Travel Time Probability Prediction Based on Constrained LSTM Quantile Regression

Travel time reliability (TTR) is widely used to evaluate transportation system performance. Adverse weather condition is an important factor for affecting TTR, which can cause traffic congestions and crashes. Considering the traffic characteristics under different traffic conditions, it is necessary to explore the impact of adverse weather on TTR under different conditions. This study conducted an empirical travel time analysis using traffic data and weather data collected on Yanan corridor in Shanghai. The travel time distributions were analysed under different roadway types, weather, and time of day. Four typical scenarios (i.e., peak hours and off-peak hours on elevated expressway, peak hours and off-peak hours on arterial road) were considered in the TTR analysis. Four measures were calculated to evaluate the impact of adverse weather on TTR. The results indicated that the lognormal distribution is preferred for describing the travel time data. Compared with off-peak hours, the impact of adverse weather is more significant for peak hours. The travel time variability, buffer time index, misery index, and frequency of congestion increased by an average of 29%, 19%, 22%, and 63%, respectively, under the adverse weather condition. The findings in this study are useful for transportation management agencies to design traffic control strategies when adverse weather occurs.

This paper discusses the travel time reliability of road network under ice and snowfall conditions. With the introduction of correction function for the influence of ice and snowfall conditions on free travel time and capacity, the function of travel time was established. According to the limitation of the current travel time reliability, the new definition was defined on the basis of quantifying the relationship between LOS (Level of Service) and travel time reliability. The breakthrough of the traditional idea that the route travel time reliability model was set by general series system was made by considering the route as a whole unit; instead of using a paralleling system; another breakthrough was made to calculate the weighted average travel time reliability of OD (Original Destination) pair. On the basis of OD pair travel time reliability, the road network reliability model was set up. A partial road network was taken as an example to validate the effectiveness and practicality of the evaluation methodology.

Travel time reliability is a major factor affecting travelers’ route and mode choice behaviors, which is an important aspect of intelligent transportation systems. The calculation of travel time reliability measures is founded on the travel time distribution function. In practice, directly fitting the route-level travel time distribution function using complete route-level travel time data is challenging. As an alternative to route-level travel time data, segment-level travel time data are more abundant and easier to obtain. However, existing estimation methods of route travel time distribution function either neglect travel time correlation among segments, or rely on historical route-level data, or assume a single distribution type for all segments or routes. To address these issues, this paper proposes a moment-based method of estimating the route travel time distribution function that uses only segment-level travel time data. The proposed method estimates the correlation coefficients of segment travel times using the Rearrangement Inequality. Then, the four moments of route travel time are analytically derived. By further employing the corrected Cornish-Fisher expansion, the proposed method ultimately provides an analytical expression for the route travel time distribution function without assuming the distribution functions of segments or routes. The accuracy of the method is examined using data from a license plate recognition system on an expressway in Shenzhen and taxis GPS in Beijing. The proposed method enables a precise calculation of route travel time reliability in road networks that is quite important to travelers’ behavioral decisions and managers’ operational decisions.

A copula-based approach for estimating the travel time reliability of urban arterial

Travel time reliability is of high importance for passengers and transit agencies in the urban rail transit system. The travel time reliability models of OD pairs, line and network were established, and a short discussion on influence factors of travel time reliability was provided. Based on the real urban rail AFC data, the distribution of travel time was analyzed and a methodology based on kernel density estimation was presented to evaluate travel time reliability. Beijing urban rail transit system was used as a case study. It concluded that the travel time reliability is related to journey distance, interchange times and travel time segment. Keywords-urban rail transit; travel time reliability; kernel density estimation

To study the relationship of different reliability indices for road network under stochastic demand, an evaluation method based on travel time reliability (TTR) was set up for level of service (Los) reliability. Assuming that travelers acquire the variation of the route travel time based on past experiences and factor such variability into their route choice considerations in the form of travel time budget, which was defined as the minimal travel time that can accommodate a specified travel time reliability and can be derived according to the probability characteristics of log-normal distribution. Accordingly, Los reliability evaluation models of link and road network were proposed based on the link flow distribution, which can be determined by a travel time budget-based variational inequality (VI) network equilibrium model and a route-based solution algorithm. Some numerical studies on a small road network were presented to validate the proposed method and algorithm.

