Introduction: Non-recurrent congestion caused by traffic incident is difficult to predict but should be dealt with in a timely and effective manner to reduce its influence on road capacity reduction and enormous travel time loss. Influence factor analysis and reasonable prediction of traffic incident duration are important in traffic incident management to predict incident impacts and aid in the implementation of appropriate traffic operation strategies. The objective of this study is to conduct a thorough review and discusses the research evolution, mainly including the different phases of incident duration, data resources, and the various methods that are applied in the traffic incident duration influence factor analysis and duration time prediction. Methods: In order to achieve the goal of this study, we presented a systematic review of traffic incident duration time estimation and prediction methods developed based on various data resource, methodologies etc. Results: based on the previous studies, we analyse (i) Data resources and characteristics: different traffic incident time phases, data set size, incident types, duration time distribution, available data resources, significant influence factors and unobserved heterogeneity and randomness, (ii) traffic incident duration analysis methods, mainly including hazard-based duration model and regression and statistical tests, (iii) traffic incident duration prediction methods and evaluation of prediction accuracy. Conclusions: After a comprehensive review of literature, this study identifies and analyses future challenges and what can be achieved in the future to estimate and predict the traffic incident duration time. Keywords: Incident duration analysis, Traffic incident duration prediction, Hazard-based duration model, Data mining, Influence factors 1 Introduction gain per incident and even considerably higher gains at One of the two main types of traffic congestion is locations with high levels of recurrent congestion (i.e., non-recurrent congestion, which is mainly due to differ- approximately €1200 per incident per minute at highly ent events, such as traffic incidents and large-scale congested locations). A larger number of traffic control sports events. Although non-recurrent congestion is dif- centres in cities and highways have deployed the Traffic ficult to predict because of its stochastic nature, address- Incident Management System (TIMS), which is consid- ing it in a timely and effective manner is important to ered as an effective tool to deal with traffic incidents, to reduce its influence on traffic conditions. Incidents nor- alleviate the influence of traffic incidents on traffic con- mally consist of two intervals: the primary is from the ditions [2, 3]. The traffic operators must understand the time of occurrence to the time when the incident is main factors that influence the traffic incident duration cleared, whereas the secondary is from the end of the and predict the traffic incident duration accurately to primary interval to the time when the facility has re- improve the TIMS efficiency. This research field has sumed normal operations. Adler et al.  demonstrated been examined in terms of two subfields with different that a one-minute duration reduction generates a €57 techniques: analysis of influence factors of traffic inci- dent duration and prediction of traffic incident duration * Correspondence: firstname.lastname@example.org time with or without the influence factor analysis. Department of Civil Engineering, Tsinghua University, Room 304, Heshanheng Building, Beijing 100084, China Full list of author information is available at the end of the article © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Li et al. European Transport Research Review (2018) 10:22 Page 2 of 13 With the development of traffic detection techniques of the specific research technique from Sections 2, 3 and TIMS over the past decades, researchers can collect and 4. A critical discussion of the future challenge data conveniently, conduct a detailed analysis of the in- and direction of traffic incident duration prediction is fluence factors of traffic incident duration time, and pre- then presented. dict traffic incident duration time in a highly accurate manner . Traffic incident duration analysis and pre- 2 Data resources and characteristics diction in TIMS and intelligent transportation systems Previous researchers employed different datasets with are currently important topics that have been applied various characteristics, such as different incident dur- with different results in previous studies. The incident ation time phases, available data types, and dataset sizes, duration time is related to various factors, such as tem- in their studies on traffic incident duration time analysis poral characteristics (e.g., time of day, day of the week, and prediction. and/or season); incident characteristics (e.g., number of vehicles involved in an incident, truck/taxi/pedestrian in- 2.1 Different traffic incident time phases volvement, number of deaths and/or injured persons); Generally, traffic incident duration time can be defined road characteristics (e.g., incident location and road con- as the time difference between the occurrence of an inci- dition); traffic characteristics (e.g., traffic volume); and dent and clearance of the incident site. The duration in- weather conditions (e.g., rain, fog, and/or snow). cludes four time phases: incident detection/reporting Various statistical methods have been traditionally ap- time, incident preparation/dispatching time, travel time, plied to analyse and predict the traffic incident duration and clearance/treatment time. Most previous studies are time. Among these methods are the following: linear/ limited by data availability, so they focus on the traffic non-parametric regression [5–7], Bayesian classifier , incident duration time that consists of the last three hazard-based duration model (HBDM) , discrete phases. The duration covers the length of time between choice model (DCM) , structure equation model the reporting of the incident and the clearance of the (SEM) , and probabilistic distribution analyses [12, road. Few studies include incident detection and