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Quickest detection theory has previously been applied to the problem of spectrum sensing. By detecting the onset of an idle channel period, quickest detectors minimize the time required to search for an idle period. These methods are based on detection of a single change point, which implies that change in the channel's usage state is assumed to occur only once. Since the channel state may transition continuously between busy and idle states via an ON-OFF process, an alternative formulation based on partially observable Markov decision processes (POMDP) has been recently proposed. In this paper, Page's cumulative sum sequential analysis method (CUSUM) and multiband multi-sensor spectrum sensing (MMSSD) based on POMDP are brought into a similar context and compared. Next, the ON-OFF process model itself is assessed. The POMDP formulation assumes an ON-OFF process model where the busy and idle periods are geometrically distributed. While this model is desirable for its analytical tractability, its applicability to reflect the dynamics of actual spectral usage, which are derived from real data traffic, is assessed.