Solution Set 5

Problem 1

Consider a toy paging system. There are four frames and six pages. In the sequence of events listed below, "Read I" means that an address in page I must be read; "Write I" means that an address in page I must be written to; "TICK" is a clock tick. (Keep in mind that the arguments to Read and Write are pages, not frames.) List the page faults that occur, and the frames chosen for the new pages, if the OS uses (A) the Not Recently Used (NRU) PRA; (B) the Second Chance PRA; (C) the aging PRA; (D) Belady's (optimal) algorithm. If the algorithm gives a tie between pages to replace, choose the one with the lower frame. Assume that memory is initially empty.
               NRU                           Second Chance
Time: Events:        Page to   Pages in            Page to  Pages in       FIFO queue
                     replace   frames (after       replace  frames (after
                               replacement)                 replacement)
   1  Write 1  FAULT.           1             FAULT.        1             [1]
   2  Read 2   FAULT.           1,2           FAULT.        1,2           [1,2]
   3  Write 3  FAULT.           1,2,3         FAULT.        1,2,3         [1,2,3]
   4  Read 4   FAULT.           1,2,3,4       FAULT.        1,2,3,4       [1,2,3,4]
   5  Write 5  FAULT. 2.        1,5,3,4       FAULT. 1.     5,2,3,4       [2,3,4,5]
   6  TICK
   7  Read 3          
   8  Read 2   FAULT. 4.        1,5,3,2 
   8  Write 1                                 FAULT. 4.     5,2,3,1       [5,2,3,1]
   9  Read 6   FAULT. 5.        1,6,3,2       FAULT. 5.     6,2,3,1       [2,3,1,6]
  11  Read 4   FAULT. 6.        1,4,3,2       FAULT. 2.     6,4,3,1       [3,1,6,4]
  12  TICK
  13  Read 1                             
  14  Write 5  FAULT. 4.        1,5,3,2.      FAULT. 3.     6,4,5,1       [1,6,4,5] 
  15  Read 3                                  FAULT. 6.     3,4,5,1       [4,5,1,3]
  16  Read 4   FAULT. 2.        1,5,3,4
  17  Read 1          
  18  TICK
  19  Write 2  FAULT. 4.        1,5,3,2       FAULT. 4.     3,2,5,1       [5,1,3,2]. 
  20  Read 5   


               Aging                          Belady's
Time: Events:        Page to   Pages in            Page to  Pages in       
                     replace   frames (after       replace  frames (after
                               replacement)                 replacement)
   1  Write 1  FAULT.           1             FAULT.         1             
   2  Read 2   FAULT.           1,2           FAULT.         1,2          
   3  Write 3  FAULT.           1,2,3         FAULT.         1,2,3       
   4  Read 4   FAULT.           1,2,3,4       FAULT.         1,2,3,4    
   5  Write 5  FAULT. 1.        5,2,3,4       FAULT. 4.      1,2,3,5  
   6  TICK
   7  Read 3          
   8  Read 2        
   8  Write 1  FAULT. 5.        1,2,3,4
   9  Read 6   FAULT. 4,        1,2,3,6       FAULT. 2.      1,6,3,5
  11  Read 4   FAULT. 6.        1,2,3,4       FAULT. 6.      1,4,3,5
  12  TICK
  13  Read 1   
  14  Write 5  FAULT. 2.        1,5,3,4
  15  Read 3   
  16  Read 4   
  17  Read 1          
  18  TICK
  19  Write 2  FAULT. 5.        1,2,3,4.      FAULT. 1.      2,4,3,5
  20  Read 5   FAULT. 2.        1,5,3,4.

Problem 2

Consider the WE 18300 hard disk described in Tanenbaum p. 301: There are 10601 cylinders, 12 tracks per cylinder, 281 sectors per track on average, 512 bytes per sector, for an overall disk capacity of 18.3 GBytes. The seek time between adjacent cylinders is 0.8 msec; the average seek time is 6.9 msec, the rotation time is 8.33 msec. Assume that the disk is not interleaved so that an entire track can be read in one rotations of the disk.