اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDynamic system optimal traffic assignment with atomic users: Convergence and stability
44
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this study, we analyse the convergence and stability of dynamic system optimal (DSO) traffic assignment with fixed departure times. We first formulate the DSO traffic assignment problem as a strategic game wherein atomic users select routes that minimise their marginal social costs, called a DSO game. By utilising the fact that the DSO game is a potential game, we prove that a globally optimal state is a stochastically stable state under the logit response dynamics, and the better/best response dynamics converges to a locally optimal state. Furthermore, as an application of DSO assignment, we examine characteristics of the evolutionary implementation scheme of marginal cost pricing. Through theoretical comparison with a fixed pricing scheme, we found the following properties of the evolutionary implementation scheme: (i) the total travel time decreases smoother to an efficient traffic state as congestion externalities are perfectly internalised; (ii) a traffic state would reach a more efficient state as the globally optimal state is stabilised. Numerical experiments also suggest that these properties make the evolutionary scheme robust in the sense that they prevent a traffic state from going to worse traffic states with high total travel times.
قيم البحث
اقرأ أيضاً
This study investigates dynamic system-optimal (DSO) and dynamic user equilibrium (DUE) traffic assignment of departure/arrival-time choices in a corridor network. The morning commute problems with a many-to-one pattern of origin-destination demand a
nd the evening commute problems with a one-to-many pattern are considered. Specifically, a novel approach to derive closed-form solutions for both DSO and DUE problems is developed. We first derive a closed-form solution to the DSO problem based on the regularities of the cost and flow variables at an optimal state. By utilizing this solution, we prove that the queuing delay at a bottleneck in a DUE solution is equal to an optimal toll that eliminates the queue in a DSO solution under certain conditions of a schedule delay function. This enables us to derive a closed-form DUE solution by using the DSO solution. We also show the theoretical relationship between the DSO and DUE assignment. Numerical examples are provided to illustrate and verify the analytical results.
A dynamical system is defined in terms of the gradient of a payoff function. Dynamical variables are of two types, ascent and descent. The ascent variables move in the direction of the gradient, while the descent variables move in the opposite direct
ion. Dynamical systems of this form or very similar forms have been studied in diverse fields such as game theory, optimization, neural networks, and population biology. Gradient descent-ascent is approximated as a Newtonian dynamical system that conserves total energy, defined as the sum of the kinetic energy and a potential energy that is proportional to the payoff function. The error of the approximation is a residual force that violates energy conservation. If the residual force is purely dissipative, then the energy serves as a Lyapunov function, and convergence of bounded trajectories to steady states is guaranteed. A previous convergence theorem due to Kose and Uzawa required the payoff function to be convex in the descent variables, and concave in the ascent variables. Here the assumption is relaxed, so that the payoff function need only be globally `less convex or `more concave in the ascent variables than in the descent variables. Such relative convexity conditions allow the existence of multiple steady states, unlike the convex-concave assumption. When combined with sufficient conditions that imply the existence of a minimax equilibrium, boundedness of trajectories is also assured.
This paper presents a systematic approach for analyzing the departure-time choice equilibrium (DTCE) problem of a single bottleneck with heterogeneous commuters. The approach is based on the fact that the DTCE is equivalently represented as a linear
programming problem with a special structure, which can be analytically solved by exploiting the theory of optimal transport combined with a decomposition technique. By applying the proposed approach to several types of models with heterogeneous commuters, it is shown that (i) the essential condition for emerging equilibrium sorting patterns, which have been known in the literature, is that the schedule delay functions have the Monge property, (ii) the equilibrium problems with the Monge property can be solved analytically, and (iii) the proposed approach can be applied to a more general problem with more than two types of heterogeneities.
We study the stochastic bilinear minimax optimization problem, presenting an analysis of the Stochastic ExtraGradient (SEG) method with constant step size, and presenting variations of the method that yield favorable convergence. We first note that t
he last iterate of the basic SEG method only contracts to a fixed neighborhood of the Nash equilibrium, independent of the step size. This contrasts sharply with the standard setting of minimization where standard stochastic algorithms converge to a neighborhood that vanishes in proportion to the square-root (constant) step size. Under the same setting, however, we prove that when augmented with iteration averaging, SEG provably converges to the Nash equilibrium, and such a rate is provably accelerated by incorporating a scheduled restarting procedure. In the interpolation setting, we achieve an optimal convergence rate up to tight constants. We present numerical experiments that validate our theoretical findings and demonstrate the effectiveness of the SEG method when equipped with iteration averaging and restarting.
In infinite-dimensional Hilbert spaces we device a class of strongly convergent primal-dual schemes for solving variational inequalities defined by a Lipschitz continuous and pseudomonote map. Our novel numerical scheme is based on Tsengs forward-bac
kward-forward scheme, which is known to display weak convergence, unless very strong global monotonicity assumptions are made on the involved operators. We provide a simple augmentation of this algorithm which is computationally cheap and still guarantees strong convergence to a minimal norm solution of the underlying problem. We provide an adaptive extension of the algorithm, freeing us from requiring knowledge of the global Lipschitz constant. We test the performance of the algorithm in the computationally challenging task to find dynamic user equilibria in traffic networks and verify that our scheme is at least competitive to state-of-the-art solvers, and in some case even improve upon them.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
