A Stackelberg Strategy for Routing Flow over Time

Routing games are used to to understand the impact of individual users' decisions on network efficiency. Most prior work on routing games uses a simplified model of network flow where all flow exists simultaneously, and users care about either their maximum delay or their total delay. Both of these measures are surrogates for measuring how long it takes to get all of a user's traffic through the network. We attempt a more direct study of how competition affects network efficiency by examining routing games in a flow over time model. We give an efficiently computable Stackelberg strategy for this model and show that the competitive equilibrium under this strategy is no worse than a small constant times the optimal, for two natural measures of optimality

A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks

In this paper we propose a LWR-like model for traffic flow on networks which allows one to track several groups of drivers, each of them being characterized only by their destination in the network. The path actually followed to reach the destination is not assigned a priori, and can be chosen by the drivers during the journey, taking decisions at junctions. The model is then used to describe three possible behaviors of drivers, associated to three different ways to solve the route choice problem: 1. Drivers ignore the presence of the other vehicles; 2. Drivers react to the current distribution of traffic, but they do not forecast what will happen at later times; 3. Drivers take into account the current and future distribution of vehicles. Notice that, in the latter case, we enter the field of differential games, and, if a solution exists, it likely represents a global equilibrium among drivers. Numerical simulations highlight the differences between the three behaviors and suggest the existence of multiple Wardrop equilibria

Dynamic and Static congestion models: A review

We begin by providing an overview of the conventional static equilibrium approach. In such model both the flow of trips and congestion delay are assumed to be constant. A drawback of the static model is that the time interval during which travel occurs is not specified so that the model cannot describe changes in the duration of congestion that result from changes in demand or capacity. This limitation is overcome in the Vickrey/Arnott, de Palma Lindsey bottleneck model, which combines congestion in the form of queuing behind a bottleneck with users' trip-timing preferences and departure time decisions. We derive the user equilibrium and social optimum for the basic bottleneck model, and explain how the optimum can be decentralized using a time-varying toll. They then review some extensions of the basic model that encompass elastic demand, user heterogeneity, stochastic demand and capacity and small networks. We conclude by identifying some unresolved modelling issues that apply not only to the bottleneck model but to trip-timing preferences and congestion dynamics in general

THE QUEUING THEORETIC APPROACH TO GROUNDWATER MANAGEMENT

In this paper I propose and develop a new framework for modeling groundwater management issues. Specifically, I apply the methods of queuing theoryfor the first time, to the best of my knowledgeto model a groundwater management problem from a long-run perspective. I characterize two simple management regimes as two different kinds of queues and then show how to pose a manager's decision problem as an optimization problem using queuing theoretic techniques. I solve for certain fundamental quantities, such as the expected system size, and then discuss the economic meaning and relevance of the queuing concepts being used. I close by discussing possible extensions to my basic models. Published in Ecological Modelling 85 (2-3, 1996):219-27.groundwater, management, stochastic, queuing, theory, Resource /Energy Economics and Policy,