Consider the following sequence of page references (each element in the sequence represents a page number): 1 2 3 4 5 2 1 3 3 2 3 4 5 4 5 1 1 3 2 5 Define the mean working set size after the k th reference as sk( ) =1 ka k t=10W(t, )0 a nd define the missing page probability after the kt h reference as mk( ) = 1 k a k t=1 F(t, ) where F ( t , ) 1 if a page fault occurs at virtual time t and 0 otherwise. a. D raw a diagram similar to that of F igure 8 .19 for the reference sequence just defined for the values 1, 2, 3, 4, 5, 6. b. Plot s20 ( ) as a function of . c. Plot m20 ( ) as a function of .
a. Perform the same type of analysis as that of Table 11.2 for the following sequence of disk track requests: 27, 129, 110, 186, 147, 41, 10, 64, 120. Assume that the disk head is initially positioned over track 100 and is moving in the direction of decreasing track number. b. Do the same analysis, but now assume that the disk head is moving in the direction of increasing track number.
One scheme to avoid the problem of preallocation versus waste or lack of contiguity is to allocate portions of increasing size as the file grows. For example, begin with a portion size of one block, and double the portion size for each allocation. Consider a file ofn records with a blocking factor of F , and suppose that a simple one-level index is used as a file allocation table. a. G ive an upper limit on the number of entries in the file allocation table as a function of F and n . b. W hat is the maximum amount of the allocated file space that is unused at any time?