Transport network pricing schemes are an integral traffic management strategy that can be implemented to reduce congestion, among other network impacts. However, the problem of determining tolls becomes much more complex when multiple sources of demand uncertainty are considered. This paper proposes a novel tolling model based on a particular variant of strategic user equilibrium in which users base their route choice decisions on a known demand distribution. The study showed that by using an average daily demand, a marginal social cost-based tolling approach could induce near optimal conditions in a strategic network. However, uncertainty was associated with the long-term future planning demand; inaccurate forecasts of future demand could result in poor realized tolling scheme performance. Therefore, this paper also proposes a method to test the robustness of a tolling scheme, which is the reliability of the link tolls under a range of future demand scenario realizations. Results demonstrated that evaluations of strategic tolling schemes differed when both the short-term and the long-term uncertainty in demand were accounted for, and furthermore suggested that future research into the integration of multiple sources of uncertainty into the pricing scheme evaluation is merited.