Dynamic Pricing with Heterogeneous Users (original) (raw)
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Transportation Research Record, 2006
This paper presents a dynamic traffic assignment model and its solution algorithm for solving bi-criterion dynamic user equilibrium (BDUE) that allows heterogeneous users with different value of time preferences. By assuming the value of time as a continuously distributed random variable across the population of trips, the BDUE problem is formulated as an infinite dimensional variational inequality (VI). Rather than solving the VI formulation directly, this study employs a generalized Frank-Wolfe algorithm to find the BDUE flow pattern. A bi-criterion time-dependent least cost path algorithm is applied to generate the extreme efficient path set, and the corresponding breakpoints naturally defines the multiple user classes, thereby generating the descent direction for a multi-class dynamic network loading. A traffic simulator is used to describe the traffic flow propagation and the spatial and temporal interactions. To circumvent the difficulty of storing the memory-intensive path set and routing policies for large-scale network applications, a simulation-based implementation technique is proposed to use the vehicle path set as a proxy for keeping track of the path assignment results. A set of numerical experiments are conducted to explore the convergence behavior of the BDUE algorithm and investigate how VOT distributions affect the path flow pattern and toll road usage under different dynamic road pricing schemes.
2007
This study develops a simulation-based dynamic traffic assignment, or dynamic user equilibrium (DUE), model for dynamic road pricing applications. This proposed model is considered as the bi-criterion DUE (BDUE) model, because it explicitly considers heterogeneous users with different values of time (VOT) choose paths that minimize the two path attributes: travel time and out-of-pocket cost. This study assumed trip-makers would select their respective least generalized cost paths, the generalized cost being the sum of travel cost and travel time weighted by the trip-maker's VOT. The VOT is modeled as a continuous random variable distributed across all users in a network. The BDUE problem is formulated as an infinite dimensional variational inequality (VI), and solved by a column generation-based algorithmic framework which embeds (i) a parametric analysis (PAM) to obtain the VOT breakpoints which determine multiple user classes, and find the set of extreme non-dominated paths, (ii) a simulator to determine experienced travel times, and (iii) a multi-class path flow equilibrating scheme to update path assignments. The idea of finding and assigning heterogeneous trips to the set of extreme non-dominated paths is based on the assumption that in the disutility minimization path choice model with convex utility functions, all trips would choose only among the set of extreme non-dominated paths. Moreover, to circumvent the difficulty of storing the grand path set and assignment results for large-scale network applications, a vehicle-based implementation technique is proposed. This BDUE model is generalized to the multi-criterion DUE (MDUE) model, in which heterogeneous users with different VOT and values of reliability (VOR) make path choices so as to minimize their path travel cost, travel time, and travel time variability. Another important extension of the BDUE model is the multi-criterion simultaneous route and departure time user equilibrium (MSRDUE) model, which considers heterogeneous trip-makers with different VOT and values of schedule delay (VOSD) making simultaneous route and departure time choices so as to minimize their respective trip costs, defined as the sum of travel cost, travel time weighted by VOT, and schedule delay weighted by VOSD. The MSRDUE problem is also solved by the column generation-based algorithmic framework. The Sequential Parametric Analysis Method (SPAM) is developed to find the VOT and VOSD breakpoints that define multiple user classes, and determine the least trip cost alternative (a combination of departure time and path) for each user class.
Transportation Research Record, 2007
Furthermore, applications of MSA for path-based, simulation-based, DTA encounter problems that get worse with an increase in congestion levels as well as network size. The first disadvantage is that MSA, in its pure-form implementation with path-based formulations, requires explicit storage of the paths set and path assignments, which can increase rapidly with the number of iterations, even for medium-size networks. A second disadvantage is that the MSA shifts traffic from inferior paths to current optimal (auxiliary) paths without regard to the relative degree of inferiority or relative difference in travel cost between a path and the current optimal path. That is, slightly suboptimal paths are penalized to the same extent as the most inferior path in the solution set; numerical experiments reveal that this property is most detrimental to efficient convergence at high congestion levels, as seen later in this paper.
Dynamic Path-Based Equilibrium Assignment With Microscopic Traffic Simulation
2005
This report summarizes research work conducted under TO4158 at the California ATMS Testbed of the Institute of Transportation Studies at the University of California, Irvine. Under this task order, the California ATMS testbed hosted two full-time PATH research postdocs (Henry Liu and Lianyu Chu) whose general responsibilities are focused on applications of ATMS in the Testbed environment. They are generally responsible for ensuring that the functional capabilities of the Testbed are designed, developed and maintained in a manner that complements and enhances the ATMS research objectives of the PATH program. Under the direction of PATH faculty researchers at UCI and the Testbed management team, they are generally responsible for software enhancements to the Laboratory "bench-top" system for modeling and evaluating ATMS, particularly with the microscopic simulation model Paramics. They also provided Caltrans the on-call support and technical guidance on various Caltrans micro-simulation projects related to the Paramics plugin modules developed at UCI.
Transportation Research Part B-methodological, 2009
A variety of analytical and simulation-based models and algorithms have been developed for the dynamic user equilibrium (DUE) traffic assignment problem. This paper aims to develop a theoretically sound simulation-based DUE model and its solution algorithm, with particular emphasis on obtaining solutions that satisfy the DUE conditions. The DUE problem is reformulated, via a gap function, as a nonlinear minimization problem (NMP). The NMP is then solved by a column generation-based optimization procedure which embeds (i) a simulation-based dynamic network loading model to capture traffic dynamics and determine experienced path travel costs for a given path flow pattern and (ii) a path-swapping descent direction method to solve the restricted NMP defined by a subset of feasible paths. The descent direction method circumvents the need to compute the gradient of the objective function in finding search directions, or to determine suitable step sizes, which is especially valuable for large-scale simulation-based DUE applications. Computational results for both small and large real road networks confirm that the proposed formulation and solution algorithm are effective in obtaining near-optimal solutions to the DUE problem.
Comparison of Methods for Path Flow Reassignment for Dynamic User Equilibrium
Networks and Spatial Economics, 2012
Models to describe or predict of time-varying traffic flows and travel times on road networks are usually referred to as dynamic traffic assignment (DTA) models or dynamic user equilibrium (DUE) models. The most common form of algorithms for DUE consists of iterating between two components namely dynamic network loading (DNL) and path inflow reassignment or route choice. The DNL components in these algorithms have been investigated in many papers but in comparison the path inflow reassignment component has been relatively neglected. In view of that, we investigate various methods for path inflow reassignment that have been used in the literature. We compare them numerically by embedding them in a DUE algorithm and applying the algorithm to solve DUE problems for various simple network scenarios. We find that the choice of inflow reassignment method makes a huge difference to the speed of convergence of the algorithms and, in particular, find that 'travel time responsive' reassignment methods converge much faster than the other methods. We also investigate how speed of convergence is affected by the extent of congestion on the network, by higher demand or lower capacity. There appears to be much scope for further improving path inflow reassignment methods.