An Exact Method for Reliable Shortest Path Problems With Correlation

Transportation networks are subject to significant travel time uncertainty as a result of traveler behavior, recurring congestion, capacity variability (construction zones, traffic incidents), variation in demand, and so on. Therefore, interest is growing in modeling and optimizing travel time reliability in such networks. This paper proposes an efficient algorithm to compute the path of maximum travel time reliability on a network with normally distributed and correlated link travel times. For this optimal reliability path (ORP) problem, it is shown that the subpath optimality condition for the deterministic shortest path problem does not hold, and consequently, a new bounds-based optimality criterion is proposed using the K shortest expected time paths and the minimum path variance on the network. An algorithm is developed to solve the ORP problem on the basis of the proposed optimality criterion and an efficient path generation procedure. Computational experiments on various test networks show the proposed algorithm to be efficient, requiring limited path enumeration. With as few as five shortest paths and 50 Monte Carlo draws, the proposed algorithm is able to find the most reliable path for realistic network sizes. Empirical investigations highlight the unreliability of the least expected time path and suboptimality of the independence assumption. The study also underscores the role of risk attitudes (reflected by reliability threshold) on the benefits of the ORP. The algorithm and empirical results have important applications for developing reliability-based routing applications for congestion mitigation and intelligent transportation systems.

Finding most reliable paths on networks with correlated and shifted log–normal travel times

The constrained reliable shortest path problem for electric vehicles in the urban transportation network

An algorithm for reliable shortest path problem with travel time correlations

SummaryTravel times are generally stochastic and spatially correlated in congested road networks. However, very few existing route guidance systems (RGS) can provide reliable guidance services to aid travellers planning their trips with taking account explicitly travel time reliability constraint. This study aims to develop such a RGS with particular consideration of travellers' concern on travel time reliability in congested road networks with uncertainty. In this study, the spatially dependent reliable shortest path problem (SD‐RSPP) is formulated as a multi‐criteria shortest path‐finding problem in road networks with correlated link travel times. Three effective dominance conditions are established for links with different levels of travel time correlations. An efficient algorithm is proposed to solve SD‐RSPP by adaptively using three established dominance conditions. The complexities of road networks in reality are also explicitly considered. To demonstrate the applicability of proposed algorithm, a comprehensive case study is carried out in Hong Kong. The results of case study show that the proposed solution algorithm is robust to take account of travellers' multiple routing criteria. Computational results demonstrate that the proposed solution algorithm can determine the reliable shortest path on real‐time basis for large‐scale road networks. Copyright © 2016 John Wiley & Sons, Ltd.

This paper addresses adaptive reliable shortest path problem which aims to find adaptive en-route guidance to maximize the reliability of arriving on time in stochastic networks. Such routing policy helps travelers better plan their trips to prepare for the risk of running late in the face of stochastic travel times. In order to reflect the stochastic characteristic of travel times, a traffic network is modeled as a discrete stochastic network. Adaptive reliable shortest path problem is uniformly defined in a stochastic network. Bellman’s Principle that is the core of dynamic programming is showed to be valid if the adaptive reliable shortest path is defined by optimal-reliable routing policy. A successive approximations algorithm is developed to solve adaptive reliable shortest path problem. Numerical results show that the proposed algorithm is valid using typical transportation networks.

Due to the influence of diverse factors, travel time is highly uncertain. Travelers are eager to find the most reliable path in multimodal networks to reduce the penalty caused by late arrival. However, the research considering the traveler preferences in multimodal transportation networks to solve the reliable path problem with given budgets is limited. Thus, we propose two multimodal reliable path models to find personalized and reliable paths. First, we build a multimodal network based on smart card data to incorporate the multimodal transfers between public and private transportation and solve corresponding parking issues effectively. Next, we build a multimodal time-reliable path model to find time-reliable paths. Further, considering traveler preferences, we design a multimodal utility-reliable path model to find personalized and reliable paths. A novel two-factor reliability bound convergence algorithm is developed to solve the proposed models and proved for its theoretical feasibility. Finally, a real-world case study is used to verify the effectiveness and efficiency of the proposed models and algorithm.

Reliable lifelong planning A*: Technique for re-optimizing reliable shortest paths when travel time distribution updating

This article studies reliable shortest path (RSP) problems in stochastic transportation networks. The term reliability in the RSP literature has many definitions, e.g., 1) maximal stochastic on-time arrival probability, 2) minimal travel time with a high-confidence constraint, 3) minimal mean and standard deviation combination, and 4) minimal expected disutility. To the best of our knowledge, almost all state-of-the-art RSP solutions are designed to target one specific RSP objective, and it is very difficult, if not impossible, to adapt them to other RSP objectives. To bridge the gap, this article develops a distributional reinforcement learning (DRL)-based algorithm, namely, DRL-Router, which serves as a universal solution to the four aforementioned RSP problems. DRL-Router employs the DRL method to approximate the full travel time distribution of a given routing policy and then makes improvements with respect to the user-defined RSP objective through a generalized policy iteration scheme. DRL-Router is 1) universal, i.e., it is applicable to a variety of RSP objectives; 2) model free, i.e., it does not rely on well calibrated travel time distribution models; 3) it is adaptive with navigation objective changes; and 4) fast, i.e., it performs real-time decision making. Extensive experimental results and comparisons with baseline algorithms in various transportation networks justify both the accuracy and efficiency of DRL-Router.

