# Suppose we have a paging system with 4 frames and 12 pages, where the number of frames denotes the number of pages that can be held in RAM at any given time. Assume the pages are accessed by some program in the order shown below, from left to right. Also, assume that the program has just started, so the frames are initially empty. How many page faults will be generated assuming that the LRU (Least Recently Used) algorithm is being used?

## Order in which pages are accessed: 3, 4, 2, 1, 4, 7, 2, 5, 3, 6, 1, 3

Reading the previous discussion on virtual memory is recommended to better understand this problem. A page fault occurs when a program tries to access a page that is mapped in address space, but not loaded in the physical memory (the RAM). In other words, a page fault occurs when a program can not find a page that it’s looking for in the physical memory, which means that the program would have to access the paging file (which resides on the hard disk) to retrieve the desired page.

The term page fault is a bit misleading as it implies that something went seriously wrong. Although page faults are undesirable – as they result in slow accesses to the hard disk – they are quite common in any operating system that uses virtual memory.

Now, we need to actually solve the problem. The easiest way to do this is to break the problem down into 12 steps (where 12 is the number of pages) to see what happens each time a page is referenced by the program, and at each step see whether a page fault is generated or not. Of course, we want to keep track of what pages are currently in the physical memory (the RAM). The first four page accesses will result in page faults because the frames are initially empty. After that, if the program tries to access a page that’s already in one of the frames then there’s no problem. But if the page that the program is trying to access is not already in one of the frames then that results in a page fault. In this case, we have to determine which page we want to take out (or ‘swap’) from the RAM, and for that we use the LRU algorithm.

Some other algorithm could be used as well – FIFO and NRU are other possibilities – and as a group these are known as page replacement algorithms. Applying the LRU algorithm to this problem is fairly straightforward – you simply remove the page that was least recently used. Proceeding in this manner leads to the chart shown below – you should try this out yourself before looking at the answer.

 Page referenced Page Fault Resulting List 3 Y 3 4 Y 3,4 2 Y 3,4,2 1 Y 3,4,2,1 4 N 3,2,1,4 7 Y 2,1,4,7 2 N 1,4,7,2 5 Y 4,7,2,5 3 Y 7,2,5,3 6 Y 2,5,3,6 1 Y 5,3,6,1 3 N 5,6,1,3

We can see that 9 page faults will be generated in this scenario.

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