Assume that we have a function for an application ofthe form f(i,p), which gives the fraction of time that exactly i processors are usable given that a total of p processors are available. This means that Σ.1 f(i, p)-1 ,ie. 100%. Assume that when i processors are in use, the applications run i times faster.
a. Rewrite Amdahl's Law so that it gives the speedup as a function of p for some application.
An application A runs on single processor for a time T seconds. Different portions of its running time can improve if a larger number of processors is used. The table below provides percentages of the application's time that can use up to P processors. For example, only one processor is useful/used for 20 percent of the time, whereas, when available, six processors can be used 15 percent of the time.
