Performance Analysis of multiprocessor architecture -part one

In developing a computational model for multiprocessors, we assume that a given computation can be divided into concurrent tasks for execution on the multiprocessor.
Equal Duration Model : In this model, it is assumed that a given task can be divided into n equal subtasks,each of which can be executed by one processor. If ts is the execution time of the whole task using a single processor, then the time taken by each processor to execute its subtask is tm ¼ ts=n. Since, according to this model, all processors are executing their subtasks simultaneously, then the time taken to execute the whole task is tm ¼ ts=n. The speedup factor of a parallel system can be defined as the ratio between the time taken by a single processor to solve a given problem instance to the time taken by a parallel system consisting of n processors to solve the same problem instance.
One important factor has been overlooked in the above derivation. This factor is the communication overhead, which results from the time needed for processors to communicate and possibly exchange data while executing their subtasks. Assume that the time incurred due to the communication overhead is called tc then the actual time taken by each processor to execute its subtask is given by tm = (ts/n)+ tc.