Standard Deviation Of Travel Time Research Articles

Time-reliability optimization for the stochastic traveling salesman problem

This paper presents a novel approach to addressing the Stochastic Traveling Salesman Problem (STSP), a classical problem in combinatorial optimization, by integrating travel time and reliability factors into the decision-making process. Traditional TSP models primarily focus on minimizing the total travel distance or cost without considering the reliability of each route. In real-world situations, especially in logistics and network design, it's just as important to have reliable routes. A reliable route means there's a good chance it will be completed successfully and on time. Our research extends the conventional STSP framework by incorporating a reliability metric for each route, alongside the standard travel time metric. A tri-objective optimization model is proposed to minimize the mean and standard deviation of travel time and maximize route reliability simultaneously. A new algorithm called Permutation Binary-Addition-Tree (BAT) is proposed to solve the problem more efficiently when there is uncertainty. Our approach marks a significant step towards more realistic and practical solutions for route optimization problems in dynamic and uncertain environments. We also present a complexity analysis of our model against traditional cost-only TSP solutions, demonstrating the efficacy of considering reliability in route planning.

Estimating network flow and travel behavior using day-to-day system-level data: A computational graph approach

To estimate network flow and travel behavior under recurrent traffic conditions, we leverage computational graphs and multi-source system-level data and solve a single-level optimization problem consistent with stochastic user equilibrium under logit assignment (SUELOGIT). Our model learns time-specific O-D matrices and utility functions and network flow parameters such as link flows, path flows, and travel times. To increase the model’s representational capacity for reproducing observed link flows and travel times, the parameters of the link performance functions are assumed link-specific. More importantly, the utility function in the route choice model is enriched with (i) link-specific parameters to capture the effect of unobserved attributes on route choices and (ii) period-specific parameters weighting the observed features in the utility function to capture the heterogeneity of travelers preferences among periods of the day. Experiments on synthetic data show that the parameters of the models can be consistently recovered and that the solution of the model satisfies the SUELOGIT conditions with high accuracy. The estimation procedure is also robust to random noise in both the observed traffic flow and travel time, and it requires very few hyperparameter tuning. Subsequently, the algorithm is deployed at a large scale using real-world multi-source data in Fresno, CA, with hourly data collected during the morning and afternoon peak periods of October 2019. The utility function includes link-specific effects and attributes such as travel time, the standard deviation of travel time, the number of traffic incidents, and socio-demographic information obtained from the US Census. We obtain estimates for the total trips and travelers’ utility function by hour of the day and for the average values of the link performance parameters that are reasonable and informative on the demand and supply characteristics of the transportation network.

Traffic Prediction and Signal Controlling Using Mode-search Optimization Based Deep Long Short Term Memory Classifier

Aim: The research aims at developing a traffic prediction and signal controlling model based on deep learning technique in order to provide congestion-free transportation in Intelligent Transport System (ITS). Need for the Research: Recent technical advancements in the ITS, industrialization, and urbanization increase traffic congestion, which leads to high fuel consumption and health issues. This signifies the need for a dynamic traffic management system to handle the traffic congestion issues that negatively affect the transportation service. Methods: For promoting congestion-free transportation in the ITS, this research aims to devise a traffic prediction and control system based on deep learning techniques that effectively controls the traffic during peak hours. The proposed mode-search optimization effectively clusters the vehicles based on the necessity. In addition, the mode-search optimization tunes the optimal hyperparameters of the deep Long Short Term Memory classifier, which minimizes the training loss. Further, the traffic signal control system is developed through the mode-search-based deep LSTM classifier for predicting the path of the vehicles by analyzing the attributes, such as velocity, acceleration, jitter, and priority of the vehicles. Result: The experimental results evaluate the efficacy of the traffic prediction model in terms of quadratic mean of acceleration (QMA), jitter, standard deviation of travel time (SDTT), and throughput, for which the values are found to be 37.43, 0.23, 8.75, and 100 respectively. Achievements: The proposed method attains the performance improvement of 5% to 42% when compared with the conventional methods.

