Search

Side collisions caused by sudden vehicle cut-ins comprise a significant proportion of traffic accidents. Due to the complex and dynamic nature of traffic environments, the warning algorithms in advanced driving assistant systems (ADAS) often misjudge and misdiagnose risk and omit necessary warnings, because they rely solely on the sensing information of the single vehicle equipped with ADAS and have limited insights from and communication with the surrounding vehicles and traffic environment. To improve the effectiveness of ADAS in cut-in scenarios, this study established a collision warning model in a vehicle-to-vehicle (V2V) communication environment. Firstly, based on the support vector machine-recursive feature elimination (SVM-RFE) lane-change intent-recognition model, the lane-change feasibility and the change rate of the lateral offset, the logical ``and'' was used to establish a lane-change behavior prediction model, and a trajectory prediction model was established based on the long short-term memory (LSTM). Then, based on the proposed comprehensive prediction model for lane-change behavior, the driving trajectory prediction model, and the oriented bounding box (OBB) detection algorithm, a collision warning model was established for a V2V environment. Finally, based on a driving simulation platform and a real-world vehicle test, a cut-in experiment in a V2V environment was designed and implemented. By comparing the warning confusion matrix and warning time, it was found that the proposed cut-in collision warning model is superior to the traditional collision warning model. The results of this study can provide new modeling ideas and a theoretical basis for ADAS to further optimize for a cut-in scenario.

China's traffic safety attracts increasing research interest. Official data show that crashes in the western region of China are more severe than those in the eastern region. However, research on crash severity in western China is scarce. This study applied a hierarchical Bayesian logistic model to examine the significant factors related to crash and vehicle/driver levels and their heterogeneous impacts on the severity of drivers' injury. Crash data were collected from Lintao, a rural mountainous county in western China. A variable was proposed to measure the relative difference between the crashworthiness of one vehicle and the aggressivity of the other vehicle in the mixed traffic flow. Results indicated that the majority of the total variance was induced by between-crash variance, showing the suitability of the utilized hierarchical modeling approach. One crash-level variable and six vehicle/driver-level variables, namely, road type, compatibility difference, age, vehicle type, drunk driving, driving unregistered vehicle, and driving years, significantly affected modeling drivers' injury severities. Among these variables, road type (national and provincial), age (young and senior drivers), driving unregistered vehicle, and drunk driving tended to increase the odds of crash-related mortality. Driving years (new drivers with less than six years of driving experience) and vehicle type (heavy vehicle) were likely to decrease the probability of fatal outcomes. Compatibility difference was relatively significant, and the possibilities of mortality in single vehicle crashes were higher than those in multivehicle and pedestrian-involved crashes. The developed methodology and estimation results provided insights into the internal mechanism of rural crashes and effective countermeasures to prevent rural crashes.

New Mexico's oil and natural gas industry has the second highest occupational fatality rate among oil and gas workers in the nation. There is currently limited data available regarding the top contributing factors to occupational mortality specific to the state's oil and gas industry. This study seeks to understand causes of mortality among oil and gas workers in New Mexico between 2008 and 2018. To facilitate this study, case reports were obtained from the New Mexico Office of the Medical Investigator, and population data was acquired from the US Department of Labor. In this 11-year span, there were 73 cases, with an average annual mortality rate of 37 deaths per 100,000 oil and gas workers. Leading causes of death were vehicle accidents (36%), cardiovascular incidents (22%), and crush injuries (19%). The majority of vehicle accidents involved single vehicle accidents, and correct seat belt use was only documented 23% of the time. The majority of cardiovascular deaths were due to arteriosclerotic and atherosclerotic cardiovascular disease. Alcohol was present in 18% of cases, and drugs were present in 19% of cases with methamphetamine present in 10% of investigated deaths. This is the first study to directly include cardiovascular incidents in the leading causes of death; otherwise, this study reflects national data reporting vehicle accidents and crush injuries as the leading causes of death. Going forward, prevention measures should effectively target safe driving practices focusing on seatbelt use, and mitigation of workplace drug and alcohol consumption.

This paper identifies factors that influence the severity of interstate crash outcomes and how they vary depending on the location and manner of collision. Four separate injury severity models were...

