User-optimal Route Choice Problem Research Articles

Dynamic user optimal route choice problem on a signalized transportation network

In this paper, we present a new route-based discrete time variational inequality (VI) ideal dynamic user optimal route choice (DUO) model on a transportation network with fixed signal timing at signalized intersections and a relaxation with gradient projection algorithm to solve the model. The new trait of our study is the queue length in red time and the throughput in green time for each cycle at each intersection can be found when traffic is in DUO status. This is different from other studies, in which either only average queue length or average delay in a period composing of multiple cycles can be found or traffic is not in DUO status. Furthermore, the optimal signal timings can be found by the algorithm. Under optimal signal timing, the total queuing delay of the network reaches minimum when traffic is in DUO status.

The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems

Dynamic user optimal simultaneous route and departure time choice (DUO-SRDTC) problems are usually formulated as variational inequality (VI) problems whose solution algorithms generally require continuous and monotone route travel cost functions to guarantee convergence. However, the monotonicity of the route travel cost functions cannot be ensured even if the route travel time functions are monotone. In contrast to traditional formulations, this paper formulates a DUO-SRDTC problem (that can have fixed or elastic demand) as a system of nonlinear equations. The system of nonlinear equations is a function of generalized origin-destination (OD) travel costs rather than route flows and includes a dynamic user optimal (DUO) route choice subproblem with perfectly elastic demand and a quadratic programming (QP) subproblem under certain assumptions. This study also proposes a solution method based on the backtracking inexact Broyden–Fletcher–Goldfarb–Shanno (BFGS) method, the extragradient algorithm, and the Frank-Wolfe algorithm. The BFGS method, the extragradient algorithm, and the Frank-Wolfe algorithm are used to solve the system of nonlinear equations, the DUO route choice subproblem, and the QP subproblem, respectively. The proposed formulation and solution method can avoid the requirement of monotonicity of the route travel cost functions to obtain a convergent solution and provide a new approach with which to solve DUO-SRDTC problems. Finally, numeric examples are used to demonstrate the performance of the proposed solution method.

An intersection-movement-based stochastic dynamic user optimal route choice model for assessing network performance

Different from traditional methods, this paper formulates the logit-based stochastic dynamic user optimal (SDUO) route choice problem as a fixed point (FP) problem in terms of intersection movement choice probabilities, which contain travelers’ route information so that the realistic effects of physical queues can be captured in the formulation when a physical-queue traffic flow model is adopted, and that route enumeration and column generation heuristics can be avoided in the solution procedure when efficient path sets are used. The choice probability can be either destination specific or origin–destination specific, resulting into two formulations. To capture the effect of physical queues in these FP formulations, the link transmission model is modified for the network loading and travel time determination. The self-regulated averaging method (SRAM) was adopted to solve the FP formulations. Numerical examples were developed to illustrate the properties of the problem and the effectiveness of the solution method. The proposed models were further used to evaluate the effect of information quality and road network improvement on the network performance in terms of total system travel time (TSTT) and the cost of total vehicle emissions (CTVE). Numerical results show that providing better information quality, enhancing link outflow capacity, or constructing a new road can lead to poor network performance.

In This Issue

In This Issue

An Intersection-Movement-Based Dynamic User Optimal Route Choice Problem

In this paper a novel variational inequality (VI) formulation of the dynamic user optimal (DUO) route choice problem is proposed using the concept of approach proportion. An approach proportion represents the proportion of travelers that select a turning or through movement when leaving a node. Approach proportions contain travelers' route information so that the realistic effects of physical queues can be captured in a formulation when a physical-queue traffic flow model is adopted, and so that route enumeration and path-set generation can be avoided in the solution procedure. In addition, the simple structure of the approach proportion representation allows us to decompose the constraint set for solving large-scale DUO route choice problems. This paper also discusses the existence and uniqueness of the solutions to the VI problem and develops a solution algorithm based on the extragradient method to solve the proposed VI problem. This solution algorithm makes use of the decomposition property of the constraint set and is convergent if the travel time functions are pseudomonotone and Lipschitz continuous. It is not necessary to know the Lipschitz constant of the travel time functions in advance. Finally, numerical examples are given to demonstrate the properties of the proposed model and the performance of the solution algorithm.

A discrete time dynamic flow model and a formulation and solution method for dynamic route choice

This paper considers the ideal dynamic user optimal (DUO) route choice problem using a route-based variational inequality approach. A discrete time dynamic flow model is developed, which uses link travel time functions to determine time-dependent network states. The proposed flow model is built on discrete time flow variables, to eliminate the discretization process of continuous time based models. Continuity of route travel time functions is proven to establish the existence of a solution, on the condition that the link travel time functions are continuous. Furthermore, flow dispersion and concentration can be simulated, which is expected to enhance the ability of capturing dynamics of traffic movements. A variational inequality formulation based on an alternative cost mapping is proposed, which is derived from a route swapping heuristic approach. As a solution method, the projection-based approach is used since the route travel time functions in our model are not smooth. To increase the performance of the projection-based methods, an efficient implementation of the projection operation is developed. Computational experiences with two example networks are provided to illustrate the model.