Estimating network travel time reliability with network partitioning

Network travel time reliability can be represented by a relationship between network space-mean travel time and the standard deviation of network travel time. The primary objective of this paper is to improve estimation of the network travel time reliability with network partitioning. We partition a heterogeneous large-scale network into homogeneous regions (clusters) with well-defined Network Fundamental Diagrams (NFD) using directional and non-directional partitioning approaches. To estimate the network travel time reliability, a linear relationship is estimated that relates the mean travel time with the standard deviation of travel time per unit of distance at the network level. The impact of different partitioning approaches, as well as the number of clusters, on the network travel time reliability relationship are also explored. To estimate individual vehicle travel times, we use two distinct approaches to allocate vehicle trajectories to different time intervals, namely trajectory and sub-trajectory methods. We apply the proposed framework to a large-scale network of Chicago using a 24-h dynamic traffic simulation. Partitioning and travel time reliability estimation are conducted for both morning and afternoon peak periods to demonstrate the impacts of travel demand pattern variations. The numerical results show that the sub-trajectory method for the network travel time reliability estimation and the directional partitioning with three clusters have the highest performance among other tested methods. The analyses also demonstrate that partitioning a heterogeneous network into homogeneous clusters may improve network travel reliability estimation by estimating an independent relationship for each cluster. Also, comparing morning and afternoon peak periods suggests that the estimated parameter for the linear network travel time reliability relationship is directly related to the coefficient of variation of density as a measure of spatial distribution of congestion across the network.

Traffic dynamics on a double layer coupled network considering physical queuing

The development of modern economy makes the problem of traffic congestion increasingly serious. Many real traffic systems can be abstracted as that a variety of networks coupled and interconnected with each other. In this paper, the traffic dynamics on a double layer coupled network system is studied based on cellular automata model considering physical queuing. We explore the effect of maximal velocities in the two layer networks on the network capacity, and the mean and standard deviation of travel time. The results show that the increase of upper network velocity is beneficial to the traffic capacity and the efficiency of long-distance travel, but will also lead to larger deviation and lower reliability. We explain the phenomena by studying the usage of upper network. Finally, we investigate the vehicle distribution by adopting the Gini coefficient. It is found that the increase of upper network speed will make the traffic load distributed more uniformly in the system.

2359 - Pareto Optimality for Assessing Multimodal Transportation Accessibility: Balancing Equity and Efficiency When Sitting Interventions

Background Travel time as a proxy for spatial accessibility in health care location-allocation studies can be particularly relevant when spatially concentrated population have a repeating pattern of infections, or a shorter return interval for services. This travel time based accessibility study focuses on a population identified as having repeat sexually transmitted infections. This population has been shown to be strongly associated with low socioeconomic status, which often corresponds to substantive reliance on public transit. Public health intervention studies barely consider transit when quantifying accessibility. Moreover, common frameworks used in these studies mostly focus on efficient allocation of services and usually disregard equity issues. Methods This study proposes a Pareto optimality approach to recommend locations that are multimodal accessible and allow equitable and efficient access to services. A simulated at-risk population, drawn from known core areas of repeat sexually transmitted infections in Kalamazoo County, Michigan, is examined. A raster-based drive time and a transit time model were developed using ArcGIS. Bi-objective optimization models were then developed to balance efficiency (by minimizing average travel time of the cohort) and equity (by minimizing variations of travel time from all simulated households). Results This raster-based cost optimization approach successfully identifies potential locations that are efficiently and equitably accessible using different transportation modes. A range of alternative solutions (Pareto frontiers) spatially and statistically enable decision makers to select from multiple locations and assess acceptable limits to travel for a given population. In our example, choosing a location, T2 over T1 means reducing the average travel time by 2.19 minutes by conceding only 11.94% increase in standard deviation of travel time. Additionally, T2 reduces the average travel time by 8.91 minutes and standard deviation by 3.7 minutes when comparing to existing facility location. In general, the spatial area bounded by the minimum average and minimum standard deviation location for a frontier line would represent the constraints to intervention location. The area then becomes a usable metric to measure transit versus private vehicle accessibility. Conclusions Improving spatial access to health facilities is important in reducing the prevalence of disease. Therefore, multimodal accessibility should be emphasized in future intervention placement research. The analysis of individual's travel time from distinct households to facility locations helps to address the inherent mismatch between current statistical methods that require detection of significant densities and the reality of individuals located on a street network or constrained by a particular transportation modality.