Introduction Roadway departure (RwD) crashes, comprising run-off-road (ROR) and cross-median/centerline head-on collisions, are one of the most lethal crash types. According to the FHWA, between 2015 and 2017, an average of 52 percent of motor vehicle traffic fatalities occurred each year due to roadway departure crashes. An avoidance maneuver, inattention or fatigue, or traveling too fast with respect to weather or geometric road conditions are among the most common reasons a driver leaves the travel lane. Roadway and roadside geometric design features such as clear zones play a significant role in whether human error results in a crash. Method: In this paper, we used mixed-logit models to investigate the contributing factors on injury severity of single-vehicle ROR crashes. To that end, we obtained five years' (2010–2014) of crash data related to roadway departures (i.e., overturn and fixed-object crashes) from the Federal Highway Administration's Highway Safety Information System Database. Results: The results indicate that factors such as driver conditions (e.g., age), environmental conditions (e.g., weather conditions), roadway geometric design features (e.g., shoulder width), and vehicle conditions significantly contributed to the severity of ROR crashes. Conclusions: Our results provide valuable information for traffic design and management agencies to improve roadside design policies and implementing appropriately forgiving roadsides for errant vehicles. Practical applications: Our results show that increasing shoulder width and keeping fences at the road can reduce ROR crash severity significantly. Also, increasing road friction by innovative materials and raising awareness campaigns for careful driving at daylight can decrease the ROR crash severity.

Most of the existing research efforts have been conducted using the random parameters ordered possibility model to investigate the unobserved heterogeneity; however, relatively few research has exp...

A deep understanding of driver behavior is an important step to improve road safety and environmental performance. Volatility can be defined as the extent of variations in driving, which can be characterized by accelerations/braking, lane change, and unusual high speed for roadways conditions. There is a lack of knowledge on what concerns the relationship between driver’s volatility and exhaust emissions and how driving volatility can be used as safety eco-indicator. This article explores a driving volatility concept for assessing tailpipe emissions and driving behavior classification. For that purpose, an empirical approach that combined vehicle activity and emission rates for light duty vehicles was used. Field measurements were collected from four probe vehicles in one partly urban/rural, and two highway routes using Portable Emission Measurement Systems, Global Positioning System receivers, and On-board Diagnostic scan tool, to measure real-world tailpipe emissions, position and engine activity data. Acceleration-based parameters, including relative positive acceleration and mean of positive acceleration, acceleration, vehicular jerk, and power demand thresholds were used to detect differences in emissions for different driving styles. Results indicated that vehicular jerk impacted carbon dioxide and nitrogen oxides per unit distance regardless of driving style and route type, especially from negative to null jerk values and during positive accelerations. There is potential to incorporate the analyzed thresholds into a driver decision support algorithm by considering safety and environmental aspects through warning messages. E. Ferreira acknowledges the support of the TEMA (Centre for Mechanical Technology and Automation) for the PhD scholarship. published

According to the reports of NITI (National Institute of Transforming India) Aayog Freight 2018, Road freight is the prime mode (59%) of transport in India with the highest per ton-mile cost than rail or water freight (NITI Aayog, 2018). This road freight usually uses heavy-duty vehicles to transmit voluminous goods and services to the destination in time. Due to this, the heavy-duty vehicle population increased on the Indian roads. Heavy-duty vehicle crashes cause a substantial economic burden to the nation and result in more severity to the involved because of differences in weight, speed, and size. Among heavy-duty vehicle crashes, a significant proportion of crashes are heavy-duty single-vehicle crashes. Single-vehicle crashes are those crashes where the vehicle drivers either involve in self-skidding or hit a stationary object (like a tree). The purpose of this study is to investigate the injury pattern in heavy-duty single vehicle crashes. For this study, the data is extracted from the RADMS (Road Accident Database Management System) database and linked with hospital data. This data includes demographic information, road, environmental and injury characteristics. Later, descriptive statistics performed on the dataset to analyse all heavy-duty single-vehicle crashes between January 2013 and December 2018. Overall, 4704 single heavy-duty vehicle crashes occurred during this period, among which 1244 were fatal crashes. Results show that male drivers aged 26 to 64 years old suffered more fatalities (88%), followed by the 18-25 age group (8%). Examination of injury information found that heavy-duty vehicle drivers mostly sustained multiple injuries (9.05%), head injuries (5.05%), followed by leg injuries (4.29%). The results showed that specific road and environmental factors increase the chance of fatal crashes among heavy-duty vehicle drivers. Furthermore, the proposed study gives insight into the injury characteristics and key contributing factors causing heavy-duty single-vehicle crashes. Finally, this study provides appropriate countermeasures and techniques that can mitigate heavy-duty single-vehicle collisions.

