Modeling demand elasticity and route overlapping in stochastic user equilibrium through paired combinatorial logit model

In this paper un equivalent mathematical programming formulation is provided for modeling demand elasticity and route overlapping in the stochastic user equilibrium (SUE) problem. The elastic demand establishes the equilibrium between supply function and demand function on the basis of microeconomics. Because the elasticity of demand is an important factor in predicting the future demand pattern and avoiding the potential biased assessment in transportation planning, the elasticity of travel demand must be modeled endogenoasly. The route overlapping problem is handled by the paired combinatorial logit (PCL) model while retaining the analytical tractability of the logit choice probability function. The PCL SUE model with elastic demand (PCL-SUE-ED) explicitly models the elasticity of travel demand and the effect of route overlapping on travel choice and route choice simultaneously. A path-based partial linearization algorithm is also developed for solving the PCL-SUE-ED model. In addition, a self-regulated averaging line search strategy is incorporated into the algorithm to minimize the computational efforts required to determine a suitable step size that guarantees convergence. Numerical results are provided to examine the features of the PCL-SUE-ED model as well as the efficiency of the path-based partial linearization algorithm.