Vehicle path selection follows the shortest path principle, while taking the shortest travel time as the optimization goal. In the real road network, affected by signal control, the travel time of the vehicle path has significant uncertainty. The shortest path algorithm with static road indicators as the weights has obvious defects in path selection. In order to solve this problem, according to the theory of distributed wave, the operating state of the vehicle under the influence of the downstream signal control is classified. The travel time of the vehicle on the road segment is classified and predicted, and the travel time prediction value set is further transformed into the travel time reliability. For the vehicle route selection of a dynamic road network, the path travel time reliability determined by the product of the road segment travel time reliability is logarithmically converted, and the Dijkstra algorithm is used to find the most reliable path as the target solution. Then, a simulation model is constructed to verify the validity of the algorithm. The experimental results prove that using the reliability of travel time as the weight of path selection and solving by Dijkstra algorithm can reflect the actual vehicle path selection more accurately. This method is a beneficial improvement to the problem of static path selection.

Finding the most reliable path with and without link travel time correlation: A Lagrangian substitution based approach

Travel time uncertainty may cause late arrival and impose a high penalty on travelers. There is a growing interest in modeling travel time uncertainty to optimize the reliability of travel time at the path and network level. Real data analysis finds that the influence factors, including day-of-week, holidays, time-of-day, road grades, traffic states, and so on, often reduce the cumulative probability of travel time even in the same facility type (the same lane number and the same divided type). Thus, a novel aggregate approach is proposed to classify the travel time data based on these influence factors. The distribution with the new aggregate approach is defined as the extended shifted lognormal (ESLN) distribution. KS test indicates that the ESLN distribution can effectively describe travel time, and outperforms normal, lognormal, gamma, and beta distribution. Travel time correlations are calculated between new aggregate groups, which can effectively reduce the complexity compared with the link to link correlations. Finally, the ESLN distribution is used to find the most reliable path in a real-world large-scale network. The comparison results between ESLN distribution and shifted lognormal (SLN) distribution show the effectiveness and improvement of the proposed method in finding the most reliable path.

ABSTRACTFinding the most reliable path that maximizes the probability of on-time arrival is commonly encountered by travelers facing travel time uncertainties. However, few exact solution algorithms have been proposed in the literature to efficiently determine the most reliable path in large-scale road networks. In this study, a two-stage solution algorithm is proposed to exactly solve the most reliable path problem. In the first stage, the upper and lower bounds of on-time arrival probability are estimated. Dominance conditions and the monotonic property of the most reliable path problem are then established. In the second stage, the multi-criteria label-setting approach is utilized to efficiently determine the most reliable path. To illustrate the applicability of the proposed solution algorithm, a comprehensive case study is carried out using a real road network with stochastic travel times. The results of case study show that the proposed solution algorithm has a remarkable computational advantage over the existing multi-criteria label-correcting algorithm.

In this paper, a double label algorithm method is created to seek a more reliable path and a minimal travel time path in a stochastic time dependent network. The idea of this paper comes from the work to dispatch the rescue vehicle to disaster area post earthquake, since the network will become unreliable due to damage by earthquake. The concept of the method is developed based on the analysis of travel time of a stochastic and time-varying network. The paper first identifies a set of relationships between the mean and variance of the travel time dynamic and stochastic in network. A shortest path is generated as more reliable path under consideration of the travel time variance and time-varying features of the arrival time at the destination. Comparing the travel time of the shortest travel time path with the travel time of the more reliable path, a reliability index can be obtained and taken as link weight to generate routing decision.

Due to the influence of various factors, travel time is highly dynamic and random, causing late arrival and imposing a high penalty on travelers. To ensure punctual arrival, this paper presents two models and algorithms to find reliable paths considering the earliest arrival time and the latest departure time. First, the 3-parameter lognormal (3P-LN) distribution is introduced to describe travel time. Next, an optimality condition based on travel time bounds is derived and established when travel time follows the 3P-LN distribution. Then, a reliable path model considering the earliest arrival time and the solution algorithm based on travel time bounds are proposed to find the earliest arrival time and the corresponding reliable path. After that, a reliable path model considering the latest departure time and the solution algorithm based on travel time bounds are developed to find the latest departure time and the corresponding reliable path. Finally, two case studies with a real-world road network in Beijing are conducted to verify the effectiveness and superiority of the proposed models and algorithms.