Road departure (RD) crashes are among the most severe crashes that can result in fatal or serious injuries, especially when involving large trucks. Most previous studies neglected to incorporate both roadside and median hazards into large-truck RD crash severity analysis. The objective of this study was to identify the significant factors affecting driver injury severity in single-vehicle RD crashes involving large trucks. A random-parameters ordered probit (RPOP) model was developed using extensive crash data collected on roadways in the state of Kentucky between 2015 and 2019. The RPOP model results showed that the effect of local roadways, the natural logarithm of annual average daily traffic (AADT), the presence of median concrete barriers, cable barrier-involved collisions, and dry surfaces were found to be random across the crash observations. The results also showed that older drivers, ejected drivers, and drivers trapped in their truck were more likely to sustain severe single-vehicle RD crashes. Other variables increasing the probability of driver injury severity have included rural areas, dry road surfaces, higher speed limits, single-unit truck types, principal arterials, overturning-consequences, truck fire occurrence, segments with median concrete barriers, and roadside fixed object strikes. On the other hand, wearing seatbelt, local roads and minor collectors, higher AADT, and hitting median cable barriers were associated with lower injury severities. Potential safety countermeasures from the study findings include installing median cable barriers and flattening steep roadside embankments along those roadway stretches with high history of RD large-truck-related crashes.

Single-vehicle crashes are of major concern in both developed as well as in Low Middle Income Countries due to the severity of injuries, particularly fatal accidents. In India, a significant proportion of crashes are single-vehicle crashes. The vehicles which are involved in accidents due to causes such as self skidding, hitting stationary objects, trees that are simply contributed by the drivers themselves are referred to as out-of-control single-vehicle crashes. The main objective of this study is to evaluate the risk factors associated with single-vehicle motorcycle collisions in Tamilnadu, India and identifies the unique characteristics and injury outcomes associated with these collisions. Crash dataset for the present study was prepared from the police-reported crashes for the past nine years that occurred within the state of Tamilnadu between 2009 and 2017. The identified contributory factors which influence injury severity include driver characteristics, crash-related factors, traffic-related factors, vehicle and environment-related factors. In this study, injury severity is classified into three categories, i.e. fatal, serious, and minor injuries. Since the outcome of the injury severity could be measured on an ordinal scale, a discrete ordered outcome model, an ordered logit model is applied. To summarise the results, thirteen of the studied factors are found to have a significant influence on the injury severity of drivers. Results show that the likelihood of fatal injuries increases in crashes where motorcyclists hit stationary fixed objects, hit trees, ran-off road, inclement weather conditions, urban areas. It is also found that winter season, north districts of Tamilnadu, single and two-lane roads, highways, village roads and, other district roads, daylight conditions, drivers who are younger and working-age group, overtaking from left, taking u-turn are associated with less likelihood of fatal crashes. To increase the overall safety of the roads, targeted countermeasures may be designed in light of injury severity of the drivers with respect to single-vehicle crashes also. This study provides useful insights for reducing injury severity in single-vehicle motorcycle crashes.

For loss and theft in the transport of radioactive materials by a single vehicle, this article summarizes the characteristics of “illegal movement” and establishes a security system that senses its inter-relationship and responds though the group network relationship. The security system reminds the vehicle crew through on-site response and linkage response. A failure detection method for on-site response is proposed, that is, the push model is used first, and when the measurement results are suspected, the pull model is used to further confirm the failure. The failure detection for linkage response adopts the push model. According to the different security requirements of the basic and enhanced transportation, the principle of setting the timeout threshold in the failure detection algorithm is proposed. In the enhanced type, the value is smaller, otherwise the value is larger. A specific timeout threshold quantification scheme is proposed. Experiments show that the method proposed in this article is effective.

In order to solve the problems of complex circuit debugging and inconvenient operation, wireless communication technology is adopted and the USR-WIFI232-B2 module is used to complete the data transmission and reception between the single vehicle simulation tester and the upper computer. The hardware circuit and software flow of the portable single vehicle simulation tester are described, the wireless communication module is configured, and the laboratory test and on-site debugging are completed. It greatly facilitates the operation of the workers and improves the debugging efficiency.

