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This paper investigates the routing efficiency problem with quality of service (QoS). A solution to this problem is needed to provide real-time communication service to connection-oriented applications, such as video and voice transmissions. We propose a new weight parameter by efficiently combining two independent measures, the cost and the delay. The weight ω plays on important role in combining the two measures. If the ω approaches 0, then the path delay is low. Otherwise the path cost is low. Therefore if we decide an ω, we then find the efficient routing path. A case study shows various routing paths for each ω. We also use simulations to show the variety of paths for each ω. When network users have various QoS requirements, the proposed weight parameter is very informative.