Bounding the inefficiency of logit-based stochastic user equilibrium

Bounding the inefficiency of selfish routing has become an emerging research subject. A central result obtained in the literature is that the inefficiency of deterministic User Equilibrium (UE) is bounded and the bound is independent of network topology. This paper makes a contribution to the literature by bounding the inefficiency of the logit-based Stochastic User Equilibrium (SUE). In a stochastic environment there are two different definitions of system optimization: one is the traditional System Optimum (SO) which minimizes the total actual system travel time, and the other is the Stochastic System Optimum (SSO) which minimizes the total perceived travel time of all users. Thus there are two ways to define the inefficiency of SUE, i.e. to compare SUE with SO in terms of total actual system travel time, or to compare SUE with SSO in terms of total perceived travel time. We establish upper bounds on the inefficiency of SUE in both situations

Efficiency Loss of Mixed Equilibrium Associated with Altruistic Users and Logit-based Stochastic Users in Transportation Network

The efficiency loss of mixed equilibrium associated with two categories of users is investigated in this paper. The first category of users are altruistic users (AU) who have the same altruism coefficient and try to minimize their own perceived cost that assumed to be a linear combination of selfish com­ponent and altruistic component. The second category of us­ers are Logit-based stochastic users (LSU) who choose the route according to the Logit-based stochastic user equilib­rium (SUE) principle. The variational inequality (VI) model is used to formulate the mixed route choice behaviours associ­ated with AU and LSU. The efficiency loss caused by the two categories of users is analytically derived and the relations to some network parameters are discussed. The numerical tests validate our analytical results. Our result takes the re­sults in the existing literature as its special cases

Price of Anarchy for Non-atomic Congestion Games with Stochastic Demands

We generalize the notions of user equilibrium and system optimum to non-atomic congestion games with stochastic demands. We establish upper bounds on the price of anarchy for three different settings of link cost functions and demand distributions, namely, (a) affine cost functions and general distributions, (b) polynomial cost functions and general positive-valued distributions, and (c) polynomial cost functions and the normal distributions. All the upper bounds are tight in some special cases, including the case of deterministic demands.Comment: 31 page

Capacity constrained stochastic static traffic assignment with residual point queues incorporating a proper node model

Static traffic assignment models are still widely applied for strategic transport planning purposes in spite of the fact that such models produce implausible traffic flows that exceed link capacities and predict incorrect congestion locations. There have been numerous attempts in the literature to add capacity constraints to obtain more realistic traffic flows and bottleneck locations, but so far there has not been a satisfactory model formulation. After reviewing the literature, we come to the conclusion that an important piece of the puzzle has been missing so far, namely the inclusion of a proper node model. In this paper we propose a novel path-based static traffic assignment model for finding a stochastic user equilibrium in which we include a first order node model that yields realistic turn capacities, which are then used to determine consistent traffic flows and residual point queues. The route choice part of the model is specified as a variational inequality problem, while the network loading part is formulated as a fixed point problem. Both problems are solved using existing techniques. We illustrate the model using hypothetical examples, and also demonstrate feasibility on large-scale networks

Generalized Multivariate Extreme Value Models for Explicit Route Choice Sets

This paper analyses a class of route choice models with closed-form probability expressions, namely, Generalized Multivariate Extreme Value (GMEV) models. A large group of these models emerge from different utility formulas that combine systematic utility and random error terms. Twelve models are captured in a single discrete choice framework. The additive utility formula leads to the known logit family, being multinomial, path-size, paired combinatorial and link-nested. For the multiplicative formulation only the multinomial and path-size weibit models have been identified; this study also identifies the paired combinatorial and link-nested variations, and generalizes the path-size variant. Furthermore, a new traveller's decision rule based on the multiplicative utility formula with a reference route is presented. Here the traveller chooses exclusively based on the differences between routes. This leads to four new GMEV models. We assess the models qualitatively based on a generic structure of route utility with random foreseen travel times, for which we empirically identify that the variance of utility should be different from thus far assumed for multinomial probit and logit-kernel models. The expected travellers' behaviour and model-behaviour under simple network changes are analysed. Furthermore, all models are estimated and validated on an illustrative network example with long distance and short distance origin-destination pairs. The new multiplicative models based on differences outperform the additive models in both tests

