Time-dependent Shortest Path Research Articles

Recognizing and Analyzing Private Car Commuters Using Big Data of Electronic Registration Identification of Vehicles

Private cars’ travel has been one of the main factors causing urban traffic congestion. Especially during morning and evening rush hours, private car commuters bring a significant burden to traffic. However, there is very little literature on them due to the lack of access to relevant data. A real-world dataset containing vehicle passing records of Electronic Registration Identification (ERI) of vehicles provides us with an opportunity to research private car commuters. We propose a regular behavior-based model to recognize private car commuters. In the model, a regular behavior-based definition of private car commuters is firstly proposed. Then, TDSP(Time dependent shortest path)-based distance measurement and a hierarchical clustering method are designed to extract regular behaviors. Furthermore, we utilize a regular threshold <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p $ </tex-math></inline-formula> to help determine regular behaviors. The experiment, which is conducted on a real-world dataset containing one-week vehicle passing records in Chongqing of China, validates the effectiveness and accuracy of the proposed model. Moreover, we analyze the mobility pattern of private car commuters, and some typical mobility patterns of them are successfully found.

An Axiomatic Approach to Time-Dependent Shortest Path Oracles

An Axiomatic Approach to Time-Dependent Shortest Path Oracles

The time-dependent shortest path and vehicle routing problem

We introduce the time-dependent shortest path and vehicle routing problem. In this problem, a set of homogeneous vehicles is used to visit a set of customer locations dispersed over a very large network where the travel times are time-dependent and therefore the shortest path between two locations may change over time. The aim of the problem is to simultaneously determine the sequence in which the customer locations are visited and the arcs traveled on the paths between each pair of consecutively visited customers, such that the total travel time is minimized. We are the first to formally define and solve this fully integrated problem, providing tight bounds to it. We then propose a dynamic time-dependent shortest path algorithm embedded within a simulated annealing metaheuristic to efficiently solve the problem. We also propose a variant of the algorithm where some time-dependent shortest paths are precomputed. We test our formulations and algorithms on a set of real-life instances generated from a dataset of the road network in Québec City, Canada. Our results indicate that the resulting models are too large to be solved even for small instances. However, the obtained bounds show that the developed simulated annealing heuristic performs very well. We also demonstrate that neglecting time-dependent information on traffic leads to imprecise estimation of the traveling time. Moreover, the results show the importance of solving the shortest paths and routing problems simultaneously, as using a set of precomputed shortest paths leads to slightly worse solutions. This work adds new research avenues to city logistics and congestion studies.

Improved AND/OR Tree Search Algorithm in Analysis of Stochastic and Time-Dependent Shortest Path Problem

Real-time vehicle guidance effectively reduces traffic jams and improves the operational efficiency of urban transportation. The trip time on a route is considered as a random process that changes with time, and the shortest path selection requires a random dynamic model and the solution of a decision-making problem. Thus, the shortest trip time is the criterion to determine the dynamic path selection by a random dynamic programming (DP) model which discretizes the trip times in the continuous segments on the route. In this study, a numerical model of random dynamic programming is established by using a probability tree model and an AND/OR (AO∗) algorithm to select the path of the shortest trip time. The results show that the branches of the probability tree are only accumulated on the “quantity” and do not cause a “qualitative” change. The inefficient accumulation of “quantity” affects the efficiency of the algorithm, so it is important to separate the accumulation of “quantity” from node expansion. The accumulation of “quantity” changes the trip time according to the entering time into a segment, which demands an improved AO∗ algorithm. The new AO∗ algorithm balances between efficiency and the trip time and provides the optimal real-time vehicle guidance on the road.

SHORTEST PATHS ON DYNAMIC GRAPHS: A SURVEY

ABSTRACT This paper provides an overview of the state-of-the art and the current research trends concerning shortest paths problem on dynamic graphs. The discussion is divided in two main topics: reoptimization and time-dependent shortest paths. Reoptimization consists in the solution of a sequence of shortest path problems in which each instance slightly differs from the previous one. The reoptimization tackles this problem wisely using information stored in an optimal solution previously computed. On the other hand, shortest path problems on time-dependent graphs are characterized by a weight function which not only depends upon the arcs but changes in time according to a certain time horizon.

A weakly coupled model of differential equations for thief tracking

In this work we introduce a novel model for the tracking of a thief moving through a road network. The modeling equations are given by a strongly coupled system of scalar conservation laws for the road traffic and ordinary differential equations for the thief evolution. A crucial point is the characterization at intersections, where the thief has to take a routing decision depending on the available local information. We develop a numerical approach to solve the thief tracking problem by combining a time-dependent shortest path algorithm with the numerical solution of the traffic flow equations. Various computational experiments are presented to describe different behavior patterns.

