A traffic congestion analysis by user equilibrium and system optimum with incomplete information
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A traffic congestion analysis by user equilibrium and system optimum with incomplete information Qiang Zhang1 · Shi Qiang Liu1
· Mahmoud Masoud2
Accepted: 14 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Nowadays, the rapid development of intelligent navigation systems has profound impacts on the routing of traffic users. With the assistance of these intelligent navigation systems, traffic users can obtain more accurate information about a traffic network such as traffic capacities, feasible paths, congestion status, etc. In this paper, we focus on a game-theory-based traffic congestion analysis model which considers incomplete traffic information (e.g., variabilities of path information) generated by intelligent navigation systems. The variabilities of path information are treated as incomplete information associated with different subsets of arcs. We adopt the notions of user equilibrium with incomplete information (UEII) and system optimum with incomplete information (SOII) in this study. Based on these two new notions, we extend two classical theorems and combine them into a new model to analyze the relationship between UEII and SOII. Finally, numerical cases are given to illustrate the implication of UEII and SOII in practical implementations. Keywords Braess paradox · Traffic congestion · Intelligent navigation systems · User equilibrium · System optimum · Incomplete information
1 Introduction In the literature on traffic congestion analysis, there is a classical problem to analyze the performance of a traffic network with a large number of users. This kind of problem assumes that the users should travel with a selfish routing manner to minimize their travel times, and all of them form a non-cooperative game called a congestion game
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Shi Qiang Liu [email protected]
1
School of Economics and Management, Fuzhou University, Fuzhou, China350105
2
Centre for Accident Research and Road Safety, Queensland University of Technology, Brisbane, QLD 4001, Australia
123
Journal of Combinatorial Optimization
by Wardrop (1952). In Wardrop’s work (1952), two following seminal principles were proposed to introduce the notions about user equilibrium and system optimum: (i) Wardrop’s first principle The journey times on all the routes actually used are equal and less than those which would be experienced by a single vehicle on any unused route. (ii) Wardrop’s second principle The average journey time tends to be the minimum. Wardrop’s first principle describes the selfish manner of each user who wants to minimize its own travel time without consideration of the total travel time of all users. The status that follows Wardrop’s first principle is known as User Equilibrium (UE) (Dafermos and Nagurney 1984). Wardrop’s second principle states a cooperative way that each user chooses his path to minimize the total travel time of all users. The traffic flow generated by the collaborative way is referred to as System Optimum (SO). According to game theory, the equilibrium of
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