In this study, a comprehensive examination, both theoretically and practically, is undertaken on Multi-Agent Reinforcement Learning algorithms (MARL). The investigation is situated within the context of real adaptive traffic signal control (ATSC) scenarios, with the primary objective being to validate the algorithms theoretical framework and evaluate their effectiveness, robustness, and applicability in real-world settings. The study uses two traffic networks in the city of Bologna, Italy, as examples. Key findings underscore the necessity of situating the algorithms within the context of a Partially Observable Markov Decision Process (POMDP), inherently characterizing them as non-Markovian. The equations are reformulated within this framework. Simulation results reveal that one of the studied algorithms, MA2C, consistently achieves significant traffic de-congestion in the considered scenarios. In general, its performance continually improves over time, resulting in a reduction of running vehicles by a factor of approximately 70 at the conclusion of the simulation. A training strategy independent of the specific vehicle flow has been implemented, rendering it adaptable for use with various traffic loads.