Forecasting travel time reliability in urban road transpo

Assessment of travel time reliability as a fundamental factor in travel behaviour has become a very important aspect in both transport modelling and economic appraisal. Improved reliability could provide a significant economic benefit if it is adequately calculated in cost-benefit analyses for which the theoretical background has already been set. However, methods to forecast travel time reliability as well as travel behaviour models including its effects are rather scarce and there is a need for development in this field. Another important aspect could be the influencing factor of reliability in travel demand management and related policy-making. Therefore, this paper intends to further analyse reliability focusing exclusively on urban road transport based on automatic measurements of journey times and traffic volumes from a dataset of the city of Budapest. The main finding and the novelty of the study is a model which can forecast the standard deviation of travel times based on the volume-capacity ratio and the free-flow travel time. The paper also provides a real-life numerical experiment in which the proposed model has been compared with other, existing ones. It proves that besides existing mean-delay-based models, travel time reliability can be forecasted based on the volume-capacity ratio with an adequate accuracy.

Finding the Most Reliable Strategy on Stochastic and Time-Dependent Transportation Networks: A Hypergraph Based Formulation

This study addresses the problem of determining the most reliable time-adaptive strategy on a stochastic and time-dependent transportation network. The reliability is measured as a conic combination of the mean and standard-deviation of travel time and is termed robust-cost. The stochastic time-dependent network is represented as a directed acyclic hypergraph, where the time-adaptive strategies correspond to the hyperpaths. This representation transforms the problem to that of determining the hyperpath with the least robust-cost on the constructed hypergraph. The minimum robust-cost strategy problem is difficult to solve because of the non-linear objective function. Consequently, the solution procedures commonly adopted in the literature —that are based on substrategy optimality and substrategy non-dominance —are not applicable to this problem. In this light, we propose a novel bounds-based iterative algorithm that determines the minimum robust-cost strategy on the stochastic and time-dependent networks. This algorithm needs to determine the least and K-best strategies in the second moment of travel time, for which an efficient procedure is also proposed. The algorithm is shown to be exact and exhibit parameterically polynomial behavior; computational tests were performed to demonstrate its efficiency. Further, tests showed that the minimum robust-cost strategy compromises little in terms of the mean travel time (0.2%–2.9%) —compared to least expected travel time strategy— with significant reduction in travel time variability (6.2%–29.8%).

Estimating freeway route travel time distributions with consideration to time‐of‐day, inclement weather, and traffic incidents

SummaryThis paper develops an efficient probabilistic model for estimating route travel time variability, incorporating factors of time‐of‐day, inclement weather, and traffic incidents. Estimating the route travel time distribution from historical link travel time data is challenging owing to the interactions among upstream and downstream links. Upon creating conditional probability function for each link travel time, we applied Monte Carlo simulation to estimate the total travel time from origin to destination. A numerical example of three alternative routes in the City of Buffalo shows several implications. The study found that weather conditions, except for snow, incur minor impact on off‐peak and weekend travel time, whereas peak travel times suffer great variations under different weather conditions. On top of that, inclement weather exacerbates route travel time reliability, even when mean travel time increases moderately. The computation time of the proposed model is linearly correlated to the number of links in a route. Therefore, this model can be used to obtain all the origin to destination travel time distributions in an urban region. Further, this study also validates the well‐known near‐linear relation between the standard deviation of travel time per unit distance and the corresponding mean value under different weather conditions. Copyright © 2016 John Wiley & Sons, Ltd.

Values of travel time in Europe: Review and meta-analysis

This paper reports the most extensive meta-analysis of values of time yet conducted, covering 3109 monetary valuations assembled from 389 European studies conducted between 1963 and 2011. It aims to explain how valuations vary across studies, including over time and between countries. In addition to the customary coverage of in-vehicle time in review studies, this paper covers valuations of walk time, wait time, service headway, parking space search time, departure time switching, time in congested traffic, schedule delay early and late, mean lateness and the standard deviation of travel time. Valuations are found to vary with type of time, GDP, distance, journey purpose, mode, the monetary numeraire and a number of factors related to estimation. Model output values of time compare favourably with earnings data, replicate well official recommended values obtained from major national studies, and are transferable across countries. These implied monetary values serve as very useful benchmarks against which new evidence can be assessed and the meta-model provides parameters and values for countries and contexts where there is no other such evidence.

