Considering tax schemes imposed on each link, we focus on upper bounds of price of anarchy (POA) using stochastic user equilibrium (SUE) flow pattern that is induced by a crowd of Stackelberg strategy controlled users.With the assumption of separability, increase, and convexity of link time function and fixed origin-destination (OD) demands of traffic network, the equivalent variational inequality (VI) for a Logit-based SUE model is firstly established and further used to obtain upper bounds on inefficiency of traffic network under condition of SUE and Stackelberg strategy.For three scenarios of link time function falling in different classes of functions in which a typical example is Bureau of Public Roads function, we numerically analyze their POA upper bounds and obtain some meaningful conclusions.