A general model for task distribution on an open heterogenous processor system

A dynamical model for the distribution of tasks on a system of heterogenous processors is introduced. The task distribution procedure is based on the perceived benefits a task provider sees in using a particular processor for the execution of his requirements. The decision is usually based on a limited amount of information and is therefore a statistical process. The degree of certainty can be regulated by the so-called gain factor and ranges from a total lack of knowledge to a complete knowledge which renders the distribution dynamics a deterministic one. An entropy function is introduced for each task. The values of the task entropies at any moment in time are a measure for the distribution of tasks on the available processors. A second entropy function, the processor entropy, is introduced. The values of the processor entropy give useful information on the real utilisation of the processor system. Some concepts from general equilibrium theory are introduced and their relevance for achieving optimal processor utilisation discussed