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In a user equipment (UE) which supports multiple radio access technologies (multi-RAT), the access technology dependent part i.e., access stratum (AS) draw significant amount of power either in active or idle state. Simultaneous switching ON all UE supported idle RAT-ASs to support multi-RAT mobility, apart from the active RAT-AS can drain battery fast. Even the periodic cell search done by idle RAT-AS can lead to significant power consumption. This paper investigates whether the idle RAT-ASs in a UE can be switched OFF when there are not many cells of the particular RAT in the neighbourhood. The authors propose using of various back-off algorithms to schedule cell search in idle RAT-AS. Using the number of searched cells as a criterion, UE achieves power saving by autonomously switching ON or OFF the idle RAT-AS. Simulation results reveal that linear back-off algorithm performs well for back-off window size of 1 whereas for higher window size binary exponential back-off algorithm performs better with respect to power saving. Also, assuming an idle WCDMA RAT-AS supported by the UE we numerically prove that our approach achieves better power saving than conventional idle mode discontinuous reception (DRX) approach proposed by the standard. Results further reveal that a combination of idle mode DRX and our proposed approach leads to even higher power saving, i.e., 94% with respect to 3GPP proposed idle mode DRX only mechanism for WCDMA.