A successful cognitive radio network (CRN) needs a fast and reliable spectrum sensing scheme to enable secondary users to utilise available channels. In this work, the authors first revisit conventional urn models for channel availability (the random independent identical distribution (i.i.d) models) and introduce a correlated Markov model which is apropos for scenarios with memory. After proposing an n-step serial search strategy, the authors investigate the performance of random and serial search schemes for the above occupancy models in terms of the mean number of steps for detection of an `open` channel. The analytical results of the average detection are then presented for different sensing schemes under both random and correlated channel model. The authors then highlight a key trade-off underlying the overall mean time to detect a free channel: it is a function of both the mean number of steps and the sensing time per step. Reduced sensing duration in each step leads to lower detection probability (Pd) thereby increasing the average number of search steps required. This suggests that there exists an optimal sensing duration that minimises the overall mean detection time; this is analytically investigated (for low signal-to-noise ratio (SNR)) and verified by simulation results under various SNR environments.