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In paged storage systems, page replacement policies generally depend on a use bit for each page frame. The use bit is automatically turned on when the resident page is referenced. Typically, a page is considered eligible for replacement if its use bit has been scanned and found to be off on µ consecutive occasions, where µ is a parameter of the algorithm. This investigation focuses on the dependence of the number of bit-scanning operations on the value of µ and on properties of the string of page references. The number of such operations is a measure of the system overhead incurred while making replacement decisions. In particular, for several algorithms, the number of scans per reference is shown to be approximately proportional to µ However, empirical results from single-program traces show that the value of µ has little effect on the miss ratio. Although the miss ratios for the bit-scanning algorithms are close to those of least recently used (LRU), it is pointed out that increasing the value of µ need not bring the bit-scanning policies closer to LRU management.