# Page Replacement Algorithms

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## The WSClock Page Replacement Algorithm

The basic working set algorithm is cumbersome since the entire page table has to be scanned at each page fault until a suitable candidate is located. An improved algorithm, that is based on the clock algorithm but also uses the working set information is called WSClock (Carr and Hennessey, 1981). Due to its simplicity of implementation and good performance, it is widely used in practice.

The data structure needed is a circular list of page frames, as in the clock algorithm, and as shown in Fig. 4-7(a). Initially, this list is empty. When the first page is loaded, it is added to the list. As more pages are added, they go into the list to form a ring. Each entry contains the Time of last use field from the basic working set algorithm, as well as the R bit (shown) and the M bit (not shown).

As with the clock algorithm, at each page fault the page pointed to by the hand is examined first. If the R bit is set to 1, the page has been used during the current tick so it is not an ideal candidate to remove. The R bit is then set to 0, the hand advanced to the next page, and the algorithm repeated for that page. The state after this sequence of events is shown in Fig. 4-7(b).

Now consider what happens if the page pointed to has R = 0, as shown in Fig. 4-7(c). If the age is greater than t and the page is clean, it is not in the working set and a valid copy exists on the disk. The page frame is simply claimed and the new page put there, as shown in Fig. 4-7(d). On the other hand, if the page is dirty, it cannot be claimed immediately since no valid copy is present on disk. To avoid a process switch, the write to disk is scheduled, but the hand is advanced and the algorithm continues with the next page. After all, there might be an old, clean page further down the line that can be used immediately.

In principle, all pages might be scheduled for disk I/O on one cycle around the clock. To reduce disk traffic, a limit might be set, allowing a maximum of n pages to be written back. Once this limit has been reached, no new writes are scheduled.

What happens if the hand comes all the way around to its starting point? There are two cases to distinguish:

1. At least one write has been scheduled.

2. No writes have been scheduled.

In the former case, the hand just keeps moving, looking for a clean page. Since one or more writes have been scheduled, eventually some write will complete and its page will be marked as clean. The first clean page encountered is evicted. This page is not necessarily the first write scheduled because the disk driver may reorder writes in order to optimize disk performance.

Figure 4-7 Operation of the WSClock algorithm. (a) and (b) give an example of what happens when R = 1. (c) and (d) give an example of R = 0.

In the latter case, all pages are in the working set, otherwise at least one write would have been scheduled. Lacking additional information, the simplest thing to do is claim any clean page and use it. The location of a clean page could be kept track of during the sweep. If no clean pages exist, then the current page is chosen and written back to disk.