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Service-oriented wireless sensor networks have recently been proposed to provide an integrated platform, where new applications can be rapidly developed through flexible service composition. In wireless sensor networks, sensors are periodically switched into the sleep mode for energy saving. This, however, will cause the unavailability of nodes, which, in turn, incurs disruptions to the service compositions requested by the applications. Thus, it is desirable to maintain enough active sensors in the system to provide each required service at any time in order to achieve dependable service compositions for various applications. In this paper, we study the cross-layer sleep scheduling design, which aims to prolong the network lifetime while satisfying the service availability requirement at the application layer. We formally define the problem, prove that the problem is NP-hard, and develop two approximation algorithms based on the LP relaxation and one efficient reordering heuristic algorithm. The proposed work will enhance the dependability of the service composition in service-oriented wireless sensor networks.