Lecture 40 Syed Mansoor Sarwar Operating Systems Lecture 40 Syed Mansoor Sarwar

© Copyright Virtual University of Pakistan Agenda for Today Review of the previous lecture Belady’s Anomaly Page Replacement Algorithms Least Frequently Used (LFU) Most Frequently Used (MFU) Page Buffering Algorithm Allocation of Frames Minimum Number of Frames Thrashing 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Review of Lecture 39 Page Replacement Page Replacement Algorithms First-In-First-Out (FIFO) Optimal Replacement Least Recently Used (LRU) 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Page Replacement 30 November 2018 © Copyright Virtual University of Pakistan

Page Replacement Algorithms First-In-First-Out (FIFO) Optimal Least Recently Used (LRU) Counter-based implementation Stack-based implementation 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan FIFO Algorithm Number of frames allocated = 3 Reference string: 1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5 Number of page faults = 9 1 4 5 2 3 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan FIFO Algorithm Number of frames allocated = 4 Reference string: 1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5 Number of page faults = 10 1 5 4 2 3 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan FIFO Algorithm Belady’s Anomaly “For some page replacement algorithms, the page fault rate may increase as the number of allocated frames increases.” 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Belady’s Anomaly 30 November 2018 © Copyright Virtual University of Pakistan

Stack Replacement Algorithms A class of page replacement algorithms with the following property: Set of pages in the main memory with n frames is a subset of the set of pages in memory with n+1 frames Do not suffer from Belady’s Anomaly Example: LRU 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan LRU Algorithm Number of frames allocated = 3 Reference string: 1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5 Number of page faults = 10 1 4 5 3 2 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan LRU Algorithm Number of frames allocated = 4 Reference string: 1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5 Number of page faults = 8 1 5 2 3 4 30 November 2018 © Copyright Virtual University of Pakistan

LRU Approximation Algorithm Use of reference bit With each page associate a bit, initially = 0 When page is referenced bit set to 1. Replace the one which is 0 (if one exists). We do not know the order, however. 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Least Frequently Used Least Frequently Used (LFU) Replace the page with the smallest reference count. Based on the locality of reference concept—least frequently used page is not in the current locality 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Most Frequently Used Most Frequently Used (MFU) The page with the smallest count was probably just brought in and has yet to be used; it will be in the locality that has just started. 30 November 2018 © Copyright Virtual University of Pakistan

Page Buffering Algorithm OS may keep a pool of free frames A process in need can be given a frame quickly Victims are selected and free frames are added to the pool in the background 30 November 2018 © Copyright Virtual University of Pakistan

Page Buffering Algorithm OS may keep a list of modified pages In the background, the modified pages are written to disk Less dirty pages in the system at page replacements Used together with FIFO replacement in the VAX/VMS operating system 30 November 2018 © Copyright Virtual University of Pakistan

Local vs Global Replacement If process P generates a page fault Select for replacement one of its frames. Select for replacement a frame from a process with lower priority number. 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Allocation of Frames Each process needs a minimum number of frames so that its execution may be guaranteed on a given machine . Example: MOV X,Y Instruction is 6 bytes long (16-bit offsets) and might span 2 pages. 2 pages to handle from. 2 pages to handle to. 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Allocation of Frames 1 2 3 4 5 6 7 8 9 Instruction X Y 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Allocation of Frames Three major allocation schemes: Fixed allocation Free frames are equally divided among processes Proportional Allocation Number of frames allocated to a process is proportional to its size Priority allocation Priority-based proportional allocation 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Frame Allocation Number of free frames = 64 Number of processes = 3 Process sizes P1 = 10 pages P2 = 40 pages P3 = 127 pages Fixed allocation 64/3 = 21 frames per process and one put in the free frames list 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Frame Allocation Proportional Allocation si = Size of process Pi S = ∑ si m = Number of free frames ai = Allocation for Pi = (si / S) * m a1 = (10 / 177) * 64 = 3 frames a2 = (40 / 177) * 64 = 14 frames a3 = (127 / 177) * 64 = 45 frames Two free frames are put in the list of free frames 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Thrashing If a process does not have “enough” pages, the page-fault rate is very high. This leads to: Low CPU utilization Operating system thinks that it needs to increase the degree of multiprogramming. Another process added to the system—serious problem! 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Thrashing A process is thrashing if it is spending more time paging (i.e., swapping pages in and out) than executing Thrashing results in severe performance problems Low CPU utilization High disk utilization Low utilization of other I/O devices 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Thrashing 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Thrashing To stop thrashing, the degree of multiprogramming needs to be reduced Local page replacement prevents thrashing to spread among several processes However, a thrashing process consumes more resources 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Recap of Lecture Belady’s Anomaly Page Replacement Algorithms Least Frequently Used (LFU) Most Frequently Used (MFU) Page Buffering Algorithm Allocation of Frames Minimum Number of Frames Thrashing 30 November 2018 © Copyright Virtual University of Pakistan

© Copyright Virtual University of Pakistan Operating Systems Lecture 40 Syed Mansoor Sarwar 30 November 2018 © Copyright Virtual University of Pakistan