Toward an analytical solution to task allocation,processor assignment,and performance evaluation of network processors

Message-passing network-based multicomputer systems emerge as a potential economical candidate to replace supercomputers. Despite enormous effort to evaluate the performance of those systems and to determine an optimum scheduling algorithm (which is known as an NP-complete), we still lack a complete and a good performance model to analyze distributed computing systems. The model is complete if all system parameters, network parameters, communication overhead parameters, and application parameters are considered explicitly in the solution. A good performance model, like a good scientific theory, should be able to explain all normal behavior, predict any abnormality in the system, and allow the designer to adjust some of the parameters, while abstracting unimportant details.In this paper, we develop a good and complete performance model, which predicts a minimum finish time, equally the maximum speed up. In addition, we develop a closed form solution which forecasts the optimum share of the parallel job (task) that has to be assigned to each processor (node). Task assignment may then be undertaken in a distributed manner, which enhances the distributive nature of the system and, thus, improve system performance. Most importantly, our analytical solution presents a mechanism to select, based on system and application parameters, the optimum number of processors (nodes) that has to be assigned to a given parallel job.The model helps the designer to study the effect of each individual parameter on the overall system performance. This then becomes a tool for a designer of a multicomputer system to manage limited resources in an optimal manner paying attention only to those parameters that are most critical.