Modern multimedia sensor networks impose strict constraints on both the delay and energy consumption when time-critical data must be reported to the sink within a limited bandwidth without any loss. Failure to transmit an event to the sink occurs for many reasons, including inherence limitations of sensors, power consumption, and reliability. We propose a mathematical model for a novel quality-of-service (QoS) routingdetermination method. The proposed scheme enables determining the optimal path to provide appropriate shared radio satisfying the QoS for a wide range of real-time intensive media. The mathematical model is based on the Lagrangian relaxation method, to control adaptive switching of hop-by-hop QoS routing protocols. The embedded criteria for each objective function are used to decide which path from source to sink will be selected. Simulation results show that, compared with existing routing protocols, the approach proposed in this paper significantly improves the packet received ratio, energy consumption, and average end-to-end delay of the sensor node.