Modeling instantaneous queuing effects in the traffic assignment problem with consideration of demand fluctuations in the modeling period

Instantaneous traffic queues, introducing fluctuated queuing delays, significantly affect the journey times and route choices of travelers particularly during the peak hour periods in congested road networks. Distinguished from average residual queues in static traffic assignment problems, instantaneous queues form and dissipate within minuscule time frames of a modeling period, triggered by an inflow exceeding link capacity, owning to instantaneous demand fluctuations. The inclusion of instantaneous queuing effects is of paramount importance, given their more frequent occurrence compared to residual queues. However, little attention has been given to these instantaneous queuing effects in static traffic assignment models for strategic planning. To fill this gap, this paper proposes a novel instantaneous traffic assignment (ITA) model to incorporate instantaneous queuing effects in congested road networks, accounting for within-period demand fluctuations. The enhanced ITA modeling framework is proposed encompassing two fixed-point problems for network loading and a logit-based stochastic user equilibrium assignment model. The ITA model is formulated as an equivalent variational inequality problem. The mathematical properties of the proposed model such as the stability of the unique solutions can be rigorously proved. An improved method of successive weighted average algorithm with an adaptive step size is developed to solve the proposed model in order to facilitate the examination of instantaneous queuing effects in real-world contexts for large-scale networks. Numerical examples are conducted to demonstrate the merits and efficacy of the proposed ITA model. The feasibility and applicability of the proposed model in reality are further illustrated in case studies of three different road networks.