The article discusses the improvement of the methodology for calculating the level of congestion of vehicles per vehicle. To assess the significance of the influence of operating conditions on the technical readiness of vehicles, the method of expert assessments was used; the methods of mathematical statistics were used in processing the answers of experts and assessing the errors of improved methods for monitoring operational factors.

Vehicular edge computing is viewed as a promising technique for relieving the overload of base station (BS) on roadside, via leveraging the computation resources of vehicles on road. However, the computing capacity of a single vehicle is limited. For the fast velocity and distribution characteristics of vehicles, when a vehicle performs task offloading to a set of neighbor vehicles, longer sensing/accessing time durations are needed. Vehicle platoon driving as an emerging technique is proposed to strengthen vehicle fuel efficiency and the freeway safety and capacity. The distributed computation resources can be centrally controlled in the vehicle platoon. In this paper, we investigate the resource allocation scheme for edge computing-based vehicle platoon on freeway to maximize the utilities of vehicles surrounding the platoon via a contract-optimization approach. Combining with BS, the vehicle platoon performs as an edge node to provide the delay-sensitive computation service for the vehicles on road. First, we design a contract-based incentive mechanism to motivate vehicles to form a vehicle platoon and share their computation resources. Then, based on the proposed vehicle platoon, a joint optimization problem is formulated to maximize the utilities of vehicles, the task offloading decision, communication and computation resource allocation schemes in both the platoon and BS are jointly optimized. Numerical results reveal that the designed contracts can incentivize vehicle's participation, and the proposed resource allocation schemes are effective.

Commercial topical medications for oral conditions are scarce and the vehicles used are not very suitable. Therefore, formulations containing active ingredients in vehicles specially designed for oral application must often be prepared. Drug compounding offers other advantages, including the possibility of combining several active ingredients in a single vehicle and prescribing drugs that are in short supply. In this article, we describe the main pharmaceutical formulations used to treat the most common diseases of the oral mucosa.

Detecting multiple license plate numbers in crowded street scenes is challenging and requires the attention of researchers. In contrast to existing methods that focus on images that are not crowded with vehicles, in this work we aim at situations that are common and complex, for example, in city environments where numerous vehicles of different types like cars, trucks, motorbike etc. may present in a single image. In such cases, one can expect large variations in license plates in terms of quality, backgrounds, and various forms of occlusion. To address these challenges, we explore Adaptive Progressive Scale Expansion based Graph Attention Network (APSEGAT). This approach extracts local information which represents the license plates irrespective of vehicle types and numbers because it works at the pixel level in a progressive way, and identifies the dominant information in the image. This may include other parts of vehicles, drivers and pedestrians, and various other background objects. To overcome this problem, we integrate concepts of graph attention networks with progressive scale expansion networks. For evaluating the proposed method, we use our own dataset, named as AMLPR, which contains images captured in different crowded street scenes in different time span, and the benchmark dataset namely, UFPR-ALPR, which provides images of a single vehicle, and another benchmark dataset called, UCSD, which contains images of cars with different orientations. Experimental results on these datasets show that the method outperforms existing methods and is effective in detecting license plate numbers in crowded street scenes.

Single-Vehicle Run Off Road (ROR) crash has been the leading crash type in terms of frequency and severity in Thailand. In this study, multinomial logit analysis was applied to identify the risk factors potentially influencing driver injury severity of single-vehicle ROR crash using accident records between 2011 and 2017 which were extracted from Highway Accident Information Management System (HAIMS) database. The analysis results show that the age of driver older than 55 years old, male driver, driver under influence of alcohol, drowsiness, ROR to left/right on straight roadway increase the probability of fatal crash, while other factors are found to mitigate severity such as the age of driver between 26-35 years old, using seatbelt, ROR and hit fixed object on straight and curve segment of roadway, mounted traffic island, intersection-related and accident in April. This study recommends the need to improve road safety campaign, law enforcement, and roadside safety features that potentially reduce level of severity of driver involving in single-vehicle ROR crash.

