Selfish Routing on Dynamic Flows

Selfish routing on dynamic flows over time is used to model scenarios that vary with time in which individual agents act in their best interest. In this paper we provide a survey of a particular dynamic model, the deterministic queuing model, and discuss how the model can be adjusted and applied to different real-life scenarios. We then examine how these adjustments affect the computability, optimality, and existence of selfish routings.Comment: Oberlin College Computer Science Honors Thesis. Supervisor: Alexa Sharp, Oberlin Colleg

Toward a general framework for dynamic road pricing

This paper develops a general framework for analysing and calculating dynamic road toll. The optimal network flow is first determined by solving an optimal control problem with statedependent responses such that the overall benefit of the network system is maximized. An optimal toll is then sought to decentralise this optimal flow. This control theoretic formulation can work with general travel time models and cost functions. Deterministic queue is predominantly used in dynamic network models. The analysis in this paper is more general and is applied to calculate the optimal flow and toll for Friesz’s whole link traffic model. Numerical examples are provided for illustration and discussion. Finally, some concluding remarks are given

System optimizing flow and externalities in time-dependent road networks

This paper develops a framework for analysing and calculating system optimizing flow and externalities in time-dependent road networks. The externalities are derived by using a novel sensitivity analysis of traffic models. The optimal network flow is determined by solving a state-dependent optimal control problem, which assigns traffic such that the total system cost of the network system is minimized. This control theoretic formulation can work with general travel time models and cost functions. Deterministic queue is predominantly used in dynamic network models. The analysis in this paper is more general and is applied to calculate the system optimizing flow for Friesz’s whole link traffic model. Numerical examples are provided for illustration and discussion. Finally, some concluding remarks are given

System optimal traffic assignment with departure time choice

This thesis investigates analytical dynamic system optimal assignment with departure time choice in a rigorous and original way. Dynamic system optimal assignment is formulated here as a state-dependent optimal control problem. A fixed volume of traffic is assigned to departure times and routes such that the total system travel cost is minimized. Although the system optimal assignment is not a realistic representation of traffic, it provides a bound on performance and shows how the transport planner or engineer can make the best use of the road system, and as such it is a useful benchmark for evaluating various transport policy measures. The analysis shows that to operate the transport system optimally, each traveller in the system should consider the dynamic externality that he or she imposes on the system from the time of his or her entry. To capture this dynamic externality, we develop a novel sensitivity analysis of travel cost. Solution algorithms are developed to calculate the dynamic externality and traffic assignments based on the analyses. We also investigate alternative solution strategies and the effect of time discretization on the quality of calculated assignments. Numerical examples are given and the characteristics of the results are discussed. Calculating dynamic system optimal assignment and the associated optimal toll could be too difficult for practical implementation. We therefore consider some practical tolling strategies for dynamic management of network traffic. The tolling strategies considered in this thesis include both uniform and congestion-based tolling strategies, which are compared with the dynamic system optimal toll so that their performance can be evaluated. In deriving the tolling strategies, it is assumed that we have an exact model for the underlying traffic behaviour. In reality, we do not have such information so that the robustness of a toll calculation method is an important issue to be investigated in practice. It is found that the tolls calculated by using divided linear traffic models can perform well over a wide range of scenarios. The divided linear travel time models thus should receive more attention in the future research on robust dynamic traffic control strategies design. In conclusion, this thesis contributes to the literature on dynamic traffic modelling and management, and to support further analysis and model development in this area

Multi-Source Multi-Sink Nash Flows over Time

Nash flows over time describe the behavior of selfish users eager to reach their destination as early as possible while traveling along the arcs of a network with capacities and transit times. Throughout the past decade, they have been thoroughly studied in single-source single-sink networks for the deterministic queuing model, which is of particular relevance and frequently used in the context of traffic and transport networks. In this setting there exist Nash flows over time that can be described by a sequence of static flows featuring special properties, so-called `thin flows with resetting\u27. This insight can also be used algorithmically to compute Nash flows over time. We present an extension of these results to networks with multiple sources and sinks which are much more relevant in practical applications. In particular, we come up with a subtle generalization of thin flows with resetting, which yields a compact description as well as an algorithmic approach for computing multi-terminal Nash flows over time

Atomic Splittable Flow Over Time Games

In an atomic splittable flow over time game, finitely many players route flow dynamically through a network, in which edges are equipped with transit times, specifying the traversing time, and with capacities, restricting flow rates. Infinitesimally small flow particles controlled by the same player arrive at a constant rate at the player's origin and the player's goal is to maximize the flow volume that arrives at the player's destination within a given time horizon. Here, the flow dynamics are described by the deterministic queuing model, i.e., flow of different players merges perfectly, but excessive flow has to wait in a queue in front of the bottle-neck. In order to determine Nash equilibria in such games, the main challenge is to consider suitable definitions for the players' strategies, which depend on the level of information the players receive throughout the game. For the most restricted version, in which the players receive no information on the network state at all, we can show that there is no Nash equilibrium in general, not even for networks with only two edges. However, if the current edge congestions are provided over time, the players can adapt their route choices dynamically. We show that a profile of those strategies always lead to a unique feasible flow over time. Hence, those atomic splittable flow over time games are well-defined. For parallel-edge networks Nash equilibria exists and the total flow arriving in time equals the value of a maximum flow over time leading to a price of anarchy of 1.ISSN:1868-896

Heuristics for a collaborative routing problem

We study the problem of computing socially optimal routes with respect to a game-theoretic dynamic flow model. We consider different algorithms to heuristically solve the problem and compare their performance