Congestion pricing is an effective management policy to reduce traffic congestion on freeways. This study accounted for the travel time difference and reliability on managed and general-purpose lanes in a modified approach to determining toll rates recently developed by others. The original approach was modified by developing an agent-based toll pricing strategy that used dynamic feedback control and accounted for trip purpose, travel time reliability (TTR), and level of income to maximize toll revenue while maintaining a minimum desired level of service on managed lanes. An external module was developed to execute the modified strategy in VISSIM, which exported the traffic data generated to an Excel spreadsheet in real time to calculate TTR, used in the route choice process. Agent-based modeling simulated drivers’ learning process and estimation of TTR from their previous commuting experience. A numerical example illustrated the modified strategy. The simulation results confirmed that, under high traffic demand, drivers with an urgent trip purpose had the highest probability of choosing managed lanes and that travel time on those lanes was more reliable than on general-purpose lanes. The modified strategy, the strategy currently deployed on I-95 express lanes, and the original strategy were compared. The modified one had a steadier increase in toll rate, significantly higher toll revenue, and speeds higher than 45 mph more frequently, compared with the current strategy. Furthermore, the modified approach was more realistic, accounted for TTR in route choice, and generated higher toll revenue under heavy traffic demand than did the original strategy.

The 6th edition of the Highway Capacity Manual (HCM-6) includes the concept of travel time reliability (TTR), which attempts to determine the distribution of average trip travel times over an extended period. TTR is an inherent part of travelers’ route choice decisions and is used by traffic managers to better quantify operations rather than simply using average travel times. The focus of this paper is on the HCM-6 urban street TTR methodology contained in Chapter 17. The approach uses historical data (e.g., weather and volume fluctuations) and simple empirical data (e.g., 1-day volume count) to provide the user with average travel time and reliability predictions for a traffic facility over an extended period (e.g., a year). To the best of the authors’ knowledge, there is no existing literature on validating the HCM-6 methodology with empirical data. The goals of this paper were to validate the HCM-6 urban street reliability methodology by comparing the empirical Bluetooth (BT) travel time distributions with the estimated HCM-6 distribution, and to propose potential HCM-6 augmentation strategies. Archived BT data from a 0.5-mi urban arterial in Lincoln, Nebraska was used for comparison. It was found that there were statistically significant differences, but minimal practical differences, between the mean of the predicted HCM-6 travel time distribution and the mean of the empirical distribution. However, the HCM-6 distribution had a lower variance than the empirical distribution. Not surprisingly, the HCM-6 model underestimated the TTR metrics (buffer index and the planning time index) by approximately 62% and 9%, respectively.

Public bus transit travel time is affected by many factors, including traffic signals and traffic condition. Transit agencies have implemented transit signal priority (TSP) strategies to reduce transit travel time and improve service reliability. However, due to the lack of empirical data, these factors' collective impact and bus travel time strategies have not been studied at the stop-to-stop segment level. This research focuses on the factors affecting travel time reliability, emphasising the variability between operators and the policy implications of such differences. One-way analysis of variance (ANOVA) statistical methods have been used to assess the quality implications of public bus transportation time reliability. This research seeks to investigate the factors affecting the travel time (TT) reliability of bus transport. Studies were conducted along three bus routes serving different areas. Factors strongly related to TT reliability include route length, number of signalised intersections, day of the week, bus stops, departure delays, bus lane, passenger boarding and alighting, weather condition, and fare structure. Based on the proposed model factors affecting TT reliability, it was found that TT is strongly affected by the number of bus stoppings and also the length of the route. The reliability of all three routes during the weekday is low because of delays in departure. The number of signalised intersections along the route affects reliability. Meanwhile, more passengers boarding and paying cash increased the travel time reliability of buses.

ABSTRACTTravel time reliability is very critical for emergency vehicle (EV) service and operation. The travel time characteristics of EVs are quite different from those of ordinary vehicles (OVs). Although EVs own highest road privilege, they may still experience unexpected delay that results in massive loss to the society. In this study, we employ the generalized extreme value (GEV) theory to measure extremely prolonged travel time and analyze the potential influential factors. First, among three GEV distributions, Weibull distributions are found to be the best distribution model according to several goodness-of-fit tests; a new reliability index is derived to measure travel time reliability. Numerical examples demonstrate the advantages of GEV-based reliability index over variance and percentile value in the applications of EV. This index will be of great practicability in the EV operation performance and reliable route choices. Second, we further investigate the potentially influential factors of EV travel time reliability. Results show that link length and left-turn traffic volume may have an adverse impact on the link reliability while more left-turn lanes may increase the travel time reliability. The influential factor study will help us understand the causes of the EV travel time delay and the differences of travel time reliability between OVs and EVs.

