Accurate real-time traffic state forecasting plays a pivotal role in traffic control research. In particular, the CIRCLES consortium project necessitates predictive techniques to mitigate the impact of data source delays. After the success of the MegaVanderTest experiment, this paper aims at overcoming the current system limitations and develop a more suited approach to improve the real-time traffic state estimation for the next iterations of the experiment. In this paper, we introduce the SA-LSTM, a deep forecasting method integrating Self-Attention (SA) on the spatial dimension with Long Short-Term Memory (LSTM) yielding state-of-the-art results in real-time mesoscale traffic forecasting. We extend this approach to multi-step forecasting with the n-step SA-LSTM, which outperforms traditional multi-step forecasting methods in the trade-off between short-term and long-term predictions, all while operating in real-time.