Once the overheads are incorporated in the model the speedup curves change dramatically. Just for the purposes of illustration we assume that overheads consist of two parts: a fixed part which is independent of the number of processors, and a non-fixed part that grows quadratically with the number of the processors used:
The fraction one over S equals one divided by the quantity of F plus the quantity one minus the fraction F over P end of quantity plus K sub one plus K sub two times P squared end quantity.
In this equation, K1 and K2 are some fixed factors. Under these assumptions the speedup curve is shown in the following figure. It is interesting to note that in this case the speedups peak out. After a certain point adding more processors is detrimental to performance as shown in the following figure.
The graph shows that all programs reach the greatest speedup at five processors and then loose this benefit as up to eight processors are added. The x-axis measures the number of processors and the y-axis measures the speedup.