This paper deals with planning of a tour for a vehicle to clear a certain set of streets in a city of snow. Our previous results on the problem contain a heuristic based on reformulation to an asymmetric traveling salesman problem (ATSP) which yields feasible solutions and upper bounds, and a relaxation of a MIP model for obtaining lower bounds. The goal now is to try to improve the solutions and bounds. In this paper we describe a branch-and-dive heuristic which is based on branch-and-bound principles. We discuss how branching can be done so that the fixations can be utilized in both the relaxation and the ATSP model, and how the search for better solutions can be done. The heuristic has been implemented and applied to real life city networks. The method is shown to outperform two other heuristics for the ATSP with precedence constraints. Funding Agencies|Swedish Research CouncilSwedish Research Council [2015-04313]

The Pickup and delivery problem (PDP) with single vehicle (SPDP) with capacity constraints is considered. The problem requires constructing the shortest cyclic route for delivery of homogeneous cargo (e.g. passengers) from all the producers to specific customers with one capacitated vehicle. A heuristic procedure, based on the gravitational analogy, for finding approximate solution is developed. A particle swarm optimization procedure is combined with the developed heuristics. Efficiency of developed procedures is empirically analyzed and compared with each other.

Roadway departure crashes are one of the core emphasis areas in Strategic Highway Safety Plans (SHSP). These crashes, especially on rural roads, lead to a disproportionately higher number of fatalities and serious injuries. The focus of this study is to identify and quantify the factors affecting injury-severity outcomes for single-vehicle roadway departure (SV-RwD) crashes on rural curved segments in Minnesota. The crash data are extracted from the Highway Safety Information System (HSIS) from 2010 to 2014. This study applied a mixed logit with heterogeneity in means and variances approach to model driver-injury severity. The approach accounts for possible unobserved heterogeneity in the data resulting from driver, roadway, traffic, environmental conditions, or any combination of these attributes. This analysis adds value to the growing body of literature because it uncovers some unobserved heterogeneity in the form the attributes specific to driver-injury severities in contrast to the standard mixed logit approach. The model results indicate that there is a complex interaction of driver characteristics and actions (male drivers, aged below 30 years of age, and unsafe speed), roadway and traffic characteristics (two-lane undivided road, county roadways, and low traffic volume), environmental conditions (adverse weather, cloudy weather, dark conditions, and dry surface conditions), and vehicle characteristics (vehicle type—sport utility vehicle involved in rollover crashes). The results also provide some evidence of the effectiveness of a highway curve safety improvement program implemented in one of the Minnesota Department of Transportation (DOT) districts.

This paper addresses a multi-objective single-product network design and operations problem that consists of selecting the suppliers, allocating the orders, routing a single vehicle to collect the ...

This paper presents an intervehicle distance control (IDC) to solve the problem of autonomous vehicle platooning, motivated by future automated highway system (AHS) or smart road which is proposed as intelligent transportation system (ITS) technology. First the velocity and position control of the single vehicle is studied based on internal model compensator. And then the platooning problem on multiple vehicles is solved in the light of multiagent concept. Moreover, the platoon condition is derived for the corresponding scheme. Further we analyze the influence of controller parameters on the whole system, and propose the guidance for parameter design. Finally some simulations are used to verify the effectiveness of the proposed IDC scheme with an analysis on controller parameters.

We consider a vehicle with two compartments that starts its route from a depot and visits N ordered customers in order to deliver new (or fresh or useful) products and to collect old (or expired or...

Long queues at signals cause fuel-consuming stop-and-go traffic. Empirical measurements have shown that driving behaviour can have an important impact on queue length and thus on the occurrence of stop and go traffic. This led to the question of whether even a few vehicles can have a measurable influence on the traffic situation in congested city traffic. In this work we use a complete microscopic spatiotemporal measurement of congested city traffic at a signal to i) calibrate a both longitudinal and latitudinal driving model and then to ii) examine how changes in single vehicle's driving behaviour could improve the situation. The model calibration is realized using a genetic algorithm. In this way, a realistic heterogeneous traffic scenario that has similar properties as empirical traffic could be simulated. We then show that already changing the behaviour of a single vehicle per traffic light cycle can significantly reduce the number of vehicles waiting in queues.

