With n processes in memory at once, the probability that all n processes are wai

Question

With n processes in memory at once, the probability that all n processes are waiting for I/O (in which case the CPU will be idle) is p^n, where n is the number of processes (or the degree of multiprogramming), and p is the fraction of time that a process spends waiting for I/O to complete.

If we assume this probability, then it follows that CPU utilization = 1 - p^n.

a. If a multiprogrammed system has 6 degrees of multiprogramming (i.e. six programs in memory), and each process spends 40% of its time waiting for I/O (0.4 ratio), what will be the CPU utilization?

b. If we have 14 programs in memory and the goal is to insure 97% CPU utilization, what is the maximum I/O wait percentage/ratio that can be tolerated?

Explanation / Answer

a) CPU utilization = 1-p^n
                   = 1-(.4)^6
                   = 1- 0.004096
                   = 99.59%

b) 0.97 = 1-(x)^14

    x^14 = 1 - 0.97
          = 0.03
         x = (0.03)^(1/14)
           = 77.96% (Maximum allowed I/O percentage ratio.)

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.