Congestion in large cities is widely recognized as a problem that impacts various aspects of society, including the economy and public health. To support the urban traffic system and to mitigate traffic congestion and the damage it causes, in this article we propose an assistant Intelligent Transport Systems (ITS) service for traffic management in Vehicular Networks (VANET), which we name FOXS-GSC, for Fast Offset Xpath Service with hexaGonS Communication. FOXS-GSC uses a VANET communication and fog computing paradigm to detect and recommend an alternative vehicle route to avoid traffic jams. Unlike the previous solutions in the literature, the proposed service offers a versatile approach in which traffic road classification and route suggestions can be made by infrastructure or by the vehicle itself without compromising the quality of the route service. To achieve this, the service operates in a decentralized way, and the components of the service (vehicles/infrastructure) exchange messages containing vehicle information and regional traffic information. For communication, the proposed approach uses a new dedicated multi-hop protocol that has been specifically designed based on the characteristics and requirements of a vehicle routing service. Therefore, by adapting to the inherent characteristics of a vehicle routing service, such as the density of regions, the proposed communication protocol both enhances reliability and improves the overall efficiency of the vehicle routing service. Simulation results comparing FOXS-GSC with baseline solutions and other proposals from the literature demonstrate its significant impact, reducing network congestion by up to 95% while maintaining a coverage of 97% across various scenery characteristics. Concerning road traffic efficiency, the traffic quality is increasing by 29%, for a reduction in carbon emissions of 10%.