title: How does this formula that calculates CPU utilization work?
body: <p>I've been given this question</p>
  
  <p>Consider a system running ten I/0-bound tasks and one CpU-bound task. Assume that the I/O-bound tasks issue and I/O operation once for every millisecond of CPU computing and that each I/O operation takes 10 milliseconds to complete. Also assume that the context-switching overhead is .1 millisecond and that all processes are long running tasks Describe the CPU utilization for round-robin scheduler when:</p>
  
  <p>a. The time quantum is 1 millisecond</p>
  
  <p>b. The time quantum is 10 milliseconds</p>
  
  <p>and I found answer for it </p>
  
  <p>The time quantum is 1 millisecond: Irrespective of which process is scheduled, the
  scheduler incurs a 0.1 millisecond context-switching cost for every context-switch.
  This results in a CPU utilization of 1/1.1 * 100 = 91%.</p>
  
  <p>The time quantum is 10 milliseconds: The I/O-bound tasks incur a context switch
  after using up only 1 millisecond of the time quantum. The time required to cycle
  through all the processes is therefore 10*1.1 + 10.1 (as each I/O-bound task
  executes for 1millisecond and then incur the context switch task, whereas the CPU-
  bound task executes for 10 milliseconds before incurring a context switch). The CPU
  utilization is therefore 20/21.1 * 100 = 94%. </p>
  
  <p>My only question how is this person deriving the formula for CPU Utilization? I can't seem to under stand where he/she is getting the numbers 20/21.1 * 100 = 94%, and 1/1.1 * 100 = 91%.</p>