A study of the dynamic behaviour of some workload allocation algorithms by means of catastrophe theory

The dynamic behaviour of some workload allocation algorithms is studied to identify instability conditions induced either by an external overload situation or by a workload reallocation, triggered by the failure of some of the requested resources. We use concepts, drawn from that part of system theory which is known as Thom's Catastrophe theory, such as the Drift and the Potential Functions. The method is then applied to workload balancing in a Distributed Database system; however our method can be extended to other kind of systems which can be found in the telecommunication networks and in the distributed computing systems areas. We first deal with simple examples to show how the instability conditions show up, then we show its application to a well known allocation algorithm (Sender Initiated) which is known to be stable under overloads and this behaviour is confirmed.