Modelling Multiprogramming

• When multiprogramming is used, the CPU utilization can be improved. Crudely put, if the average process computes only 20% of the time it is sitting in memory at once, the CPU should be busy all the time.
• Unrealistically optimistic, assumes that all five processes will never be waiting for I/O at the same time.
• Suppose that a process spend a fraction $p$ of its time waiting for I/O to complete. With $n$ processes in memory at once, the probability that all $n$ processes are waiting for I/O is $p^n$. The CPU utilization is then given by the formula:
  
  $$CPU~utilization=1-p^n$$
  
  

• Figure 11 shows the CPU utilization as a function of $n$, which is called the degree of multiprogramming.

  Figure 11: CPU utilization as a function of the number of processes in memory.

  
• For the sake of complete accuracy, it should be pointed out that the probabilistic model is only an approximation. Context switching overhead is ignored.