A method performed by a terminal in a wireless communication system, the method comprising: receiving, from a base station via a radio resource control, RRC, signaling, discontinuous reception, DRX, related information including a timer value related to an on-duration, a timer value related to a DRX inactivity, a timer value related to a short DRX cycle, a short DRX cycle length value, and a long DRX cycle length value; receiving, from the base station, a DRX Medium Access Control, MAC, Control Element, CE, with a zero bit payload, the MAC CE including a logical channel identifier, LCID, in case that a timer related to on-duration is running; identifying a type of the MAC CE based on the LCID; in case that the type of the MAC CE is associated with a short DRX: stopping the timer related to on-duration and the timer related to DRX inactivity; and maintaining a DRX cycle with the short DRX cycle length value; and in case that the type of the MAC CE is associated with a long DRX: stopping the timer related to on-duration, the timer related to DRX inactivity, a the timer related to the short DRX cycle, a HARQ RTT Timer and a DRX Retransmission timer; and changing the DRX cycle from the short DRX cycle length value to the long DRX cycle length value, wherein the type of the MAC CE is associated with the short DRX in case that a value of the LCID is 11110, and wherein the type of the MAC CE is associated with the long DRX in case that the value of the LCID is 11010. receiving, from a base station via a radio resource control, RRC, signaling, discontinuous reception, DRX, related information including a timer value related to an on-duration, a timer value related to a DRX inactivity, a timer value related to a short DRX cycle, a short DRX cycle length value, and a long DRX cycle length value; receiving, from the base station, a DRX Medium Access Control, MAC, Control Element, CE, with a zero bit payload, the MAC CE including a logical channel identifier, LCID, in case that a timer related to on-duration is running; identifying a type of the MAC CE based on the LCID; in case that the type of the MAC CE is associated with a short DRX: stopping the timer related to on-duration and the timer related to DRX inactivity; and maintaining a DRX cycle with the short DRX cycle length value; and stopping the timer related to on-duration and the timer related to DRX inactivity; and maintaining a DRX cycle with the short DRX cycle length value; and in case that the type of the MAC CE is associated with a long DRX: stopping the timer related to on-duration, the timer related to DRX inactivity, a the timer related to the short DRX cycle, a HARQ RTT Timer and a DRX Retransmission timer; and changing the DRX cycle from the short DRX cycle length value to the long DRX cycle length value, stopping the timer related to on-duration, the timer related to DRX inactivity, a the timer related to the short DRX cycle, a HARQ RTT Timer and a DRX Retransmission timer; and changing the DRX cycle from the short DRX cycle length value to the long DRX cycle length value, wherein the type of the MAC CE is associated with the short DRX in case that a value of the LCID is 11110, and wherein the type of the MAC CE is associated with the long DRX in case that the value of the LCID is 11010.