## 6 The Numerical Quantization Evaluation  
The neural network described in Section 3 was trained and tested in MATLAB to validate the traffic forecasting system and to compute the necessary parameters for real-time implementation using the previously described hardware and software platform. Using floating-point types on a microprocessor without a math coprocessor is inefficient, both in terms of code size and execution speed [15]. Therefore, one should consider replacing code that uses floating-point operations with code that uses integers, because these are more efficient. The Cortex M3 ARM architecture does not have a math co-processor or the operation required (specifically, an activation function should be implemented in floating  
Figure 12: Overall performance (infinite precision) [15]. point implementations). Our implementation uses the C compiler support for floating point representation. In the representation of a signed 32-bit floating-point number, the exponent is 8 bits, and the mantissa is 23 bits. For a signed 64-bit floating-point number, the exponent is 11 bits, and the mantissa is 52 bits. The functions _dot product_, _sigmoid_, and _tanh_ were implemented in C language using 32-bit floating-point variable representations to determine the forecasting system accuracy with finite precision. The statistics of quantization errors (mean and standard deviation) for the _dot product_ function are represented in Table 1. The quantization errors for this function are cumulative and, therefore, they depend on the number of features and number of classes. The statistics of quantization errors for the other mentioned functions are not dependent on the number of features. These  
communication network load. Two scenarios were evaluated considering how often the vehicles read traffic sensors: periodically or change-triggered input reading. In both scenarios, a LSTM neural network is involved. This neural network predicts the information in the graph node (traffic and/or speed on edges from node) using as features real or predicted traffic information. Input data filtering is also evaluated. The main results show that filtering improves the forecasting accuracy in both scenarios with a slight increase in computational effort. The second scenario performs better than the first scenario but is sensitive to relatively slow changes in traffic. Also, the paper analyzes and evaluates how a neural network can be implemented and tested using common microcontrollers. The impact of variables' quantization on the prediction and the total system computation time were considered. The experiments show that the implementation of the LSTM neural network has very good performance. The accuracy does not decrease significantly due to the finite precision of the microcontrollers' registers, and the implementation time is in real time for a reasonable number of features and classes in a traffic forecasting system. The proposed neural network framework is flexible and requires a small memory amount for coding. It can be used easily to realize various neural network models. More sophisticated models of graph-based neural network testing using the proposed framework could be assessed. Conceptualization, S.Z. and M.V. ; methodology, R.Z. ; software, S.Z. ; validation, D.G., R.Z. and M.V. ; formal analysis, D.G. ; investigation, M.V. ; resources, M.V. ; data curation, R.Z. ; writing--original draft preparation, S.Z. ; writing--review and editing, M.V. and S.Z. ; visualization, D.G. ; funding acquisition, S.Z. and M.V. All authors have read and agreed to the published version of the manuscript. The research leading to these results received funding from the Research Centre on Systems Software and Networks in Telecommunication (CCSRST) and from the NO Grants 2014-2021 under Project contract no. 42/2021, RO-NO-2019-0499--\"A Massive MIMO Enabled IoT Platform with Networking Slicing for Beyond 5G IoV/V2X and Maritime Services\"--SOLID-B5G. Not applicable. The data presented in this study are available on request from the corresponding author.