K shortest paths in stochastic time-dependent networks

A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns successors to nodes as a function of time. In some particular cases, the shortest origin-destination path must nevertheless be chosen a priori, since time-adaptive choices are not allowed. Unfortunately, finding the a priori shortest path is NP-hard, while the best time-adaptive strategy can be found in polynomial time. In this paper, we propose a solution method for the a priori shortest path problem, and we show that it can be easily adapted to the ranking of the first K shortest paths. Moreover, we present a computational comparison of time-adaptive and a priori route choices, pointing out the effect of travel time and cost distributions. The reported results show that, under realistic distributions, our solution methods are effectiveShortest paths; K shortest paths; stochastic time-dependent networks; routing; directed hypergraphs

An Efficient Monte Carlo-based Probabilistic Time-Dependent Routing Calculation Targeting a Server-Side Car Navigation System

Incorporating speed probability distribution to the computation of the route planning in car navigation systems guarantees more accurate and precise responses. In this paper, we propose a novel approach for dynamically selecting the number of samples used for the Monte Carlo simulation to solve the Probabilistic Time-Dependent Routing (PTDR) problem, thus improving the computation efficiency. The proposed method is used to determine in a proactive manner the number of simulations to be done to extract the travel-time estimation for each specific request while respecting an error threshold as output quality level. The methodology requires a reduced effort on the application development side. We adopted an aspect-oriented programming language (LARA) together with a flexible dynamic autotuning library (mARGOt) respectively to instrument the code and to take tuning decisions on the number of samples improving the execution efficiency. Experimental results demonstrate that the proposed adaptive approach saves a large fraction of simulations (between 36% and 81%) with respect to a static approach while considering different traffic situations, paths and error requirements. Given the negligible runtime overhead of the proposed approach, it results in an execution-time speedup between 1.5x and 5.1x. This speedup is reflected at infrastructure-level in terms of a reduction of around 36% of the computing resources needed to support the whole navigation pipeline

Job Selection in a Network of Autonomous UAVs for Delivery of Goods

This article analyzes two classes of job selection policies that control how a network of autonomous aerial vehicles delivers goods from depots to customers. Customer requests (jobs) occur according to a spatio-temporal stochastic process not known by the system. If job selection uses a policy in which the first job (FJ) is served first, the system may collapse to instability by removing just one vehicle. Policies that serve the nearest job (NJ) first show such threshold behavior only in some settings and can be implemented in a distributed manner. The timing of job selection has significant impact on delivery time and stability for NJ while it has no impact for FJ. Based on these findings we introduce a methodological approach for decision-making support to set up and operate such a system, taking into account the trade-off between monetary cost and service quality. In particular, we compute a lower bound for the infrastructure expenditure required to achieve a certain expected delivery time. The approach includes three time horizons: long-term decisions on the number of depots to deploy in the service area, mid-term decisions on the number of vehicles to use, and short-term decisions on the policy to operate the vehicles

Analysis of adaptive algorithms for an integrated communication network

Techniques were examined that trade communication bandwidth for decreased transmission delays. When the network is lightly used, these schemes attempt to use additional network resources to decrease communication delays. As the network utilization rises, the schemes degrade gracefully, still providing service but with minimal use of the network. Because the schemes use a combination of circuit and packet switching, they should respond to variations in the types and amounts of network traffic. Also, a combination of circuit and packet switching to support the widely varying traffic demands imposed on an integrated network was investigated. The packet switched component is best suited to bursty traffic where some delays in delivery are acceptable. The circuit switched component is reserved for traffic that must meet real time constraints. Selected packet routing algorithms that might be used in an integrated network were simulated. An integrated traffic places widely varying workload demands on a network. Adaptive algorithms were identified, ones that respond to both the transient and evolutionary changes that arise in integrated networks. A new algorithm was developed, hybrid weighted routing, that adapts to workload changes

Robust Route Planning in Intermodal Urban Traffic

Passengers value reliable travel times but are often faced with delays in intermodal urban traffic. To improve their mobility experience, we propose a robust route planning tool that provides routes guaranteeing a certain probability of on-time arrival and satisfying additional constraints. The constraints can limit the number of transfers, time-dependent trip costs and other relevant resources. To find such routes, we extend the time-dependent reliable shortest path problem by adding constraints on time-dependent and stochastic edge weights. An exact solution method based on multi-objective A* search is proposed to solve this problem. By applying our algorithm to a showcase featuring an actual city, we hope to answer relevant questions for policy-makers and contribute to smarter mobility in the future

A mean-variance model for stochastic time-dependent networks.

