This article proposes a novel methodology that uses the bi-level programming formulation to calibrate the expected total demand and the corresponding demand variability of traffic networks. In the bi-level formulation the upper-level is either a new maximum likelihood estimation method or a least squares method and the lower-level is the strategic user equilibrium assignment model (StrUE) which accounts for the day-to-day demand volatility. The maximum likelihood method proposed in this article has the ability to utilize information from day-to-day observed link flows to provide a unique estimation of the total demand distribution, whereas the least squares method is capable of capturing link flow variations. The lower-level StrUE model can take the total demand distribution as input, and output a set of link flow distributions which can then be compared to the link-level observations. The mathematical proof demonstrates the convexity of the model, and the sensitivity to the prediction error is analytically derived. Numerical analysis is conducted to illustrate the efficiency and sensitivity of the proposed model. Some possible future research is discussed in the conclusion.