We study random and periodic sleep schedules from the point of view of delay in detecting the target.We consider sleep schedules in which a sensor in“inactive”mode wakes up either randomly or periodically to detect presence of the target within its vicinity resulting into two sleep schedules:(a)random wake-up schedule,and(b)periodic wake-up schedule respectively.Specifically,we analyse and obtain for the random wake-up schedule the expected delay in detection, and the delay,such that with probability P,the delay is less than the computed value.For the periodic wake-up schedule we show that there exists an upper bound on the delay.Further we compute the average value of delay.We have shown that the theoretically computed averages and the upper bounds on the delay match with the simulation results for the random wake-up and periodic wake-up schedules. We study random and periodic sleep schedules from the point of view of delay in detecting the target. We consider sleep schedules in which a sensor in “inactive” mode wakes up either randomly or periodically to detect presence of the target within (a) random wake-up schedule, and (b) periodic wake-up schedule respectively. Specifically, we analyze and obtain for the random wake-up schedule the expected delay in detection, and the delay, such that with probability P, the delay is less than the computed value. For the periodic wake-up schedule we show that there exists an upper bound on the delay. Focus we compute the average value of delay. We have shown that the theoretically computed averages and the upper bounds on the delay match with the simulation results for the random wake-up and periodic wake-up schedules.