CS 540 - Operating Systems - Test 2 - Name: Date: Friday ...

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Part 2: (67 points) 1. (8 pts.) P is a set of processes. R is a set of resources. E is a set of request or assignment edges. The sets P, R, and E are as follows: P = {P 1 , P 2 , P 3 }, R = {R 1 , R 2 , R 3 }, E = {P 1 → R 1 , P 1 → R 2 , P 2 → R 2 , P 2 → R 3 , P 3 → R 2 , P 3 → R 3 , R 1 → P 2 , R 2 → P 2 , R 3 → P 1 }. R 1 has one instance. R 2 has two instances. R 3 has one instances. (a) Draw the resource-allocation graph. (b) Is there any deadlock in this situation? Briefly Explain. Ans: (a) The resource-allocation graph is shown as follows: ✛✘ ✛✘ ✛✘ P1 P2 P3 ✚✙ ✚✙ ✚✙ ◗❳❳2 ❳ ◗◗◗◗◗ ❳ ❳❳ ✻◗ ✑ ❳ ◗◗◗◗◗◗ ✑ ❳❳ ❳ ✑ ❳❳ ✑ ❄✑ ✑✑✑✑✑✑✑✸ ❳ ✑ ❳ ◗ ❄ ✑ ❳ ❳❳ ✑✰ ❳❄ R1 R2 R3 (b) Consider the resource-allocation graph. There are four cycles in the system: P1 → R1 → P2 → R3 → P1, P1 → R2 → P2 → R3 → P1, P2 → R2 → P2, P2 → R3 → P1 → R1 → P2. P1 cannot finish because P1 needs R1 and R2 but can only acquire R2 while R1 is held by P2. P2 cannot finish because P2 needs R2 and R3 but can only acquire R2 while R3 is held by P1. P3 cannot finish because P3 needs R1 and R3 but can only acquire R2 while R3 is held by P1. P1, P2, and P3 cannot progress. The deadlock occurs. 2. (a) (2 pts.) What is Belady’s anomaly? (b) (2 pts.) Give two page-replacement algorithms that do not suffer from Belady’s anomaly. (c) (3 pts.) What is the working set model? (d) (2 pts.) What is the cause of thrashing? (e) (2 pts.) How does the system detect thrashing? Ans: (a) more page frames might not always have fewer page faults. This is called Belady’s anomaly. (b) LRU and optimal algorithms suffer from Belady’s anomaly. (c) Paging systems keep each process. working set in memory before letting the process run. This approach is called the working set model. (d) Thrashing is caused by under-allocation of the minimum number of pages read required by a process, forcing it to continuously page fault. (e) The system can detect thrashing by evaluating the level of CPU utilization as compared to the level of multiprogramming.
3. (10 pts.) Consider a swapping system in which memory consists of 540K as shown below: xxx P3 xxxx P5 xxxxx P7 xx where xx.. indicates the unused memory. 0 60 140 220 320 420 500 540 Note that P3, P5, and P7 are processes in memory. Assume that process P3 was just swapped into memory and that new processes arrive in the order P8, P9, P10, P11 and are of size 70K, 50K, and 80K, 40K respectively. How would each of the first-fit, next-fit, best-fit, and worst-fit algorithms place processes of P8, P9, P10, and P11? If a process won’t fit, write ’out of memory’ in the appropriate slot. Ans: first fit: P9 x P3 P8 x P5 P10 x P7 P11 0 50 60 140 210 220 320 400 420 500 540 next fit: xxx P3 P8 x P5 P9 P11 x P7 xx P10: out of memory 0 60 140 210 220 320 370 410 420 500 540 best fit: P9 x P3 P8 x P5 P10 xx P7 P11 0 50 60 140 210 220 320 400 420 500 540 worst fit: P11 x P3 P9 x P5 P8 xx P7 xx P10: out of memory 0 40 60 140 190 220 320 390 420 500 540 4. (10 pts.) The time required to read a word in memory (including the time to access associative memory) is 80 nanoseconds when the page number is in the associative memory. The access time of associative memory is 10 nanoseconds. (a) Find a formula that expresses the effective access time as a function of the hit ratio. (b) What hit ratio is needed to achieve the effective access time to 101 nanoseconds? Ans: (a) Let e and t be the access time to associative memory and ordinary memory respectively. Assume the hit ratio be h. e + t = 80, 10 + t = 80, t = 70 Effective Access Time = h×80+(1−h)×(10+2×70) = 80h+(1−h)×150 = 80h+150−150h = 150 − 70h (b) 150 − 70h ≤ 101, 70h ≥ 49, h ≥ 70% The hit ratio should be 70%. 5. (8 pts.) A computer has four page frames. The time of loading, time of last access, and the R and M bits for each page are as shown below (the times are in clock ticks): Page Loaded Last Referenced R M 0 140 270 1 1 1 230 260 0 1 2 126 280 1 0 3 162 265 0 0 (a) Which page will NRU replace? (b) Which page will FIFO replace? (c) Which page will LRU replace? (d) Which page will second chance replace? Ans: (a) Page 3 because R and M bits are 0. (b) Page 2 because it is oldest (loaded at 126). (c) Page 1 because is least recently referenced (referenced at 260). (d) Page 3 because it is oldest and not referenced (loaded at 162 and R = 0).
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CS 540 - Operating Systems - Test 2 - Name: Date: Friday ...

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