This article proposes an extension of the strategic user equilibrium proposed by Waller and colleagues and Dixit and colleagues. The proposed model relaxes the assumption of proportional Origin-Destination (O-D) demand, as it accounts for users’ strategic link choice under independently distributed O-D demands. The convexity of the mathematical formulation is proved when each O-D demand is assumed to follow a Poisson distribution independently; link flow distributions and users’ strategic link choice are also proved to be unique. Network performance measures are given analytically. A numerical analysis is conducted on the Sioux Falls network. A Monte Carlo method is used to simulate network performance measures, which are then compared to the results computed from the analytical expression. It is illustrated that the model is capable of accounting for demand volatility while maintaining computation efficiency.