Recently power saving is a vital issue for wireless devices of 4G and 5G networks. A device enters in sleeping mode (short and long sleep cycle) when there is no arrival of traffic but wakeup once the arrival of traffic. Before wakeup, the UE user equipment (UE) spends the rest of the sleeping cycle which incurs a delay of service. There is a tradeoff between the length of a sleep cycle (power saving factor ids higher for longer sleep cycle) and mean delay of service. In this paper, a Markov chain is designed including timer inactivity, short sleep, and long sleep and active service states. The closedform solution of the chain is performed using node equations hence comparison of performance is made with previous work in the context of power-saving factor and mean delay. Both the power saving factor and mean delay of this paper are found marginally better than the previous work at lower packet arrival rate but at higher arrival rate performance are almost the same but claims some explanations.