Road Pricing Design Based on Game Theory and Multi-agent Consensus

Consensus theory and noncooperative game theory respectively deal with cooperative and noncooperative interactions among multiple players/agents. They provide a natural framework for road pricing design, since each motorist may myopically optimize his or her own utility as a function of road price and collectively communicate with his or her friends and neighbors on traffic situation at the same time. This paper considers the road pricing design by using game theory and consensus theory. For the case where a system supervisor broadcasts information on the overall system to each agent, we present a variant of standard fictitious play called average strategy fictitious play(ASFP) for large-scale repeated congestion games.Only a weighted running average of all other players actions is assumed to be available to each player. The ASFP reduces the burden of both information gathering and information processing for each player. Compared to the joint strategy fictitious play(JSFP) studied in the literature, the updating process of utility functions for each player is avoided. We prove that there exists at least one pure strategy Nash equilibrium for the congestion game under investigation, and the players actions generated by the ASFP with inertia(players reluctance to change their previous actions) converge to a Nash equilibrium almost surely. For the case without broadcasting, a consensus protocol is introduced for individual agents to estimate the percentage of players choosing each resource, and the convergence property of players action profile is still ensured. The results are applied to road pricing design to achieve socially local optimal trip timing. Simulation results are provided based on the real traffic data for the Singapore case study.

Effect of longitudinal lift distribution on sonic boom of a canard-wing-stabilator-body configuration

After the last flight of the Concorde in 2003,sonic boom has been one of the obstacles to the return of a supersonic transport aircraft to service.To reduce the sonic boom intensity to an acceptable level,it is of great significance to study the effect of lift distribution on far-field sonic boom,since lift is one of the most important contributors to an intense sonic boom.Existing studies on the longitudinal lift distribution used low-fidelity methods,such as Whitham theory,and in turn,only preliminary conclusions were obtained,such as that extending the lift distribution can reduce sonic boom.This paper uses a newly developed high-fidelity prediction method to quantitatively study the effect of longitudinal lift distribution on the sonic boom of a Canard-Wing-Stabilator-Body(CWSB)configuration.This high-fidelity prediction method combines near-feld CFD simulation with far-field propagation by solving the augmented Burgers equation.A multipole analysis method is employed for the extraction of near-field waveform in order to reduce computational cost.Seven configurations with the same total lift but different distributions are studied,and the quantitative relationship between the longitudinal lift distribution and far-field sonic boom intensity is investigated.It is observed that a small lift generated by the stabilator can prevent aft-stabilator and aft-fuselage shocks from merging,while the balanced lift generated by the canard and wing can effectively keep the corresponding shocks further apart,which is beneficial for reducing both the on-track and off-track sonic boom.In turn,the acoustic level perceived at the ground can be reduced by 5.9 PLdB on-track and 5.4 PLdB off-track,on average.