New results on resource sharing problems with random agent arrivals and an application to economic dispatch in power systems

We consider linear resource sharing problems with multiple agents. Agents are heterogeneous, with heterogeneity modelled by a tuple of parameters taking value according to an underlying probability distribution, and share a fixed resource amount. We provide an evaluation of a vital indicator for the correct operation of the agents, namely, the probability that the optimal resource share alters in case of a new agent arrival. We view this problem under a data driven lens, and provide a purely a-posteriori and prior-independent characterization of the above mentioned probability by exploiting recent developments in the so called scenario approach theory. The proposed framework is demonstrated on an economic dispatch example in power systems, where agents can be thought of as generating units participating in the power market.