Travel time distribution studies are fundamental for supporting transportation system reliability studies, particularly for urban road networks. However, such studies are generally based on travel time data sets with limited sample sizes, which provide inconsistent findings. In this paper, a large amount of travel time data collected from the emerging radio frequency identification (RFID) technique are used to conduct empirical investigations and estimations of travel time distributions, and three major findings are determined. First, travel time data are shown to have a complex statistical structure: the travel time distribution is in general peaky, multi-modal, and skewed to the right, which cross validates findings shown in previous publications. Second, unimodal distribution models are shown to be unable to capture the complex statistical dynamics embedded in the travel time data; therefore, a multistate distribution model is more appropriate for modeling travel time distributions. In this respect, a three-component gaussian mixture model (GMM) is tested and results consistently outperform those of unimodal distribution models. Finally, the aggregation time interval is shown to have a trivial effect on the shape of travel time distributions: the travel time distribution is stable under different aggregation time intervals. Future work is recommended to investigate further travel time variabilities and travel time distribution estimations.

The impact of work zones on mean travel time and travel time reliability has gained attention as agencies focus on performance measurement. Travel time reliability in work zones often has been difficult for agencies to quantify because of the time and expense required to collect travel time data. Several private-sector companies have begun to sell travel time data; this availability has created an opportunity to examine cost-effectively work zone impacts on travel time reliability on a broader basis. The Virginia Department of Transportation recently acquired probe vehicle-based travel time data for 2010 from a private-sector data provider. These data were used to calculate measures of travel time reliability at 15 work zones and to examine factors that affected travel time reliability. Travel time reliability was quantified with 95th percentile travel time, a buffer index, and a planning time index. The work zones experienced a statistically significant degradation across all measures of travel time reliability as compared with baseline conditions. Work zone mean buffer index, planning time index, and 95th percentile travel time rates were higher by 48%, 18%, and 16%, respectively. Although lane closures occurred during off-peak periods, work zones that involved lane closures experienced increases in their mean buffer index, planning time index, and 95th percentile travel time with rates of 67%, 23%, and 22%, respectively. Annual average daily traffic per lane and the number of access points per mile were found to have the most obvious relationships with declines in reliability at work zones.

In this paper, a model to estimate travel time reliability is proposed assuming a stochastic user equilibrium. Travel time reliability is defined as the probability that travel time between the origin and destination does not exceed a standard travel time corresponding to each service level. Also it is shown how to calculate travel time reliability in a large-scale network. This model is applied to the road network in the Hanshin area to evaluate new lines in the national road plan from the viewpoint of travel time reliability. Some important links and lines in the future road network are evaluated from the viewpoint of travel time reliability.

The rapid progress of information technology (IT) may provide us with new insights into understanding traffic phenomena, and could help mitigate traffic problems. One of the key applications of IT to traffic and transport analysis is the identification of the location of moving objects using the Global Positioning System (GPS). It is expected that detailed traffic analysis could be carried out using these data. In this article, we first summarize the various applications of probe data in transport analysis. GPS data are merely a sequence of locations, and further data transformation such as map-matching, data-reduction, processing, and reporting is needed to use them effectively. We then discuss the application of bus probe data to evaluating travel time variability and the level of service (LOS) of roads. A methodology for evaluating the road network from the viewpoint of travel time stability and reliability using bus probe data is proposed. Travel time distributions of arbitrary routes are estimated by statistically summing up directly observed multiple travel time distributions. Based on the development of methodologies to estimate travel time distributions of arbitrary routes covered by the bus probe survey, this study proposes an approach to evaluate the LOS of road networks based on the concept of travel time reliability.

Traffic incidents are recognised as one of the key sources of non-recurrent congestion that often leads to reduction in travel time reliability (TTR), a key metric of roadway performance.A method is proposed here to quantify the impacts of traffic incidents on TTR on freeways.The method uses historical data to establish recurrent speed profiles and identifies nonrecurrent congestion based on their negative impacts on speeds.The locations and times of incidents are used to identify incidents among non-recurrent congestion events.Buffer time is employed to measure TTR.Extra buffer time is defined as the extra delay caused by traffic incidents.This reliability measure indicates how much extra travel time is required by travellers to arrive at their destination on time with 95% certainty in the case of an incident, over and above the travel time that would have been required under recurrent conditions.An extra buffer time index (EBTI) is defined as the ratio of extra buffer time to recurrent travel time, with zero being the best case (no delay).A Tobit model is used to identify and quantify factors that affect EBTI using a selected freeway segment in the Southeast Queensland, Australia network.Both fixed and random parameter Tobit specifications are tested.The estimation results reveal that models with random parameters offer a superior statistical fit for all types of incidents, suggesting the presence of unobserved heterogeneity across segments.What factors influence EBTI depends on the type of incident.In addition, changes in TTR as a result of traffic incidents are related to the characteristics of the incidents (multiple vehicles involved, incident duration, major incidents, etc.) and traffic characteristics.