Stochastic shortest path problems with recourse

Caption title.Includes bibliographical references (p. 22-23).Supported by the C.S. Draper Laboratory. DL-H-441625 Supported by a grant from Siemens A.G.George H. Polychronopoulos, John N. Tsitsiklis

A tutorial on recursive models for analyzing and predicting path choice behavior

The problem at the heart of this tutorial consists in modeling the path choice behavior of network users. This problem has been extensively studied in transportation science, where it is known as the route choice problem. In this literature, individuals' choice of paths are typically predicted using discrete choice models. This article is a tutorial on a specific category of discrete choice models called recursive, and it makes three main contributions: First, for the purpose of assisting future research on route choice, we provide a comprehensive background on the problem, linking it to different fields including inverse optimization and inverse reinforcement learning. Second, we formally introduce the problem and the recursive modeling idea along with an overview of existing models, their properties and applications. Third, we extensively analyze illustrative examples from different angles so that a novice reader can gain intuition on the problem and the advantages provided by recursive models in comparison to path-based ones

Stochastic Route Planning in Public Transport

Journey planning is a key process in public transport, where travelers get informed how to make the best use of a given public transport system for their individual travel needs. A common trait of most available journey planners is that they assume deterministic travel times, but vehicles in public transport often deviate from their schedule. The present paper investigates the problem of finding journey plans in a stochastic environment. To fully exploit the flexibility inherent in multi-service public transport systems, we propose to use the concept of a routing policy instead of a linear journey plan. A policy is a state-dependent routing advice which specifies a set of services at each location from which the traveler is recommended to take the one that arrives first. We consider current time dependent policies, that is, when the routing advice at a given location is based solely on the current time. We propose two heuristic solutions that find routing policies that perform better than deterministic journey plans. A numerical comparison shows the achievable gains when applying the different heuristic policies based on extensive simulations on the public transport network of Budapest. The results show that the probability of arriving on time to a given destination can be significantly improved by following a policy instead of a linear travel plan

Stochastic on-time arrival problem in transit networks

This article considers the stochastic on-time arrival problem in transit networks where both the travel time and the waiting time for transit services are stochastic. A specific challenge of this problem is the combinatorial solution space due to the unknown ordering of transit line arrivals. We propose a network structure appropriate to the online decision-making of a passenger, including boarding, waiting and transferring. In this framework, we design a dynamic programming algorithm that is pseudo-polynomial in the number of transit stations and travel time budget, and exponential in the number of transit lines at a station, which is a small number in practice. To reduce the search space, we propose a definition of transit line dominance, and techniques to identify dominance, which decrease the computation time by up to 90% in numerical experiments. Extensive numerical experiments are conducted on both a synthetic network and the Chicago transit network.Comment: 29 pages; 12 figures. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0

Exact Algorithms for the Canadian Traveller Problem on Paths and Trees

The Canadian Traveller problem is a stochastic shortest paths problem in which one learns the cost of an edge only when arriving at one of its endpoints. The goal is to find an adaptive policy (adjusting as one learns more edge lengths) that minimizes the expected cost of travel. The problem is known to be #P hard. Since there has been no significant progress on approximation algorithms for several decades, we have chosen to seek out special cases for which exact solutions exist, in the hope of demonstrating techniques that could lead to further progress. Applying techniques from the theory of Markov Decision Processes, we give an exact solution for graphs of parallel (undirected) paths from source to destination with random two-valued edge costs. We also offer a partial generalization to traversing perfect binary trees

Design and evaluation of improvement method on the Web information navigation - a stochastic search approach

With the advent of fast growing Internet and World Wide Web (WWW), more and more companies start the electronic commerce to enhance the business competitiveness. On the other hand, more and more people surf on the Web for information gathering/processing. Due to unbalanced traffic and poorly organized information, users suffer the slow communication and disordered information organization. The information provider can analyze the traffic and uniform resource locator (URL) counters to adjust the organization; however, heterogeneous navigation patterns and dynamic fluctuating Web traffic make the tuning process very complicated. Alternatively the user may be provided with guidance to navigate through the Web pages efficiently. In this paper, a Web site was modeled as a Markov chain associated with the corresponding dynamic traffic and designated information pages. We consider four models: inexperienced surfers on guidance-less sites, experienced surfers on guidance-less sites, sites with the mean-length guidance, and sites with the known-first-arc guidance (generalized as sites with dynamic stochastic shortest path guidance). Simulation is conducted to evaluate the performance of the different types of navigation guidance. We also propose a reformulation policy to highlight the hyperlinks as steering guidance. The evolution on complexity and applicability is also discussed for the design guideline of general improvement methods. The paper concludes with the summary and future directions.published_or_final_versio