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Write a program that will demonstrate the difference between using a local page replacement policy and a global one for the simple case of two processes. You will need a routine that can generate a page reference string based on a statistical model. This model has $N$ states numbered from $0$ to $N − 1$ representing each of the possible page references and a probability $p_{i}$ associated with each state $i$ representing the chance that the next reference is to the same page. Otherwise, the next page reference will be one of the other pages with equal probability.

- Demonstrate that the page reference string-generation routine behaves properly for some small $N.$
- Compute the page fault rate for a small example in which there is one process and a fixed number of page frames. Explain why the behavior is correct.
- Repeat part $(b)$ with two processes with independent page reference sequences and twice as many page frames as in part $(b).$
- Repeat part $(c)$ but using a global policy instead of a local one. Also, contrast the per-process page fault rate with that of the local policy approach.