Network Traffic Flow Evolution Research Articles

Analysis of Stability-To-Chaos in the Dynamic Evolution of Network Traffic Flows under a Dual Updating Mechanism

This paper proposes a traffic-flow evolutionary model under a dual updating mechanism that describes the day-to-day (DTD) dynamics of traffic flow and travel cost. To illustrate the concept, a simple two-route network is considered. Based on the nonlinear dynamic theory, the equilibrium stability condition of the system is derived and the condition for the division between the bifurcation and chaotic states of the system is determined. The characteristics of the DTD dynamic evolution of network traffic flow are investigated using numerical experiments. The results show that the system is absolutely stable when the sensitivity of travelers toward the route cost parameter (θ) is equal to or less than 0.923. The bifurcation appears in the system when θ is larger than 0.923. For values of θ equal to or larger than 4.402, the chaos appears in the evolution of the system. The results also show that with the appearance of chaos, the boundary and interior crises begin to appear in the system when θ is larger than 6.773 and 10.403, respectively. The evolution of network traffic flow is always stable when the proportion of travelers who do not change the route is 84% or greater.

Chaotic Behavior of Traffic-Flow Evolution with Two Departure Intervals in Two-Link Transportation Network

In this study, the influence of traveler's departure time choice in day-to-day dynamic evolution of traffic flow in a transportation network is investigated. Combining historical information and real-time information, a dynamic evolution model of traffic flow with a study period divided into two intervals is proposed for a simple two-link network. Then, the evolution of network traffic flow is investigated using numerical experiments. Three types of information are considered: (1) only historical information, (2) only real-time information, and (3) both historical and real-time information. The results show that the dynamic evolution of network traffic flow under the three types of information is similar. However, the possibility of chaos occurrence under both historical and real-time information is smaller than that under two individual types of information. When chaos occurs, the chaotic behavior in traffic-flow evolution under only real-time information is relatively less complex than that under the other two types of information.

Impact of personalised route recommendation in the cooperation vehicle-infrastructure systems on the network traffic flow evolution

ABSTRACTInspired by the prevailing recommendation system application, personalised travel factors are introduced into route recommendation in order to provide more human-oriented travel service. With real-time information provided by the cooperation vehicle-infrastructure systems (CVIS), four real travel factors including distance, grade, time and toll are adopted to construct a route feature vector and an individual traveler preference feature vector, respectively. A novel route recommendation model based on Pearson’s correlation coefficient is formulated. A searching algorithm of all feasible routes is designed that achieves a better balance of time and space complexity. Considering that the traveler has heterogeneity in the numerous ways of using route recommendation information and choosing a satisfactory route, individual compliance with the route recommendation is creatively proposed and used to imitate a day-to-day route choice. A specific simulation with Monte Carlo method is conducted on a test network to show the dynamic evolution features of network traffic flow.

Network Traffic Flow Evolution Model Based on Disequilibrium Theory

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.

Modeling and simulation of network traffic flow evolution based on incomplete information feedback strategies in the ATIS environment

Considering both the high complexity of urban traffic flow systems and the bounded rationality of travelers, providing traffic information to all travelers is an effective method to induce each individual to make a more rational route-choice decision. Within Advanced Traveler Information System (ATIS) working environment, temporal and spatial evolution processes of traffic flow in urban road networks are closely related to strategies of providing traffic information and contents of information. In view of the day-to-day route-choice situations, this study constructs original updating models of the cognitive travel time of travelers under four conditions, including not providing any route travel time, only providing the most rapid route travel time, only providing the most congested route travel time, and providing all the routes travel times. The disaggregate route-choice approach is adopted for simulation to reveal the relationship between the evolution process of network traffic flow and the strategy of providing traffic information. The simulation shows that providing traffic information to all travelers cannot improve the operational efficiency of road networks. It is noteworthy that an inappropriate information feedback strategy would lead to intense variation in various routes traffic flow. Compared with incomplete information feedback strategies, it is inefficient and superfluous to provide complete traffic information to all travelers.

