||One fundamental issue in sensor networks is the coverage problem. Using coverage control, the space resources of networks are optimally utilized, and the monitoring and transfer are done better. K-coverage is a classic issue in wireless sensor network (WSN) deployment. Existing works typically assumes that every position in the monitoring field is covered by at least k sensor nodes at any given time. This may not always be necessary because certain events to be monitored will last only for a short period of time. In this work, we study a new way of k-coverage. We include the time dimension in the traditional k-coverage problem, and denote it as tk-coverage. In the context of tk-coverage, sensor nodes can apply periodical sleeping strategies. A corresponding tk-coverage (TKC) model is proposed to analyze the detection delay according to the duration of the event u. The proposed tk-coverage can balance detection delay by adjusting the sleeping strategies of sensor nodes. Comprehensive simulations have been conducted to validate the effectiveness and demonstrate the efficiency of this solution.