Perron-Frobenius measure of systemic risk of cascading overload in complex clouds: Work in progress

Dynamic resource sharing has both positive and negative effects on the system performance. Current research mostly concentrates on the positive effect resulting from the statistical multiplexing gain. However, the negative effect resulting from the unavoidable overhead, e.g., due to coordination or delays for accessing distant resources, may outweight the positive effect. This possibility has been demonstrated analytically and through simulations as well as has been observed in operational networks with dynamic routing, when a positive effect of bandwidth sharing is offset by using unnecessary long routes. Emergence and proliferation of cloud computing necessitates better understanding of the risk of cascading overload in highly distributed complex resource sharing systems. This paper, which represents work in progress, attempts to make a case for the Perron-Frobenius eigenvalue of the mean-field equations linearized about the "operational" system equilibrium to be viewed as a measure of the systemic risk of cascading overload in complex resource sharing systems. For simplicity of the exposition we consider a loss service model. Future research will investigate practical applicability and a possibility of online estimation of the proposed risk measure.