{start}}+(R-1)\Delta t]\), using the given link information, date, time, and weather. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Data Class** & **Data Subclass** & **Example \#1** & **Example \#2** & **Example \#3** \\ \hline \multirow{3}{*}{**Link information**} & Route number & 10 & 10 & 10 \\ \cline{2-5}  & Route direction & To East & To East & To East \\ \cline{2-5}  & Linkshift & 50 km & 50 km & 50 km \\ \hline \multirow{3}{*}{**Date \& time**} & Date \& time information & 23 September 2016 23:55 & 24 September 2016 0:00 & 24 September 2016 0:05 \\ \cline{2-5}  & Day of the year & 267 & 268 & 268 \\ \cline{2-5}  & Day of the week & Wednesday & Thursday & Thursday \\ \cline{2-5}  & Holiday & No & No & No \\ \hline \multirow{3}{*}{**Hourly weather**} & Avg. temperature & 21.3 \({}^{\circ}\)C & 16.2 \({}^{\circ}\)C & 16.2 \({}^{\circ}\)C \\ \cline{2-5}  & Avg. windspeed & 2.5 m/s & 8.1 m/s & 8.1 m/s \\ \cline{2-5}  & Rainfall & No, 0 mm & Yes, 5 mm & Yes, 5 mm \\ \cline{2-5}  & Snowfall & No, 0 mm & No, 0 mm & No, 0 mm \\ \hline \multirow{3}{*}{**Daily weather of city \#1**} & Min/Max temperature & 16.3 \({}^{\circ}\)C/26.8 \({}^{\circ}\)C & 16.4 \({}^{\circ}\)C/28.0 \({}^{\circ}\)C & 16.4 \({}^{\circ}\)C/28.0 \({}^{\circ}\)C \\ \cline{1-1} \cline{2-5}  & Cloudiness & Light & Heavy & Heavy \\ \cline{1-1} \cline{2-5}  & Rainfall/Snowfall & No/No & Yes/No & Yes/No \\ \hline \multirow{2}{*}{...} &... &... &... &... \\ \cline{1-1} \cline{2-5}  &... &... &... &... \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Examples of input data used in our traffic forecasting system. 2. **The iterative traffic predictor** computes the speeds and single-lane flows for each link type (e.g., ordinary link, terminus link, and interchange link) of the following intervals \([t_{\text{start}}+R\Delta t,t_{\text{end}}]\) sequentially, i.e., starting from \(t_{\text{start}}+R\Delta t\), followed by \(t_{\text{start}}+(R+1)\Delta t\),..., \(t_{\text{end}}\).