Methods of mathematical forecasting of the time of execution of complex sets of jobs in parallel distributed computer systems

A procedure of mathematical forecasting of the time of executing complex sets of interrelated software modules (tasks and/or their fragments) in parallel distributed computer systems which takes into account the fact that the time of interprocessor data exchange can be commensurable with that of executing a software module was described for the first time. The times of both interprocessor data exchanges and software module executions were regarded as random variables. Both static planning and dynamic task scheduling were studied. A procedure was proposed for determining with regard for high dimensionality of the mathematical models at hand the upper bound of the number of states of the terminating Markov process describing the model that realizes each user-defined set of interrelated tasks.