This paper investigates the M/M/c queueing model with priority and variable matching rates, aiming to optimize service efficiency in practical scenarios such as ride-hailing platforms. By employing the methods of quasi-birth-and-death processes and matrix geometric solutions, steady-state equations are established to analyze the effects of customer arrival rates, matching rates, and priority on system performance. The study reveals that appropriately adjusting the matching rate and service threshold can significantly reduce customer queue lengths and enhance user experience. During busy periods, the priority mechanism effectively increases server utilization and ensures the service quality for high-priority customers. Comparative results indicate that the proposed model reduces average queue length by 34.4% and 39.5% compared to two baseline models without priority, demonstrating its effectiveness and applicability in improving service efficiency.