Let α be the percentage of program code that can be executed simultaneously by n computers in a cluster, each computer using a different set of parameters or initial conditions. Assume that the remaining code must be executed sequentially by a single processor. Each processor has an execution rate of x MIPS.
a. Derive an expression for the effective MIPS rate when using the system for exclusive execution of this program, in terms of n, a, and x.
b. If n = 16 and x = 4 MIPS, determine the value of α that will yield a system performance of 40 MIPS.