The Minimum Step Linkage Algorithm and Cumulative Cost Model for Time‐Dependent Shortest Paths

AbstractReal‐word road networks are typically time‐dependent, but research on time‐dependent shortest paths (TDSPs) is not as rich as that on static shortest paths (SSPs). For large networks, some speed‐up techniques are usually applied to compute SSPs. Unfortunately, many of these techniques are impractical for TDSPs, especially the techniques requiring a precomputation because the number of time instances may be incredibly large or even infinite. Therefore, this study introduced a new TDSP technique that is able to overcome the issue of infinite time instances by utilizing network geometry alone for the pre‐computation, namely the Minimum Step Linkage (MSL) algorithm. It works with a data model called Cumulative Cost Model (CCM). The theoretical concepts of the new data model and algorithm are described, and its performances were tested and compared with existing algorithms through a series of simulations.

Development and implementation of algorithms for vehicle routing during a no-notice evacuation

AbstractThis article develops and implements time-dependent shortest path and assignment algorithms for vehicle routing and assignment during a no-notice evacuation. A time-dependent shortest path algorithm with arc labeling is designed to improve computer storage space efficiency. Visual Basic for Application (VBA) is used to improve time efficiency of both shortest path and assignment algorithms. Performance of the algorithms is analyzed and compared through implementation in VBA and the General Algebraic Modeling System (GAMS). Since VBA seamlessly integrates with Microsoft Excel and enables efficient data manipulation, the algorithms implemented in VBA are more efficient and obtain optimal solutions faster than those implemented in the GAMS. The shortest path algorithm with arc labeling implemented in VBA may be used for real-time vehicle routing for large road networks during no-notice evacuations.

Hierarchical time-dependent shortest path algorithms for vehicle routing under ITS

ABSTRACTThe development of efficient algorithms for vehicle routing on time-dependent networks is one of the major challenges in routing under intelligent transportation systems. Existing vehicle routing navigation systems, whether built-in or portable, lack the ability to rely on online servers. Such systems must compute the route in a stand-alone mode with limited hardware processing/memory capacity given an origin/destination pair and departure time. In this article, we propose a computationally efficient, yet effective, hierarchical algorithm to solve the time-dependent shortest path problem. Our proposed algorithm exploits community-based hierarchical representations of road networks, and it recursively reduces the search space in each level of the hierarchy by using our proposed search strategy algorithm. Our proposed algorithm is efficient in terms of finding shortest paths in milliseconds for large-scale road networks while eliminating the need to store preprocessed shortest paths, shortcuts, lower bounds, etc. We demonstrate the performance of the proposed algorithm using data from Detroit, New York, and San Francisco road networks.

Solution approaches for determining user-oriented paths on dynamic networks

This paper addresses the time dependent multi-objective constrained shortest path problem. Solving the problem aims at providing the user a Pareto-optimal solution associated with an efficient path. The solution process takes into account information given by the user in order to obtain a path, satisfying his/her requirements. For the first time, more than two criteria are considered and the reference point methodology is used to define the aggregation function. In addition, knapsack-like constraints are introduced in the formulation in order to model budget restrictions. Dynamic-programming-based algorithms are devised and tested on randomly generated networks and on real life instances derived from US city maps. The computational results underline that the proposed algorithms are able to solve the problem in a reasonable amount of time. This is a good result since the problem considered contains features of three NP-hard problems: the multi-objective, the constrained and the time dependent shortest path problems.

A Variable Time-Discretization Strategies-Based, Time-Dependent Shortest Path Algorithm for Dynamic Traffic Assignment

Within the simulation-based dynamic traffic assignment (SBDTA) model, the time-dependent shortest path (TDSP) algorithm plays a crucial role in the path-set update procedure by solving for the current optimal auxiliary solution (shortest path). Common types of TDSP algorithms require temporal discretization of link/node time/cost data, and the discretization could affect the solution quality of TDSP and of the overall SBDTA as well. This article introduces two variable time-discretization strategies applicable to TDSP algorithms. The strategies are aimed at determining the optimal time discretization for time-dependent links/nodes travel time data. The first proposed strategy produces a specific discretization interval for each link. The second proposed strategy generates time-varying intervals for the same link over the analysis period. The proposed strategies are implemented in a link-based time-dependent A* algorithm in a SBDTA model DynusT and tested with two numerical experiments on two traffic networks. The results show that the proposed discretization methods achieve the research goal—to flexibly and scalably balance the memory usage and run time for SBDTA without degrading the convergence. This property is rather important when dealing with a large real-world network with a long analysis period.

