When the system load is high or congestion occurs, a base station (BS) in the IEEE 802.16e metropolitan area network (MAN) is not able to transmit all buffered packets to mobile stations (MSs) within a frame interval, resulting in extra energy consumption for MSs to wake up for receiving pending packets. To save energy for such a situation, we first propose a schedulingbased delay-tolerant traffic indication message (D-TIM) scheme to enable a BS to properly schedule queued packets for non-real-time variable rate (NRT-VR) and best effort (BE) using information of delay threshold (DT), which can be derived from QoS parameters, and to determine the time offset between the frame in which an MS has to wake up and the frame containing a TIM message. With the time offset, MSs are able to wake up more precisely so that energy can be efficiently saved and less packet delay can be reached. Furthermore, two variants of D-TIM are also proposed for solving the problem of higher jitter to the unsolicited grant service (UGS). Through simulation, we demonstrate that D-TIM outperforms other related schemes in the literature in terms of energy efficiency and packet delay and the two variants reduce jitter greatly as compared to D-TIM while maintaining good energy efficiency and less packet delay.