The quality of service satisfiability thesis: resource and performance prediction for multi-processor systems and random schedules

A quality of service satisfiability thesis is established which provides a very general condition for determining the number of processors needed by a system in order to satisfy the quality of service required by a multi-task random schedule which is presented to the system for servicing. Since "processors" and "schedules" are abstract representations of general servicing "resources" and uncertain task "environments", the thesis has utility for studying and predicting resource requirements and associated performances in a variety of application domains. Uniformly distributed random schedules are used to illustrate the significance of the thesis.