Finding the cost-optimal path with time constraint over time-dependent graphs

Shortest path query is an important problem and has been well studied in static graphs. However, in practice, the costs of edges in graphs always change over time. We call such graphs as time-dependent graphs. In this paper, we study how to find a cost-optimal path with time constraint in time-dependent graphs. Most existing works regarding the Time-Dependent Shortest Path (TDSP) problem focus on finding a shortest path with the minimum travel time. All these works are based on the following fact: the earliest arrival time at a vertex v can be derived from the earliest arrival time at v 's neighbors. Unfortunately, this fact does not hold for our problem. In this paper, we propose a novel algorithm to compute a cost-optimal path with time constraint in time-dependent graphs. We show that the time and space complexities of our algorithm are O ( kn log n + mk ) and O (( n + m ) k ) respectively. We confirm the effectiveness and efficiency of our algorithm through conducting experiments on real datasets with synthetic cost.

A simulation-based dynamic traffic assignment model with combined modes

This paper presents a dynamic traffic assignment (DTA) model for urban multi-modal transportation network by con­structing a mesoscopic simulation model. Several traffic means such as private car, subway, bus and bicycle are con­sidered in the network. The mesoscopic simulator consists of a mesoscopic supply simulator based on MesoTS model and a time-dependent demand simulator. The mode choice is si­multaneously considered with the route choice based on the improved C-Logit model. The traffic assignment procedure is implemented by a time-dependent shortest path (TDSP) al­gorithm in which travellers choose their modes and routes based on a range of choice criteria. The model is particularly suited for appraising a variety of transportation management measures, especially for the application of Intelligent Trans­port Systems (ITS). Five example cases including OD demand level, bus frequency, parking fee, information supply and car ownership rate are designed to test the proposed simulation model through a medium-scale case study in Beijing Chaoy­ang District in China. Computational results illustrate excel­lent performance and the application of the model to analy­sis of urban multi-modal transportation networks.

City Logistics

This paper addresses freight management in large, congested urban settings. Congestion creates a substantial variation in travel time (speeds) during morning peak and evening peak periods. Besides the day-to-day dynamics of traffic conditions, traffic incidents contribute significantly to urban congestion, resulting in unplanned travel delays. Urban route designs that ignore such significant variations are often found to be inefficient or even infeasible (in regard to delivery or pickup time windows) in a congested traffic environment. This limitation may lead to delays, higher operational costs, and inferior customer service. To take the dynamics of traffic conditions into account, the proposed modeling framework includes an underlying dynamic network traffic simulation-assignment model that is able to compute time-dependent shortest paths (TDSPs) and simulate individual vehicles on a realistic representation of urban road network elements, including signalization, ramp metering, and other operational controls. A two-phase set-partitioning–based heuristic approach is proposed to construct freight vehicle routes. No parameter tuning is required. The integrated modeling framework was first tested on a small network, and then the application was demonstrated on a real-world urban network, the Chicago, Illinois, area network, with problem instances of up to 500 customers with TDSPs updated at 10-min intervals.

A speedup technique for dynamic graphs using partitioning strategy and multithreaded approach

There are many pre-processing-based speedup techniques for shortest path problems that are available in the literature. These techniques have an increased demand because of large datasets in such applications such as roadmaps, web search engines and mobile data sets. Pre-processing for the Time-Dependent Shortest Path Problem is still a demanding process that involves graph or network partitioning strategy. Efficient pre-processing of graphs or networks reduces the shortest path computation time while parallelizing the pre-processing phase improves the speedup of the system. In this paper, a speedup technique called Recursive Spectral Bisection (RSB) combined with the Elliptic Convolution of the shortest path method is proposed for dynamic Time-Dependent networks. The same method has been parallelized, and the results are tested on three types of graphs. It is observed that the Time-Dependent RSB combined with the Elliptic Convolution of the shortest path method has no update time, and the Query Performance Loss (QPL) is reduced in planar and road networks compared to random networks. In road networks, the proposed method achieves an average speedup in a QPL of 140. The use of the Parallel speedup technique results in an average speedup in a QPL of more than 1 in the planar and road networks.

Least-Latency Routing over Time-Dependent Wireless Sensor Networks

We consider the problem of least-latency end-to-end routing over adaptively duty-cycled wireless sensor networks. Such networks exhibit a time-dependent feature, where the link cost and transmission latency from one node to other nodes vary constantly in different discrete time moments. We model the problem as the time-dependent Bellman-Ford problem. We show that such networks satisfy the first-in-first-out (FIFO) property, which makes the time-dependent Bellman-Ford problem solvable in polynomial-time. Using the β-synchronizer, we propose a fast distributed algorithm to construct all-to-one shortest paths with polynomial message complexity and time complexity. The algorithm determines the shortest paths for all discrete times in a single execution, in contrast with multiple executions needed by previous solutions. We further propose an efficient distributed algorithm for time-dependent shortest path (TDSP) maintenance. The proposed algorithm is loop-free with low message complexity and low space complexity of O(maxdeg), where maxdeg is the maximum degree for all nodes. We discuss a suboptimal implementation of our proposed algorithms that reduces their memory requirement. The performance of our algorithms are experimentally evaluated under diverse network configurations. The results reveal that our algorithms are more efficient than previous solutions in terms of message cost and space cost.

