A demand paging system takes 50 time units to handle a page...

A demand paging system takes 50 time units to handle a page fault and 200 time units to replace a dirty page. Access time of memory is 2 time units. Probability of page fault and dirty page is $P$. Average access time is 4 time units. Then what is the value of $P ?$ (A) $0.037$ (B) $0.027$ (C) $0.012$ (D) $0.042$

Key Concepts

Demand Paging System

A demand paging system is a memory management technique where pages are loaded into memory only when they are needed, rather than pre-loading an entire program. This minimizes memory usage but can lead to delays if a page is not already in memory.

Page Fault

A page fault occurs when a referenced memory page is not found in main memory, prompting the operating system to fetch the missing page from secondary storage. This causes a significant delay compared to normal memory access times.

Dirty Page

A dirty page is a page in memory that has been modified since it was loaded from disk. When such a page is replaced, it must first be written back to disk, thereby incurring additional time overhead compared to simply loading an unmodified page.

Average Memory Access Time

Average memory access time is a performance metric that accounts for both the normal memory access time and the increased time due to events like page faults or dirty page replacements. It is computed as a weighted average based on the probability of these events and their respective access times.

Probability and System Overhead

The probability of encountering events like a page fault or a dirty page directly affects the overall system performance. When these events occur, they introduce delays proportional to the time penalties associated with handling them, which must be factored into performance calculations such as the average access time.

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