Pruning Algorithms to Determine Reliable Paths on Networks with Random and Correlated Link Travel Times

This study addresses various formulations of the optimal reliability path problem on stochastic networks. Robust-Cost is adopted as the measure of reliability, which is defined as a weighted combination of the mean and standard deviation of travel time. The principal problem solved is the Minimum Robust-Cost Path (MRCP) problem in the presence of Correlated link travel times. It is shown that the subpath optimality and subpath non-dominance principles, which are conventionally adopted in the literature, cannot be used to solve this problem. In this light, this study proposes an algorithm based on the subpath pruning approach, which eliminates nonoptimal subpaths by using a pruning criterion. We construct the novel pruning criterion, which depends on only two independent objectives, by transforming the network and using efficient shortest path algorithms. The correctness of the algorithm is established, and its good practical performance is demonstrated on real-world networks. Furthermore, the pruning procedure is generalized with suitable modifications to solve three related problems: (i) the MRCP problem with independent link travel times, (ii) the K-best Robust-Cost Paths problem, and (iii) the MRCP problem with stochastic nondominance constraints. These extensions demonstrate the potential wider applications of the proposed solution approach.

Integrating the mean–variance and scheduling approaches to allow for schedule delay and trip time variability under uncertainty

Uncertainty of travel times and the impact on travel choice behavior has been recognized as an increasingly important research direction in the past decade. This paper proposes an extension to the popular scheduling approach to model traveler’s departure time choice behavior under uncertainty, with the main focus on a richer representation of uncertainty. This more general approach incorporates a separate term to reflect the risk aversion associated with uncertainty. Recognizing the correlation between expected schedule delay and travel time variability, the schedule delay components in the generalized approach are defined in terms of expected travel time, which differs from the scheduling approach. This approach is developed based on the analytical investigation of the relationship between the expected schedule delay and the mean and standard deviation of travel time. An analytical equivalence was found between the scheduling approach and the general approach given a departure time t. To investigate the empirical performance of the generalized approach, two state preference (SP) data sets are used; one from China with a symmetric travel time distribution and the other from Australia with an asymmetric distribution. Both studies show empirical evidence of an equivalence in respect of statistical fit between the generalized and the scheduling approaches, as found from analytical investigations. The Chinese study gives support in the generalized model to including both the mean–variance and the scheduling effects; whereas the Australian study finds only the mean–variance specification has statistical merit. Despite the different travel contexts, it is noteworthy in both empirical settings, that the parameter estimate for arriving earlier than the preferred arrival time (PAT) in the generalized model is positive. This suggests that commuters tend to prefer to arrive earlier in order to guarantee he/she will not be late. This paper contributes to a better understanding of performances of different reliability measures and their relationships. The practical value of the various unreliability measures is provided showing that these indicators are easy to obtain for inclusion in project appraisal.

Transit-Based Emergency Evacuation with Transit Signal Priority in Sudden-Onset Disaster

This study presents methods of transit signal priority without transit-only lanes for a transit-based emergency evacuation in a sudden-onset disaster. Arterial priority signal coordination is optimized when a traffic signal control system provides priority signals for transit vehicles along an evacuation route. Transit signal priority is determined by “transit vehicle arrival time estimation,” “queuing vehicle dissipation time estimation,” “traffic signal status estimation,” “transit signal optimization,” and “arterial traffic signal coordination for transit vehicle in evacuation route.” It takes advantage of the large capacities of transit vehicles, reduces the evacuation time, and evacuates as many evacuees as possible. The proposed methods were tested on a simulation platform with Paramics V6.0. To evaluate and compare the performance of transit signal priority, three scenarios were simulated in the simulator. The results indicate that the methods of this study can reduce the travel times of transit vehicles along an evacuation route by 13% and 10%, improve the standard deviation of travel time by 16% and 46%, and decrease the average person delay at a signalized intersection by 22% and 17% when the traffic flow saturation along an evacuation route is0.8<V/C≤1.0andV/C>1.0, respectively.