Algorithm for Route Planning via Facilities with Time Dependent

In today’s century , people are looking for faster and efficient communication for travelling from source to destination via facilities. As the human tendency always try to go from source to cover or attend some facilities and then reach to destination within a required time. This paper focus on algorithm for optimal route planning via facility ( i.e petrol, grocery etc) with time dependent shortest path. The algorithm proposed here to minimize the travel time and provide a optimal path from source to destination with the facilities come in our path. We present here a algorithm on route planning which minimize the distance as well as time from source to destination.

최적 경로 탐색을 이용한 자전거 경로 선정에 관한 연구

다익스트라 알고리즘은 네트워크 상에서 최단경로를 찾는 것으로 널리 알려져 있다. 그러나, 최적 경로 탐색을 위하여 임의점과의 최단거리만 고려해서 선택하는 다익스트라 알고리즘보다 목표점까지 휴리스틱 요소를 고려하여 판단하는 <TEX>$A^*$</TEX> 알고리즘에 대한 연구가 더 필요하다. 따라서, 본 연구에서는 자전거 경로 선정을 위한 다익스트라 알고리즘과 <TEX>$A^*$</TEX> 알고리즘의 성능을 비교하였다. 이를 위하여, 자전거 경로 선정 요소를 이용하여 경사에 따른 수평거리와 평균 속도를 계산하였다. 그리고 다익스트라 알고리즘과 <TEX>$A^*$</TEX> 알고리즘을 적용해 최단거리와 최단시간에 따른 자전거 경로 선정을 수행하였다. 실험 결과 대규모 지역에서 <TEX>$A^*$</TEX> 알고리즘이 다익스트라 알고리즘보다 경로 선정 처리 시간이 빠르게 나타났다. 향후 최적 경로선정 알고리즘은 자전거 노선 계획이나 자전거 실시간 모바일 앱에 활용될 수 있다. Dijkstra's algorithm is one of well-known methods to find shortest paths over a network. However, more research on <TEX>$A^*$</TEX> algorithm is necessary to discover the shortest route to a goal point with the heuristic information rather than Dijkstra's algorithm which aims to find a path considering only the shortest distance to any point for an optimal path search. Therefore, in this paper, we compared Dijkstra's algorithm and <TEX>$A^*$</TEX> algorithm for bicycle route selection. For this purpose, the horizontal distance according to slope angle and average speed were calculated based on factors which influence bicycle route selection. And bicycle routes were selected considering the shortest distance or time-dependent shortest path using Dijkstra's or <TEX>$A^*$</TEX> algorithm. The result indicated that the <TEX>$A^*$</TEX> algorithm performs faster than Dijkstra's algorithm on processing time in large study areas. For the future, optimal path selection algorithm can be used for bicycle route plan or a real-time mobile services.

Development of One-to-One Shortest Path Algorithm Based on Link Flow Speeds on Urban Networks

Finding shortest paths on time dependent networks is an important task for scheduling and routing plan and real-time navigation system in ITS. In this research, one-to-one time dependent shortest path algorithms based on link flow speeds on urban networks are proposed. For this work, first we select three general shortest path algorithms such as Graph growth algorithm with two queues, Dijkstra`s algorithm with approximate buckets and Dijkstra`s algorithm with double buckets. These algorithms were developed to compute shortest distance paths from one node to all nodes in a network and have proven to be fast and efficient algorithms in real networks. These algorithms are extended to compute a time dependent shortest path from an origin node to a destination node in real urban networks. Three extended algorithms are implemented on a data set from real urban networks to test and evaluate three algorithms. A data set consists of 4 urban street networks for Anaheim, CA, Baltimore, MD, Chicago, IL, and Philadelphia, PA. Based on the computational results, among the three algorithms for TDSP, the extended Dijkstra`s algorithm with double buckets is recommended to solve one-to-one time dependent shortest path for urban street networks.

Framework of a Time-Based Simulation Model for the Analysis of Airfield Operations

This paper presents the framework of a new microscopic simulation model called Virginia Tech airfield simulation model (VTASIM) developed to study aircraft operations at airports. The model presented is designed and built under the concept of the time-based simulation model in which aircraft states are updated at fixed time intervals. By employing a vehicle-following model, VTASIM can portray aircraft movements on taxiways in great detail and with more accuracy than traditional discrete-event based airport simulation models. In order to find efficient taxiing routes between gates and runways, the model employs a time-dependent shortest path algorithm. Another unique feature of the model is its ability to capture the communication activities between pilots and controllers, which may cause delays in airfield operations especially at busy airports. This paper describes the methods and the structure of the model. The model is applied to Ronald Reagan Washington National Airport to illustrate its functionality.