ANALYSIS OF LANE-BLOCKING EVENTS WITH AN ANALYTICAL DYNAMIC TRAFFIC ASSIGNMENT MODEL

An analytical-based dynamic traffic assignment (DTA) model intended for off-line analysis and evaluation of non-recurring lane-blocking events is proposed. Formulated as a variational inequality (VI), this model solves an ideal dynamic user-optimal (DUO) route choice problem. A diagonalization algorithm is proposed to solve the model to a prespecified convergence using a targe-scale, real-life traffic network. Adjustments of link capacities triggered by external lane-blocking events and internal modeled traffic phenomena are explicitly considered in the solution algorithm to capture queue formation and dissipation. The proposed solution procedure approximates route choices based on anticipatory and non-anticipatory traffic

Heuristics for the stochastic/dynamic user-optimal route choice problem

A stochastic/dynamic user-optimal route choice problem that assumes time-dependent route travel times Gumbel distributed is formulated by a variational inequality and the corresponding equilibrium conditions are introduced. Two K-shortest-path based heuristics called K-shortest-path (KSP) and restricted K-shortest-path (RKSP) are proposed and make comparisons with a link-based heuristic called stochastic dynamic method (SADA). Numerical examples show that both the KSP and RKSP are superior to the SADA in terms of total CPU time. While both the KSP and RKSP have fully taken the advantage of computational efficiency, the latter is more practical by taking into account the thresholds of an overlapping ratio and route travel time difference.

Dynamic User-Optimal Departure Time/Route Choice with Hard Time-Windows

This paper is a follow-up study to the dynamic user-optimal departure time/route choice problem, by imposing hard time-windows on origin departure times and on destination arrival times. However, by an appropriate network representation, the dynamic user-optimal departure time/route choice problem with hard time-windows is mathematically equivalent to the dynamic user-optimal route choice problem and can be solved accordingly by the nested diagonalization method. The enhancements of the proposed model are that off-peak and peak phenomena within the analysis period can be properly differentiated and that the influence of earlier departures on latter ones can be naturally presented. A numerical example is provided for demonstration.

A fuzzy user-optimal route choice problem using a link-based fuzzy variational inequality formulation

A link-based fuzzy user-optimal route choice problem embedding link interactions is formulated using the variational inequality approach. To avoid prohibitive arithmetic computations and by taking a plausible point estimate of each link travel time interval at a certain α-cut level, this fuzzy problem reduces to a crisp user-optimal route choice model, which may be readily solved by the so-called diagonalization method. The corresponding user-optimal conditions are explicitly stated and demonstrated by means of a numerical example.

Dynamic Capacitated User-Optimal Route Choice Problem

Link capacity side constraints are explicitly incorporated into the variational inequality-based dynamic user-optimal route choice problem. The corresponding dynamic capacitated user-optimal conditions for each origin-destination pair and time interval state that the generalized route travel times (composed of route travel times and queuing delays) experienced by travelers are equal and minimal. An augmented Lagrangian dual method that embeds the gradient projection algorithm is then proposed and validated with a numerical example. The computational performance of the gradient projection algorithm is also compared with the disaggregate simplicial decomposition algorithm in a preliminary attempt.

Comparison of Link-Based Versus Route-Based Algorithms in the Dynamic User-Optimal Route Choice Problem

One link-based algorithm (Frank-Wolfe) and three route-route based algorithms are compared for use in the dynamic user-optimal route choice problem. Computational experience with five test networks indicates that the route-based algorithms are in general superior to the link-based algorithm in terms of execution time but slightly inferior in terms of memory requirement.

A model and an algorithm for the dynamic user-optimal route choice problem

This paper formulates a discrete-time, link-based dynamic user-optimal route choice problem using the variational inequality approach. The proposed model complies with the dynamic user-optimal equilibrium condition in which for each origin-destination pair, the actual travel time experienced by travelers departing during the same interval is equal and minimal. A nested diagonalization procedure is then proposed and demonstrated with a numerical example.

A link-based variational inequality formulation of ideal dynamic user-optimal route choice problem

The ideal dynamic user-optimal (DUO) route choice problem is to determine vehicle flows on each link at each instant of time resulting from drivers using actual minimal-time routes. Actual route time is the travel time incurred while driving along the route. In a previous paper, we presented a route-based optimal control model for the ideal DUO route choice problem. However, this model is not appropriate for large-scale transportation networks because some degree of route enumeration is necessary to solve the model. In this paper, we first present the traffic network constraints and link-based DUO route choice conditions. Then, we introduce a link-based variational inequality (VI) formulation for the ideal DUO route choice problem so that route enumeration can be avoided in both the formulation and the solution procedure. By proving the necessity and sufficiency of this VI, we demonstrate that the VI formulation is equivalent to the link-based DUO route choice conditions.

Solving an Instantaneous Dynamic User-Optimal Route Choice Model

Dynamic models of the behavior of automobile drivers in choosing routes through urban transportation networks are required for the design and operation of intelligent transportation systems generally, and traveler information systems in particular. In this paper, drivers' route choice behavior based on current, or instantaneous, information on network conditions is described using an optimal control theory formulation. The time-dependent origin-destination vehicle trip pattern is assumed to be known. The instantaneous dynamic user-optimal route choice problem is to allocate vehicle flows to the current minimal-cost routes, defined as the routes that minimize the route travel cost between each decision node (any node on the route including the origin) and the destination node based on the currently prevailing travel times. The continuous time formulation of the problem is transformed into a discrete time nonlinear programming (NLP) formulation. Each of a sequence of NLPs is then solved by an algorithm based on the Frank-Wolfe technique. In this sequence, approximate link travel times are updated iteratively in order to represent flow propagation over routes. Computational results from applying the algorithm to two test networks conclude the paper.