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This paper develops an effective randomized on-demand QoS routing algorithm on networks with inaccurate link-state information. Several new techniques are proposed in the algorithm. First, the maximum safety rate and the minimum delay for each node in the network are pre-computed, which simplify the network complexity and provide the routing process with useful information. The routing process is dynamically directed by the safety rate and delay of the partial routing path developed so far and by the maximum safety rate and the minimum delay of the next node. Randomness is used at the link level and depends dynamically on the routing configuration. This provides great flexibility for the routing process, prevents the routing process from overusing certain fixed routing paths, and adequately balances the safety rate and delay of the routing path. A network testing environment has been established and five parameters are introduced to measure the performance of QoS routing algorithms.Experimental results demonstrate that in terms of the proposed parameters, the algorithm outperforms existing QoS algorithms appearing in the literature.