Let α be the percentage of a program code which can be executed simultaneously by n processors of a multiprocessor system. Assume that the remaining code must be executed sequentially on a single processor. Each processor has an execution rate of x MIPS, and all of the processors are equally capable. (a) Derive an expression for the effective MIPS rate when using the system to execute this program, in terms of the parameters n, x, and α.
(b) Let consider the synchronization overhead. When adding an additional processor, the total number of instructions will be increased byβpercent. These added instructions are for synchronization only and they canbe executed in parallel. What will be the speedup of the multiprocessor system?