Sigman 9622657 Research centers on the generalization of the duality theory between one dimensional insurance risk models and one-dimensional stochastic content models to multidimensional queueing network, inventory network, multi-population, and multiple income source models, leading to upper and lower bounds for computing important probabilities of interest. Stochastic content models such as inventory, fluid, storage, reservoir and queueing models are already known to share an elegant duality with insurance risk models in the special case when the state space of the models can be characterized by non-negative real numbers. To handle network, multi-population and multi-source models, it is necessary to expand this duality to the multi-dimensional state-space cases. It is expected that such a duality would contribute to the creation of a general theory for multi-dimensional risk processes (which currently does not exist) and applications of this theory to insurance, business, population, inventory, queueing, etc., would be extremely useful.
