Reducing transmission traffic delay is one of the most important issues that need to be considered for routing protocols, especially in the case of multimedia applications over vehicular ad hoc networks (VANET). To this end, we propose an extension of the FzGR (fuzzy geographical routing protocol), named MNH-FGR (multi-next-hops fuzzy geographical routing protocol). MNH-FGR is a multipath protocol that gains great extensibility by employing different link metrics and weight functions. To schedule multimedia traffic among multiple heterogeneous links, MNH-FGR integrates the weighted round-robin (WRR) scheduling algorithm, where the link weights, needed for scheduling, are computed using the multi-constrained QoS metric provided by the FzGR. The main goal is to ensure the stability of the network and the continuity of data flow during transmission. Simulation experiments with NS-2 are presented in order to validate our proposal. Additionally, we present a neural network algorithm to analyze and optimize the performance of routing protocols. The results show that MNH-FGR could satisfy critical multimedia applications with high on-time constraints. Also, the DNN model used can provide insights about which features had an impact on protocol performance.