The impact of travelers’ rationality degree heterogeneity in the Advanced Traveler Information System on the network traffic flow evolution

The interplay between traffic information, which is normally distributed by the Advanced Traveler Information System (ATIS) and travelers’ decision behaviors, is prone to lead to high complexity in the evolution process of network traffic flow. Considering the obvious heterogeneity that is reflected in the numerous ways that travelers adopt ATIS information and choose routes, the lognormal distribution is adopted to describe the heterogeneity of travelers’ rationality degree. Introducing habitual factors of traveler route choice, modeling ideas of Multi-Agent and Mixed Logit are utilized to construct the day-to-day evolution model of network traffic flow, which is based on the value difference of travelers’ cognitive travel time. Furthermore, an integrated simulation algorithm based on the Monte Carlo method is specially designed to solve the previous evolution model. The simulation indicates that a lower individual difference and a higher rationality degree would lead to a more obvious aggregation phenomenon of network traffic flow and inefficiency of operation in road networks.

Day-to-day dynamical evolution of network traffic flow with elastic demand

Network traffic flow is an aggregated result of a huge number of travelers' route choices, which is influenced by the travelers' choice behaviors. So day-to-day traffic flow is not static, but presents a complex and tortuous day-to-day dynamic evolution process. Studying day-to-day dynamic evolution of network traffic flow, we can not only know whether the traffic network equilibrium can be reached and how the process is achieved, but also can know what phenomenon will occur in the evolution of network traffic flow if the equilibrium is not reached. In a real traffic system, taking day as scale unit, the day-to-day network traffic demand is variable and changes with everyday's traffic network state. The travelers' route choices are also influenced by the previous day's behaviors and network state. Then, will the day-to-day network traffic flow evolution be stable? If it is unstable, when will bifurcation and chaos occur? In this paper we discuss the day-to-day dynamic evolution of network traffic flow with elastic demand in a simple two-route network. The dynamic evolution model of network traffic flow with elastic demand is formulated. Based on a nonlinear dynamic theory, the existence and uniqueness of the fixed point of dynamic evolution model are proved, and an equilibrium stability condition for the dynamic evolution of network traffic flow with elastic demand is derived. Then, the evolution of network traffic flow is investigated through numerical experiments by changing the three parameters associated with travelers, which are the sensitivity of travelers' travel demand to travel cost, the randomness of travelers' route choices, and travelers' reliance on the previous day's actual cost. Our findings are as follows. Firstly, there are three kinds of final states in the evolution of network traffic flow: stability and convergence to equilibrium, periodic motion and chaos. The final state of the network traffic flow evolution is related to the above three parameters. It is found that under certain conditions the bifurcation diagram of the network traffic flow evolution reveals a complicated phenomenon of period doubling bifurcation to chaos, and then period-halving bifurcation. Meanwhile, the chaotic region is interspersed with odd periodic windows. Moreover, the more sensitive to cost the travelers' travel demand the more likely the system evolution is to be stable. The smaller the randomness of travelers' route choices, the less likely the system evolution is to be stable. The lower the degree of travelers' reliance on the previous day's actual cost, the more likely the system evolution is to be stable.

Modelling travellers’ en-route path switching in a day-to-day dynamical system

ABSTRACTTravellers’ en-route path switching is a very common travel adjustment behaviour which can significantly influence the whole day-to-day network traffic flow evolution process. This study encapsulated travellers’ sequential path adjustment mechanism into a day-to-day dynamical system, to capture travellers’ en-route switching effect without actually building a complicated within-day model to go with. According to different path choice behaviours and traffic information sources, three traveller groups were contained in the dynamical system, including the conservative travellers, the adventurous travellers unequipped with advanced traveller information systems (ATISs) and the ATIS-assisted adventurous travellers. In the proposed day-to-day dynamical model, a fixed point problem was established for achieving the heterogeneous traffic flow caused by travellers’ en-route path switching. Some stability analysis of the proposed dynamical system was accomplished in the numerical experiment. The effect of en-route path switching behaviour was investigated and it was found to influence both the stability of the dynamical system and the average travel time of adventurous travellers.

