Intelligent Transportation System (ITS) offers outstanding features, including security applications and emergency alerts. Unfortunately, ITS limits traffic control services, adaptability, and adjustability due to the traffic volume. Hence, expanding the standard Vehicular Ad hoc Networks (VANET) framework is a requirement. As a result, in the latest days, the concept of Software-Defined Networking based Vehicular Ad hoc Networks (SDN-VANETs) has drawn considerable attention, creating VANETs smarter. The SDN-VANETs design is capable of addressing the aforementioned VANET issues. The integrated (analytically) SDN architecture is customizable and it also contains domain knowledge about the VANET architecture. Packet forwarding is a fundamental challenge in VANET wherein a router, as in the form of an RSU, determines the next hop of every signal in the pipeline to provide it to its recipient as fast as possible. Reinforcement Learning (RL) is used to develop autonomous routing protocol rules; however, the limitation of RL's depth prevents it from representing more comprehensively dynamic network conditions, restricting its true value. In this research, we present a VANET infrastructure based on SDN + EDGE with a new Deep Reinforcement Learning (DRL) route optimization framework, "Gated Recurrent Reinforcement Learning (GRRL)" neural network, whereby each router has its hybrid GRU + Feed Forward Neural Network (NN) for learning and making decisions in an entirely distributed environment. The GRRL collects routing characteristics from valuable information about huge backlog packets and previous operations, substantially approximating the weighting scheme of Q-learning. We also enable every route to connect with its immediate neighbors regularly such that a more comprehensive view of network topology may be integrated. Trial findings demonstrated that the multi-agent GRRL strategy could achieve a delicate balance between congestion awareness and the fastest routes, considerably reducing packet transmission time in general network topologies compared to its competitors.