This work considers a parallel task execution strategy in vehicular edge computing (VEC) networks, where edge servers are deployed along the roadside to process offloaded computational tasks of vehicular users. To minimize the overall waiting delay among vehicular users, a novel task offloading solution is implemented based on the network cooperation balancing resource under-utilization and load congestion. Dual evaluation through theoretical and numerical ways shows that the developed solution achieves a globally optimal delay reduction performance compared to existing methods, which is also validated by the feasibility test over a real-map virtual environment. The in-depth analysis reveals that predicting the instantaneous processing power of edge servers facilitates the identification of overloaded servers, which is critical for determining network delay. By considering discrete variables of the queue, the proposed technique's precise estimation can effectively address these combinatorial challenges to achieve optimal performance.