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In this paper we study the problem of joint design of routing and resource allocation in cognitive radio based wireless mesh networks. Our study focuses on a cognitive system model in which secondary nodes have delay sensitive traffic with packet delivery deadline, which limits the packet lifetime inside the network. The network is analyzed from a queuing theory perspective, and the joint routing and resource allocation problem is formulated as a non-linear integer programming problem. The objective is to optimize the overall packet dropping probability. We then present an efficient solution method based on the relaxation of the integer valued constraints. Numerical results demonstrate the efficacy of the proposed joint design and the solution procedure.