Shortest Paths in Stochastic Time-Dependent Networks with Link Travel Time Correlation (original) (raw)

Adding an Extra Link Reduce Travel Time in Road Networks – Myth or Fact?

Any real life situation where there are nodes and edges, can be modeled as graphs. Road networks are one such example where roads can be modeled as edges and nodes can be modeled as cities. Such a model can be used to analyze and optimize various processes that take place in a road network. These models are commonly used to optimize the distance or time of travel between cities. In this study a model is developed where the speed of a vehicle is a linear function of the traffic volume. This model can be used identify locations of possible traffic congestion. When traffic congestion is observed in a road network traffic planners tend to add extra links to divert some of the traffic. This act which is done with the good intention sometimes worsens the situation. Such a situation can occur in a road network where there are two parallel roads between two cities and the two roads are connected in between by one or more links. This paper explores the criteria under which this problem can arise and suggest recommendations. A simulation run done with hypothetical data in a road network between Piliyandala and Horana in Sri Lanka is used in the study to illustrate the problem.

Variances of link travel time estimates: implications for optimal routes

International Transactions in Operational Research, 1999

In this paper, we explore the consequences of using link travel time estimates with high variance to compute the minimum travel time route between an origin and destination pair. Because of platoon formation or for other reasons, vehicles on a link separated by small headways tend to have similar travel times. In other words, the covariance of link travel times of distinct vehicles which are close together may not be zero. It follows that the variance of the mean of travel times obtained from a sample of n vehicles on a same link over small time intervals is of the form a + b/n where a and b would usually be positive. This result has an important implication for the quality of road network travel time information given by Intelligent Transportation Systems (ITS)Ðthat the variance of the estimate of mean travel time does not go to zero with increasing n. Thus the quality of information disseminated by ITS is not necessarily improved by increasing the market penetration of vehicles monitoring the system with the necessary equipment (termed probe vehicles). Estimates of a and b for a set of links are presented in the paper and consequences for probe-based ITS are explored by means of a simulation of such a system which is operational on an actual network.

Simulation-Based Method for Finding Minimum Travel Time Budget Paths in Stochastic Networks with Correlated Link Times

Transportation Research Record: Journal of the Transportation Research Board, 2014

The aim of this study was to solve the minimum path travel time budget (MPTTB) problem, in which the travel time budget was the reliability index. This index was defined as the sum of the mean path travel time and the scaled standard deviation, which included the covariance matrix to consider correlation. Two existing solution methods in the literature, the outer approximation algorithm and Monte Carlo simulation method, were applied to solve the MPTTB problem. The former method approximated the hard nonlinear constraint of the MPTTB problem by a series of linear cuts generated iteratively and repeatedly solved a mixed integer program. The latter method, which was a simulation-based method, included two stages. The first stage founded a set of candidate paths, and the second stage generated the distribution of travel times for the existing paths in the candidate set. The numerical results for these two solution methods were conducted on the Chicago sketch network, and results showed that the methods found comparable solutions though they have respective advantages and drawbacks. Although the outer approximation algorithm demonstrated promising performance, it still relied on repeatedly solving a mixed integer program (subproblem) with a commercial solver, which could be a challenging task in its own right.

The Short-Term Prediction of Link Travel Times in Signal Controlled Road Networks

IFAC Proceedings Volumes, 1994

Effective monitoring and efficient control of traffic in congested urban road networks are the usual goals of Urban Traffic Control (UTC) systems. The short-term prediction of link travel times would extend the capabilities of UTC significantly. particularly where collective or individual Dynamic Route Guidance (DRG) is implemented, since predictions of link travel times arising from hypothetical tra ffic flows are required to evaluate alternative route recommendations, before a recommendation is made. The potential for predicting link travel times from traffic flow on the approaches to the junction is examined using ARIMA techniques.

Value of travel time reliability: A review of current evidence

2012

Travel time reliability is a fundamental factor in travel behavior. It represents the temporal uncertainty experienced by travelers in their movement between any two nodes in a network. The importance of the time reliability depends on the penalties incurred by the travelers. In road networks, travelers consider the existence of a trip travel time uncertainty in different choice situations (departure time, route, mode, and others). In this paper, a systematic review of the current state of research in travel time reliability, and more explicitly in the value of travel time reliability is presented. Moreover, a meta-analysis is performed in order to determine the reasons behind the discrepancy among the reliability estimates.

Expected shortest paths in dynamic and stochastic traffic networks

Transportation Research Part B-methodological, 1998

AbstractÐThe dynamic and stochastic shortest path problem (DSSPP) is de®ned as ®nding the expected shortest path in a trac network where the link travel times are modeled as a continuous-time stochastic process. The objective of this paper is to examine the properties of the problem and to identify a technique that can be used to solve the DSSPP given information that will be available in networks with Intelligent Transportation System (ITS) capabilities. The paper ®rst identi®es a set of relationships between the mean and variance of the travel time of a given path and the mean and variance of the dynamic and stochastic link travel times on these networks. Based on these relationships it is shown that the DSSPP is computationally intractable and traditional shortest path algorithms cannot guarantee an optimal solution. A heuristic algorithm based on the k-shortest path algorithm is subsequently proposed to solve the problem. Lastly, the trade-o between solution quality and computational eciency of the proposed algorithm is demonstrated on a realistic network from Edmonton, Alberta. #

How to estimate, take into account, and improve travel time reliability in transportation networks

Many urban areas suffer from traffic congestion. Intuitively, it may seem that a road expansion (e.g., the opening of a new road) should always improve the traffic conditions. However, in reality, a new road can actually worsen traffic congestion. It is therefore extremely important that before we start a road expansion project, we first predict the effect of this project on traffic congestion.

Prediction of link travel times in the context of Nottingham’s urban road network

2003

Abstract: Traffic congestion is becoming a serious environmental threat that must be resolved quickly. Traditionally, travel information systems have been specific to a particular mode of transport. For instance, traffic information (road conditions broadcast) has been directed at drivers. Instead, travel information systems are now being developed which incorporate route guidance systems to divert drivers away from the congested areas either by change of travel mode or travel route. The mobile travel information system developed at The Nottingham Trent University enables progression from a passive mode of interaction between traffic control systems and road-users (one-way flow of information) to an active mode. The integration of data concerning traffic flows and individual journey plans thus makes it possible to perform optimisation of travel. This paper focuses on the issue of provision of real-time information about urban travel and assistance with planning travel. Nottingham’s ...