In this paper, a nonlinear revision protocol is proposed and embedded into the traffic evolution equation of the classical proportional-switch adjustment process (PAP), developing the present nonlinear pairwise swapping dynamics (NPSD) to describe th
e selfish rerouting evolutionary game. It is demonstrated that i) NPSD and PAP require the same amount of network information acquisition in the route-swaps, ii) NPSD is able to prevent the over-swapping deficiency under a plausible behavior description; iii) NPSD can maintain the solution invariance, which makes the trial and error process to identify a feasible step-length in a NPSD-based swapping algorithm is unnecessary, and iv) NPSD is a rational behavior swapping process and the continuous-time NPSD is globally convergent. Using the day-to-day NPSD, a numerical example is conducted to explore the effects of the reaction sensitivity on traffic evolution and characterize the convergence of discrete-time NPSD.
Based on the reliability budget and percentile travel time (PTT) concept, a new travel time index named combined mean travel time (CMTT) under stochastic traffic network was proposed. CMTT here was defined as the convex combination of the conditional
expectations of PTT-below and PTT-excess travel times. The former was designed as a risk-optimistic travel time index, and the latter was a risk-pessimistic one. Hence, CMTT was able to describe various routing risk-attitudes. The central idea of CMTT was comprehensively illustrated and the difference among the existing travel time indices was analysed. The Wardropian combined mean traffic equilibrium (CMTE) model was formulated as a variational inequality and solved via an alternating direction algorithm nesting extra-gradient projection process. Some mathematical properties of CMTT and CMTE model were rigorously proved. In the end, a numerical example was performed to characterize the CMTE network. It is founded that that risk-pessimism is of more benefit to a modest (or low) congestion and risk network, however, it changes to be risk-optimism for a high congestion and risk network.
The scheduling utility plays a fundamental role in addressing the commuting travel behaviours. In this paper, a new scheduling utility, termed as DMRD-SU, was suggested based on some recent research findings in behavioural economics. DMRD-SU admitted
the existence of positive arrival-caused utility. In addition, besides the travel-time-caused utility and arrival-caused utility, DMRD-SU firstly took the departure utility into account. The necessity of the departure utility in trip scheduling was analysed comprehensively, and the corresponding individual trip scheduling model was presented. Based on a simple network, an analytical example was executed to characterize DMRD-SU. It can be found from the analytical example that: 1) DMRD-SU can predict the accumulation departure behaviors at NDT, which explains the formation of daily serious short-peak-hours in reality, while MRD-SU cannot; 2) compared with MRD-SU, DMRD-SU predicts that people tend to depart later and its gross utility also decrease faster. Therefore, the departure utility should be considered to describe the travelers scheduling behaviors better.
