Abstract
The disequilibrium theory in economics is used to depict the network traffic flow evolution process from disequilibrium to equilibrium. Three path choice behavior criteria are proposed, and the equilibrium traffic flow patterns formed by these three criteria are defined as price regulation user equilibrium, quantity regulation user equilibrium, and price-quantity regulation user equilibrium, respectively. Based on the principle of price-quantity regulation user equilibrium, the method of network tatonnement process is used to establish a network traffic flow evolution model. The unique solution of the evolution model is proved by using Picard’s existence and uniqueness theorem, and the stability condition of the unique solution is derived based on stability theorem of nonlinear system. Through numerical experiments, the evolution processes of network traffic flow under different regulation modes are analyzed. The results show that all the single price regulation, single quantity regulation, and price-quantity regulation can simulate the evolution process of network traffic flow. Price-quantity regulation is the combination of price regulation user equilibrium and quantity regulation user equilibrium, which thus can simulate the evolution process of network traffic flow with multiple user class.
Highlights
Network traffic flow evolution model is mainly used to study the network traffic flow evolution process and traffic fluctuations, which is an important part of traffic network design and traffic management strategy optimization
Pathtravel time is regarded as price, path-residual capacity is regarded as quantity, and the influence of price-quantity on the distribution of traffic flow on the road network is analyzed
This paper proposes three types of path choice behavior criterion based on disequilibrium theory and defines the stable state of network traffic flow formed by these three criteria as price regulation user equilibrium, quantity regulation user equilibrium, and price-quantity regulation user equilibrium, respectively
Summary
Network traffic flow evolution model is mainly used to study the network traffic flow evolution process and traffic fluctuations, which is an important part of traffic network design and traffic management strategy optimization. Random utility theory and expected utility theory are based on the assumption of traveler’s complete rationality, and they are widely applied in the analysis of travel choice behavior and the description of traffic flow evolution law. In the face of many uncertain factors, people’s judgment and Mathematical Problems in Engineering decision-making behavior are not completely rational, but greatly influenced by personal habit preference, risk attitude, and so on, so it is bounded rationality Both prospect theory and regret theory are based on the hypothesis of bounded rationality and can better describe the evolution process of network traffic flow in uncertain scenarios. Pathtravel time is regarded as price, path-residual capacity is regarded as quantity, and the influence of price-quantity on the distribution of traffic flow on the road network is analyzed.
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