Traditional models of route generation are based on choosing routes that minimize expected travel-time between origin and destination. The variance of the least-time path is not included in the path selection. In addition, due to congestion in transportation networks, travel times are time-dependent and stochastic in nature. This research focuses on the time dependency as well as the stochastic nature of traffic flow.The computational performance of the algorithms was evaluated through numerical experiments using randomly generated networks. A regression curve relating the running time to number of nodes, arc density, number of time intervals, and the number of discrete arc travel times has been generated for each algorithm. The results show that number of nodes and arc density influence the running time worse than linearly. The proposed algorithms were illustrated using a real-life network and near-real time travel information between Beverly Hills and Garden Grove in Los Angeles, California. The data was generated using the Freeway Performance Measurement System (PaMS) run by California Department of Transportation and the University of California at Berkeley. The illustration showed that more research is needed in extracting travel time information from real-life data which is vast and influenced by several factors such as the day of the week, holidays, time of the day, accidents. However, through the illustration we were able to demonstrate how the proposed algorithms can be used with near real-time information.Two algorithms are developed for determining a minimum travel time variance path and minimum mean-variance path assuming a priori best path routing policy. Under this policy, drivers use the path that corresponds to the minimum travel time variance to their destination node determined prior to the actual departure time at an origin node. We prove that both algorithms reach the optimal solution in finite number of steps but have non-polynomial running times. In addition, two algorithms, specialized modified label correcting and label setting algorithms, are developed for determining minimum mean-variance travel time path for time-adaptive routing problem. These algorithms allow the travel to define the route as he/she travels from the origin to the destination. Both algorithms reach optimal solution in finite number of steps and have polynomial computational complexity

Adaptive Route Choice in Stochastic Time-Dependent Networks: Routing Algorithms and Choice Modeling

Transportation networks are inherently uncertain due to random disruptions; meanwhile, real-time information potentially helps travelers adapt to realized traffic conditions and make better route choices under such disruptions. Modeling adaptive route choice behavior is essential in evaluating Advanced Traveler Information Systems (ATIS) and related policies to better provide travelers with real-time information. This dissertation contributes to the state of the art by estimating the first latent-class routing policy choice model using revealed preference (RP) data and providing efficient computer algorithms for routing policy choice set generation. A routing policy is defined as a decision rule applied at each link that maps possible realized traffic conditions to decisions on the link to take next. It represents a traveler\u27s ability to look ahead in order to incorporate real-time information not yet available at the time of decision. A case study is conducted in Stockholm, Sweden and data for the stochastic time-dependent network are generated from hired taxi Global Positioning System (GPS) traces through the methods of map-matching and non-parametric link travel time estimation. A latent-class Policy Size Logit model is specified with two additional layers of latency in the measurement equation. The two latent classes of travelers are policy users who follow routing policies and path users who follow fixed paths. For the measurement equation of the policy user class, the choice of a routing policy is latent and only its realized path on a given day can be observed. Furthermore, when GPS traces have relatively long gaps between consecutive readings, the realized path cannot be uniquely identified. Routing policy choice set generation is based on the generalization of path choice set generation methods, and utilizes efficient implementation of an optimal routing policy (ORP) algorithm based on the two-queue data structure for label correcting. Systematic evaluation of the algorithm in random networks as well as in two large scale real-life networks is conducted. The generated choice sets are evaluated based on coverage and adaptiveness. Coverage is the percentage of observed trips included in the generated choice sets based on a certain threshold of overlapping between observed and generated routes, and adaptiveness represents the capability of a routing policy to be realized as different paths over different days. It is shown that using a combination of methods yields satisfactory coverage of 91.2%. Outlier analyses are then carried out for unmatching trips in choice set generation. The coverage achieves 95% for 100% threshold after correcting GPS errors and breaking up trips with intermediate stops, and further achieves 100% for 90% threshold. The latent-class routing policy choice model is estimated against observed GPS traces based on the three different sample sizes resulting from coverage improvement, and the estimates appear consistent across different sample sizes. Estimation results show the policy user class probability increases with trip length, and the latent-class routing policy choice model fits the data better than a single-class path choice model or routing policy choice model. This suggests that travelers are heterogeneous in terms of their ability and willingness to plan ahead and utilize real-time information. Therefore, a fixed path model as commonly used in the literature may lose explanatory power due to its simplified assumptions on network stochasticity and travelers\u27 utilization of real-time information

Least expected time paths in stochastic, time-varying transportation networks

The authors consider stochastic, time-varying transportation networks, where the arc weights (arc travel times) are random variables with probability distribution functions that vary with time. Efficient procedures are widely available for determining least time paths in deterministic networks. In stochastic but time-invariant networks, least expected time paths can be determined by setting each random arc weight to its expected value and solving an equivalent deterministic problem. This paper addresses the problem of determining least expected time paths in stochastic, time-varying networks. Two procedures are presented. The first procedure determines the a priori least expected time paths from all origins to a single destination for each departure time in the peak period. The second procedure determines lower bounds on the expected times of these a priori least expected time paths. This procedure determines an exact solution for the problem where the driver is permitted to react to revealed travel times on traveled links en route, i.e. in a time-adaptive route choice framework. Modifications to each of these procedures for determining least expected cost (where cost is not necessarily travel time) paths and lower bounds on the expected costs of these paths are given. Extensive numerical tests are conducted to illustrate the algorithms` computational performance as well as the properties of the solution