Price of anarchy for reliability-based traffic assignment and network design

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Modeling truck toll competition between two cross-border bridges under various regimes

The competition between a new publicly-owned cross-border bridge and the existing Ambassador Bridge is modeled in this thesis as a duopoly game where each bridge\u27s strategy is its toll level. We assume the Ambassador Bridge always wants to maximize its profit, while the new bridge may have various objective functions. The competition between the two bridges has a natural bi-level structure, with the upper level being the two bridges setting their respective tolls, and the lower level being the road users choosing their routes. The competition equilibrium (i.e. Nash equilibrium) emerges when each bridge cannot improve its objective function by unilaterally changing its truck toll level. The Mesh Method is employed to solve this bi-level equilibrium problem in a simulation context. The obtained results of different competition regimes provide valuable insights about the nature of the toll competition that will likely emerge in the future

Modeling consumer behaviour in the presence of network effects

Consumer choice models are a key component in fields such as Revenue Management and Transport Logistics, where the demands for certain products or services are assumed to follow a particular form, and sellers or market-makers use that information to adjust their strategies accordingly, choosing for example which products to display (assortment problem) or their prices (pricing problem). In the last couple of decades, online markets have taken a lot of relevance, providing a setting where consumers can compare easily different products, before deciding to buy them. More information is now available, and the purchasing decisions not only depend on the quality, prices and availability of the products, but also on what previous consumers think about them (phenomenon commonly known as Network Effects). Hence, in order to create a suitable model for this kind of market, it is relevant to understand how the collective decisions affect the market evolution. In this thesis we consider a particular subset of those online markets, cultural markets, where the products are for example songs, video games or ebooks. This kind of market has the special feature that its products have unlimited supply (since they are just a digital copy), and therefore we can exploit this in our models, to justify assumptions of the asymptotic behaviour of the market. We study some variations of the traditional Multinomial Logit (MNL) model, characterising the behaviour of consumers, where their purchasing decisions are affected by the quality and prices (initially fixed) of the available products, as well as their visibilities in the market interface and the consumption patterns of previous users. We focus particularly on the parameters associated to the network effects, where depending on the strength of the network effects, it is possible to explain: herd behaviours, where an alternative overpowers the rest; as well as more well-distributed settings, where all the alternatives receive enough attention giving a notion of fairness, since higher quality products get a larger market share. Finally, using the model where market shares are distributed according to the quality of the products, we study pricing strategies, where sellers can either collaborate or compete. We analyse the effect of both type of strategies into the choice model

Socially Optimal Personalized Routing With Preference Learning

Traffic congestion has become inescapable across the United States, especially in urban areas. Yet, support is lacking for taxes to fund expansion of the existing network. Thus, it is imperative to find novel ways to improve efficiency of the existing infrastructure. A major obstacle is the inability to enforce socially optimal routes among the commuters. We propose to improve routing efficiency by leveraging heterogeneity in commuter preferences. We learn individual driver preferences over the route characteristics and use these preferences to recommend socially optimal routes that they will likely follow. The combined effects of socially optimal routing and personalization help bridge the gap between utopic and user optimal solutions. We take the view of a recommendation system with a large userbase but no ability to enforce routes in a highly congested network. We (a) develop a framework for learning individual driver preferences overtime, and (b) devise a mathematical model for computing personalized socially optimal routes given (potentially partial) information on driver preferences. We evaluated our approach on data collected from Amazon Mechanical Turk and compared with Logistic Regression and our model improves prediction accuracy by over 12%

Game Theory Relaunched

The game is on. Do you know how to play? Game theory sets out to explore what can be said about making decisions which go beyond accepting the rules of a game. Since 1942, a well elaborated mathematical apparatus has been developed to do so; but there is more. During the last three decades game theoretic reasoning has popped up in many other fields as well - from engineering to biology and psychology. New simulation tools and network analysis have made game theory omnipresent these days. This book collects recent research papers in game theory, which come from diverse scientific communities all across the world; they combine many different fields like economics, politics, history, engineering, mathematics, physics, and psychology. All of them have as a common denominator some method of game theory. Enjoy