Introduction. The article considers the problem of distribution of available and leased vehicles for servicing the stochastic flow of long-distance freight orders. The content of the problem is that the total amount of jobs should be divided between the available vehicles and those that can be rented from partners, so that the overall efficiency of transport processes and the total profit of the enterprise are maximum. The problem is relevant today because the requirements for carriers are growing, their operational management tasks are becoming more complicated, and effective methods that provide guaranteed accurate optimal solutions are unknown. The purpose of research is to determine the signs of organizational and technological compatibility of transport process tasks, the implementation of which in united flow is effective. The use of such features should lead to a guaranteed accurate solution of the problem of distribution of vehicles with a random nature of input flows. Results. The vehicles ordering that arise stochastically is NP-difficult task of strong sense. Additional classification features of orders are offered, which allow us to find a guaranteed stable solution. This solution is possible due to the fact that compatible or partially compatible orders are pre-combined into sets that are intended to be executed in a single flow, and single vehicle. The model of nonlinear programming is applied. To distribute the dynamic input flow of orders the distribution problem was solved with a stable result. The solution criterion is the total profit that the road carrier can receive with the proposed sequence of orders. Optimization at linear approximation of total profit on signs of compatibility of orders is executed. Conclusions. Structural modeling of the integrated transport process should be carried out for specific signs of compatibility of the incoming flow of orders. A sign of compatibility of orders is the coefficient of time unevenness, has a positive effect on the ability to obtain a higher maximum total profit. Linear approximation of the model gives more than 100% error of results.

Traffic conflicts based surrogate safety indicators have been applied extensively on real trajectories and in simulation. Such indicators can be useful to assess the safety of a given scenario without the need to use real crash data (which in many cases may be unavailable). Unfortunately, all traffic conflict indicators that are commonly used have a structural limitation: they are not able to consider potential conflicts with roadside obstacles or barriers and conflicts between vehicles which are travelling on non-conflicting trajectories. This limitation is a serious limitation since crash data analy sis shows that at least 40% of fatal crashes are originated by single vehicle accidents against a fixed object or by vehicles travelling in opposite directions. This paper is intended as a concept paper that presents an alternative view on conflict safety indicators showing that new indicators can be generated by the perturbation of vehicle trajectories overcoming the above indicated limitations.

Recently, the ever-increasing vehicle population has become a severe challenge to traffic safety, especially the problem of a single-vehicle overtaking a platoon on the Two-Lane Two-Way (TLTW) road. Platooning has the potential to improve traffic efficiency and safety. However, there exists a perilous situation of “Neither overtake nor give up” when the single-vehicle overtakes a platoon on the TLTW road. This paper presents a flexible framework to automatically filter a large quantity of Advanced Driver Assistance Strategies (ADAS) and select the most suitable driver assistance information for the single-vehicle overtakes a platoon on the TLTW road. A step-by-step Single Vehicle Overtakes Platoon (SVOP) algorithm is designed to generate the coarse ADAS, which had given plenty of consideration to the vehicle safety, traffic efficiency, and driving comfort. Then, this paper obtains the raw data about the single-vehicle overtakes a platoon on the TLTW by using CARLA, which can help us to get 20 drivers' upper and down boundaries of both velocity and acceleration. In addition, the extracted ranges of velocity and acceleration are used to quantitatively analyse the drivers' driving features and filter the ADAS information. Finally, a Bayesian nonparametric approach is developed to segment driver's driving raw data temporal sequences into small analytically interpretable components without using prior knowledge. So that the accurately overtaking characteristics can be obtained, and the ADAS can be further filtered. Experimental results demonstrate that the obtained coarse ADAS are only valid in theory but not acceptable by most of the drivers. Nonetheless, by leveraging the nonparametric Bayes algorithm, the driver's overtaking behavior can be divided into different primitives, from which some could obtain the driver's acceptance range for the velocity and acceleration. 92.3% ~ 94.78% invalid SVOP ADAS could be filtered out by leveraging the primitive-based SVOP approach. Thus, after filtering, the overtaking scheme is the most acceptable strategy for drivers.

We consider an inventory routing problem in which a single vehicle is responsible for the transport of a commodity from a set of supply locations to a set of demand locations. At each location the inventory must be kept within predefined bounds, and the location specific supply and demand rates are constant throughout the time horizon. Each location can be visited several times during the time horizon, and the vehicle can visit the locations in any order as long as the capacity of the vehicle is not exceeded. Two models are presented, each defined on a different extended network. In a location-event model, the nodes are indexed by the location and the number of visits made so far to that location, while in a vehicle-event model the nodes are indexed by the location and the number of visits so far on the vehicle route. Both models are based on continuous time formulations. They are tightened with valid inequalities, and a new branching algorithm is designed to speed up the solution time of the models. Computational tests based on a set of maritime transportation instances are reported to compare both models and the corresponding tightened variants.