Toward an automated methodology for the valuation of reliability

There is a significant body of research related to the valuation of reliability in transportation. Such work has tended to rely on the stated preference methodology, where respondents are asked to make trade-offs between the mean and standard deviation of travel time. The literature has suggested that a revealed preference (RP) methodology may provide an alternative means of estimating a value of reliability. In this article we show how emerging data sources reveal travelers' preferences and, in combination with traditional choice modeling methods, can be used to estimate a value of reliability. We illustrate this RP methodology using smart-card data from the multimodal public transport network of London, UK. We are able to estimate a useable “reliability ratio” for three of four public transport modes modeled, and account for an unexpected result based upon the data available.

Accounting for travel time variability in the optimal pricing of cars and buses

A number of studies have shown that in addition to travel time and cost as the common influences on mode, route and departure time choices, travel time variability plays an increasingly important role, especially in the presence of traffic congestion on roads and crowding on public transport. The dominant focus of modelling and implementation of optimal pricing that incorporates trip time variability has been in the context of road pricing for cars. The main objective of this paper is to introduce a non-trivial extension to the existing literature on optimal pricing in a multimodal setting, building in the role of travel time variability as a source of disutility for car and bus users. We estimate the effect of variability in travel time and bus headway on optimal prices (i.e., tolls for cars and fares for buses) and optimal bus capacity (i.e., frequencies and size) accounting for crowding on buses, under a social welfare maximisation framework. Travel time variability is included by adopting the well-known mean–variance model, using an empirical relationship between the mean and standard deviation of travel times. We illustrate our model with an application to a highly congested corridor with cars, buses and walking as travel alternatives in Sydney, Australia. There are three main findings that have immediate policy implications: (i) including travel time variability results in higher optimal car tolls and substantial increases in toll revenue, while optimal bus fares remain almost unchanged; (ii) when bus headways are variable, the inclusion of travel time variability as a source of disutility for users yields higher optimal bus frequencies; and (iii) including both travel time variability and crowding discomfort leads to higher optimal bus sizes.

Analysis of Impacts on Dispatcher's Route Choice Behaviour by Road Improvements on Using a Trial and Error Learning Model

In previous research, a route choice behavior model was constructed using trial and error type learning dynamics derived from evolutionary game theory. The model can represent the route choice behavior seen in logistics companies, such as the consideration of daily variations in travel time and variations in travel time due to traffic accidents, the choice of multiple routes, and the changing of route choice behavior based on evaluations of past route choice behavior. After having adopted an actual strategy (route choice), the model is such that the strategy is assumed to change according to whether the strategy was successful or not. This paper used this model to analyze the effect of actual planned road projects on the route choice behavior of logistics companies. Analysis was shown to be possible by using the micro-simulation package VISSIM to estimate the change in the average travel time and the standard deviation of the travel time due to road projects, and using the results as the input value for the model. Furthermore, by observing the transition in route selectivity, it was possible to understand how route selectivity varies and the way in which the selectivity finally converges according to the change in the average travel time and in the standard deviation of travel time due to road projects.

A bi-objective user equilibrium model of travel time reliability in a road network

Travel time, travel time reliability and monetary cost have been empirically identified as the most important criteria influencing route choice behaviour. We concentrate on travel time and travel time reliability and review two prominent user equilibrium models incorporating these two factors. We discuss some shortcomings of these models and propose alternative bi-objective user equilibrium models that overcome the shortcomings. Finally, based on the observation that both models use standard deviation of travel time within their measure of travel time reliability, we propose a general travel time reliability bi-objective user equilibrium model. We prove that this model encompasses those discussed previously and hence forms a general framework for the study of reliability related user equilibrium. We demonstrate and validate our concepts on a small three-link example.

