Probabilistic elements in analysis of performance of multiprocessor systems

The paper presents important probabilistic elements that should be taken into consideration in the analysis of performance of classical multiprocessor systems. These elements represent the following quantities: modified arrival rate for processor requests and a few probabilities, which determine the frequency of certain events when a multiprocessor system is working. There are four peculiar events: service of another job, existence of the queue, a processor request while the given task is waiting into the queue and the return of another task into the queue while the given task is waiting in the queue. The first three events happen more often when a system consists of less number of processors, whereas the fourth event happens more often when more processors work in a system. Including (or not) the probabilities of these events to the analysis of performance of multiprocessor systems exerts its much influence on the precision of computations. All the mentioned quantities were described in detail. Formulas for these quantities were derived. Examples of applications of the formulas to the prediction of performance of various multiprocessor systems were presented.