Day-to-Day dynamical evolution of network traffic flow under bounded rational view

The formation mechanism of network traffic flow and its evolution law are closely related to daily activities of travelers. The current studies indicate that the law of network traffic flow evolution is day-to-day; therefore, using days as the scale unit is an important way to illustrate the evolution of network traffic flow. In previous studies, travelers in the network were tacitly assumed to be entirely rational. When the rationality of travelers is limited, the dynamics of the evolution law needs to be re-examined. This paper presents the utility maximization hypothesis in a logit model by using the bounded rationality hypothesis and develops a bounded rational binary logit (BRBL) model. We apply the BRBL model to a day-to-day network traffic flow distribution and discuss the evolution law of day-to-day network traffic flow under the assumption of the limited rationality of travelers. Through a numerical experiment, this paper analyzes the evolution characteristics of network traffic flow. The results are as follows. Firstly, the final state of the network traffic flow process is not only correlated to the cost-sensitivity of travelers and dependence on actual cost, but also strongly related to the degree of the nationality of travelers. Secondly, the system will be either bifurcated or chaotic when either cost-sensitivity increases or dependence on actual cost increases. Moreover, within the group of travelers whose rationality level is low, no matter what the cost-sensitivity of travelers and the dependence on actual cost are, the evolution results are asymptotically stable. Finally, in particular, in certain circumstances, it is easy to achieve stability when the rationallty degree of travelers is very high or very low, while it is not easy to achieve stability when the rationality degree of travelers is medium.

Chaotic behavior in the dynamical evolution of network traffic flow and its control

This paper presents the day-to-day dynamic evolution of network traffic flow in a simple two-route network. Firstly, a day-to-day dynamical assignment model is formulated, which can depict the evolution of network traffic flow. We have proved that the fixed point of the dynamical system, which is the stochastic user equilibrium solution, exists and is unique. Secondly, based on nonlinear dynamics theory, an equilibrium stability condition for the network is derived. Moreover, the evolution of network traffic flow is investigated through numerical experiments. Meanwhile, periodic and chaotic flows are discovered under certain conditions. Finally, a chaotic control method is derived considering OD demand as control variable.

Network Traffic Flow Evolution Model Considering OD Demand Mutation

Abstract Considering such a fact that the traffic demand freshly entering a network does not have perfect information about traffic condition and then might choose travel routes randomly, we propose an improved network traffic flow evolution model in this article. The model's properties and fixed points are investigated. The fixed points of the model, which are different from traditional user equilibrium state or part user equilibrium state, can better formulate the result of traffic flow assignment in realization. Simulation results obtained from a grid network show that the model can be used to approximately model the process of realizing user equilibrium state, the network flow can indeed evolve to one or more fixed points, and the initial values of all available path flows can be zero.

Chaos and bifurcation in dynamical evolution process of traffic assignment with flow “mutation”

Considering such a fact that the traffic demands freshly entering a network do not have perfect information about traffic condition and may then choose routes randomly, in this paper, we present an improved network traffic flow evolution model. The model’s properties and fixed points are investigated. Numerical results obtained from a grid network show that the system can converge to one or more fixed points without requiring of positive route flows at initial time, and can be used to approximately simulate the process of realizing user equilibrium state. It is found that oscillations and such apparently irregular behaviors as chaos occur when the model parameter representing intensity of adjusting route flow and OD demand exceeds some values. Bifurcation diagrams of some route flows and OD demands with respect to this model parameter are presented.

Some Consistency Conditions for Dynamic Traffic Assignment Problems

This paper explores some critical issues in modeling network traffic flow for predictive user optimal dynamic traffic assignment. They include the role of FIFO (first-in-first-out) in link, path and network traffic dynamics, minimal set representation of link traffic evolution, and consistency conditions for link models. It is found that (1) link FIFO plays a central role in modeling link, path and network traffic flow evolution, and (2) the dimension of a minimal state set that adequately describes link traffic flow under FIFO is two. Moreover, two sufficient FIFO conditions are provided, and pitfalls in using these conditions to enforce FIFO are pointed out. Finally, ramifications of these findings to DTA modeling are also discussed.