In the paper, we consider the end-to-end routing and link scheduling problem for multi-hop wireless sensor networks. The efficient link scheduler under our consideration is intended to assign time slots to different users so as to minimize channel usage subject to constraints on data rate, delay bound, and delay bound violation probability. We also present a coupled robust multi-path routing structure satisfying the restriction of flows over fading channels based on an SINR-based interference model. Here the effective capacity (EC) model is used and then the joint routing and link scheduling can be formulated as a mixed integer optimization problem. Moreover, because the mixed integer optimization problem is NP-complete, we propose a computationally feasible EC-based Column-Generation-Algorithm (EC-CGA) to search for a sub-optimal solution. Simulation results are given to evaluate the performance of our proposed scheme.