UNIVERSITY OF WISCONSIN-MADISON
Computer Sciences Department
CS 537
Spring 2000 		A. Arpaci-Dusseau
Solutions to Quiz #6: Wednesday, March 29

Memory Management

Problem 1: General Memory Allocation (60 points)

Assume that you have free memory partitions of size 100KB, 500KB, 200KB, 300KB, and 600KB (in this order) and that memory requests for 212KB, 417KB, 112KB, and 426KB arrive.

a)Show how a First-Fit allocation algorithm would assign the requests to free memory. (Do NOT assume rotating First-Fit). Clearly show the size of each piece of memory after each request arrives. 

Original:  100KB  500KB  200KB  300KB  600KB
212KB:     100KB *288KB* 200KB  300KB  600KB
417KB:     100KB  288KB  200KB  300KB *183KB*
112KB:     100KB *176KB* 200KB  300KB  183KB
426KB:     FAILS: Cannot be allocated
b)Show how a Best-Fit allocation algorithm would assign the same requests. Clearly show the size of each piece of memory after each request arrives. 
Original:  100KB  500KB  200KB  300KB   600KB
212KB:     100KB  500KB  200KB  *88KB*  600KB
417KB:     100KB  *83KB* 200KB   88KB   600KB
112KB:     100KB   83KB  *88KB*  88KB   600KB
426KB:     100KB   83KB   88KB   88KB  *174KB*
c)Show how a Worst-Fit allocation algorithm would assign the same requests. Clearly show the size of each piece of memory after each request arrives. 
Original:  100KB  500KB  200KB  300KB  600KB
212KB:     100KB  500KB  200KB  300KB *388KB*
417KB:     100KB  *83KB* 200KB  300KB  388KB
112KB:     100KB   83KB  200KB  300KB *276KB*
426KB:     FAILS: Cannot be allocated

Problem 2: Buddy-Allocation (40 points)

Consider a system with 1MB of available memory and requests for 42KB, 396KB, 10KB, and 28KB. Show the amount of memory allocated for each request and the state of memory after each request. 

XXXX indicates that the block of the size above has been allocated
Original      :  1MB


42KB --> 64KB :  64KB 64KB 128KB 256KB 512KB
                 XXXX 

396KB -->512KB:  64KB 64KB 128KB 256KB 512KB
                 XXXX                  XXXX

10KB --> 16KB:   64KB 16KB 16KB 32KB 128KB 256KB 512KB
                 XXXX XXXX                       XXXX

28KB --> 32KB:   64KB 16KB 16KB 32KB 128KB 256KB 512KB
                 XXXX XXXX      XXXX             XXXX
b)Why does internal fragmentation occur with buddy allocation? How much internal fragmentation exists in this scenario?

Internal fragmentation is wasted memory visible only to the process making the memory request. Internal fragmentation occurs in buddy allocation because memory requests must be rounded up to the nearest power of 2.

Amount: (64-42) + (512-396) + (16-10) + (32 - 28) = 148KB

c)Why does external fragmentation occur with buddy allocation? How much external fragmentation exists in this scenario?

External fragmentation is wasted memory visible to the system outside of the requesting processes. External fragmentation occurs because not all requests (even after they've been rounded up to the nearest power of two) are the same size; therefore, it is possible that a memory request will not be able to satisfied, even when there is enough total free memory in the system.

Amount: 16 + 128 + 256 = 400KB

As a check, the amount of fragmentation in the system and the usefully allocated memory should equal 1MB:

148KB + 400KB + 42KB + 396KB + 10KB +28KB = 1024KB = 1MB

as desired.