A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times

Heavy and uncertain traffic conditions exacerbate the commuting experience of millions of people across the globe. When planning important trips, commuters typically add an extra buffer to the expected trip duration to ensure on-time arrival. Motivated by this, we propose a new traffic assignment model that takes into account the stochastic nature of travel times. Our model extends the traditional model of Wardrop competition when uncertainty is present in the network. The focus is on strategic risk-averse users who capture the trade-off between travel times and their variability in a mean-standard deviation objective, defined as the mean travel time plus a risk-aversion factor times the standard deviation of travel time along a path. We consider both infinitesimal users, leading to a nonatomic game, and atomic users, leading to a discrete finite game. We establish conditions that characterize an equilibrium traffic assignment and find when it exists. The main challenge is posed by the users' risk aversion, since the mean-standard deviation objective is nonconvex and nonseparable, meaning that a path cannot be split as a sum of edge costs. As a result, even an individual user's subproblem—a stochastic shortest path problem—is a nonconvex optimization problem for which no polynomial time algorithms are known. In turn, the mathematical structure of the traffic assignment model with stochastic travel times is fundamentally different from the deterministic counterpart. In particular, an equilibrium characterization requires exponentially many variables, one for each path in the network, since an edge flow has multiple possible path-flow decompositions that are not equivalent. Because of this, characterizing the equilibrium and the socially optimal assignment, which minimizes the total user cost, is more challenging than in the traditional deterministic setting. Nevertheless, we prove that both can be encoded by a representation with just polynomially many paths. Finally, under the assumption that the standard deviations of travel times are independent from edge loads, we show that the worst-case ratio between the social cost of an equilibrium and that of an optimal solution is not higher than the analogous ratio in the deterministic setting. In other words, uncertainty does not further degrade the system performance in addition to strategic user behavior alone.

A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times

Heavy and uncertain traffic conditions exacerbate the commuting experience of millions of people across the globe. When planning important trips, commuters typically add an extra buffer to the expected trip duration to ensure on-time arrival. Motivated by this, we propose a new traffic assignment model that takes into account the stochastic nature of travel times. Our model extends the traditional model of Wardrop competition when uncertainty is present in the network. The focus is on strategic risk-averse users who capture the tradeoff between travel times and their variability in a mean-standard deviation (mean-stdev) objective, defined as the mean travel time plus a risk-aversion factor times the standard deviation of travel time along a path. We consider both infinitesimal users, leading to a non-atomic game, and atomic users, leading to a discrete finite game.We establish conditions that characterize an equilibrium traffic assignment and find when it exists. The main challenge is posed by the users’ risk aversion, since the mean-stdev objective is non-convex and non-separable, meaning that a path cannot be split as a sum of edge costs. As a result, even an individual user’s sub-problem — a stochastic shortest path problem — is a non-convex optimization problem for which no polynomial time algorithms are known. In turn, the mathematical structure of the traffic assignment model with stochastic travel times is fundamentally different from the deterministic counterpart. In particular, an equilibrium characterization requires exponentially many variables, one for each path in the network, since an edge-flow has multiple possible path-flow decompositions that are not equivalent. Because of this, characterizing the equilibrium and the socially-optimal assignment, which minimizes the total user cost, is more challenging than in the traditional deterministic setting. Nevertheless, we prove that both can be encoded by a representation with just polynomially-many paths. Finally, for the case of uncertainty parameters that are independent from edge loads, we show that although an equilibrium assignment results in a total user cost that is higher than that of the socially-optimal one, it is not higher than the analogous ratio in the deterministic setting. In other words, uncertainty does not further degrade the system performance in addition to strategic user behavior alone.

Spatial and temporal visualization of transit operations performance data at a network level

The operational performance of public transport networks is an important aspect of urban planning and development. Despite the network focus of services and delays which are often focused spatially, little research has examined the spatial pattern of operational performance of urban public transport.This paper explores the operational performance of on-road public transport using spatial and historical analysis at a network wide level. Operational performance is investigated through analysis of stop level Automatic Vehicle Location (AVL) data and utilizes visualization techniques in geographical information systems (GISs) to explore spatial and temporal patterns of change. The network in question is the Melbourne tram (streetcar) network, which has a large historical dataset of AVL data since 2001 providing information on scheduled arrival times, actual arrival times, times of departure, and more.Statistical analysis is undertaken to determine average travel times and the standard deviation of travel times. The statistical analysis is then imported into a GIS package for further analysis; the Inverse Distance Weighted (IDW) methodology is used to explore spatial variations in data. Outputs include observation of travel times across the network, a reliability analysis investigating actual vs. scheduled travel times and coefficients of variation, and trend analyses to observe the change in tram travel time and change in coefficient of variation.Through this analysis, various changes in travel time and reliability were observed between 2001 and 2010. Vast areas saw improvements in travel time and reliability, while some areas were identified to have deteriorated performance. This paper identifies that the spatial representation of large datasets is of great value in an ongoing monitoring of the network and a powerful reporting tool on a network level basis. Moreover, the results identify transit issues for the Melbourne tram network planners for further investigation.