Sensitivity analysis of the travel time variable for Q-generalized logit traffic assignment with the implicit route-based approach

In the urban transportation planning problem, transportation-network-equilibrium assignments based on the q-generalized logit model can solve the shortcomings of the logit-based model. However, in large cities facing traffic jams, travel time always fluctuates. If we change the travel time variable, the traffic equilibrium will change and we need to run the model again. The calculation time will be very large if we have to run the model many times to find the optimal model. To solve the above problem, a sensitivity analysis method of the travel time variable without using route-based variables is proposed in this paper. Based on the depth-first search algorithm, the general formulation of the derivative of the implicit function, and the chain rule of differentiation, the change in traffic flow on links concerning the variable travel time has been effectively calculated. Therefore, the approximate equilibrium could be calculated without having to rerun the model to save computational time. Finally, a hypothetical road network and a real traffic network in Japan will be used to evaluate the computational efficiency of the proposed method.