recov- 13]. A new research field based on data-driven empirical ery time , as well as define the duration time as the algorithms and supported by unprecedented data avail- time difference from the time the Freeway Courtesy Pa- ability has recently emerged for traffic incident duration trol (FCP) vehicle arrives on the scene to the time the prediction with an increasing amount of published lit- FCP leaves the scene after clearing the incident . erature. Different data mining (DM)-machine learning Other studies focus on the clearance time [11, 24–27], (ML) approaches have been employed to estimate and response time [28, 29], or different time phases [9, 30]. predict the traffic incident duration time; some of these One study divides the response time into two parts: approaches are the following: decision trees (DT) and preparation time of the response team and travel time of classification trees model (CTM) [14, 15], artificial the response vehicles . The different divisions or def- neural networks (ANN) [16–18], genetic algorithm (GA) initions of traffic incident duration time in various stud- , and support/relevance vector machine (SVM/ ies cause difficulty in comparing their results. The RVM) . Several researchers have recently begun to difference in previous studies is also subject to used dif- utilize a hybrid method  to predict the traffic inci- ferent data resources. A deeper investigation of traffic dent duration and apply the advantages of the aforemen- incident duration time is possible and necessary with the tioned methods. availability of more detailed data in the future. Several reviews have also summarized such studies on traffic incident duration modelling [4, 21, 22], but the 2.2 Data size rapid development of prediction techniques and avail- Traffic incident duration is determined by various fac- able data have presented a new requirement to review tors, including several potential factors that cannot be the development of traffic incident duration analysis and observed. These factors make the traffic incident dur- prediction. This study attempts to review previous stud- ation extremely heterogeneous by nature. Utilizing a lar- ies on several aspects of traffic incident duration analysis ger data set is a possible approach to improve the and prediction. The main tasks are to compare these analysis and prediction accuracy. The adopted datasets previous studies, identify the critical conceptual charac- in most previous studies includes hundreds or thousands teristics of traffic incident analysis and prediction, and of incident records, some of which are more than 30,000 discuss the future development tendency of traffic inci- in number [24, 26, 31, 32]. Only a few studies utilise in- dent duration prediction. cident datasets with less than 100 records [16, 17, 33]. The rest of this paper is organized as follows. First, an Generally, studies with small datasets are more specific, analysis of the available literature is conducted to but estimation and prediction of traffic incident duration present the current views and describe the development time benefit more from a dataset with thousands of Li et al. European Transport Research Review (2018) 10:22 Page 3 of 13 records. Larger datasets tend to be better and more are appropriate for the different incident duration phase comprehensively reflect the characteristics of traffic inci- times [9, 30] or incident types [23, 36, 37]. However, dent duration. Smith, Smith  could not demonstrate that the accident clearance time conforms to a convenient prob- 2.3 Incident types abilistic distribution. Selection of the appropriate distri- Most previous studies have obtained their incident/acci- bution is one of the key tasks in the analysis and dent data sets from different traffic incident record sys- prediction of traffic incident duration time. Recent tems or TIMS; they also have not differentiated the research  shows that the mixture models may be a incident types, although the incident data include vari- potential direction for traffic incident duration time ous incident types such as crashes and other events [13, distribution. 30, 34]. For example, 10 incident types are included in the adopted database of two studies [34, 35], namely, 2.5 Available data resources broken-down vehicle, broken-down lorry, accident, fire, Most of these previous studies only employ the traffic flooding, fuel spillage, gas leak, police incident, collapsed incident dataset, which commonly includes the following manhole, and traffic light failure. However, several stud- information items: time, location, incident type, truck, ies divide the data set into different types to capture the taxi, or other special vehicle involvement, as well as inci- characteristics of the various incident types, such as dent severity (e.g., number of deaths and injured per- hazards, stationary vehicles, and crashes [23, 36–38]; sons) and weather condition. The data records in disabled and abandoned vehicles ; and collision, dis- different traffic incident datasets vary according to the abled vehicles, and traffic hazard . Most previous different data collection methods and purposes. For ex- studies also utilize the incident data set from highways ample, several incident datasets include geographical or freeways between cities or urbanized regions; few of and/or environmental attributes, whereas others do not. these studies adopt data from arterial roads and streets Notably, two studies [45, 46] have sequential informa- in cities. Previous studies [9, 25, 30] revealed that inci- tion available in textual form during the incident dent location variables significantly influence traffic inci- process, which can be useful in predicting the duration dent clearance, which imply that locations have different of traffic incidents. characteristics (such as traffic conditions and geograph- Owing to limited data availability, only some parts of ical attributes) and procedures and training for their previous studies employ other types of related datasets, local Incident Response Team. Critical analyses of the such as the traffic flow data, except for the traffic inci- effects of different incident locations are still limited dent dataset [16, 17, 24, 26, 47]. Ghosh et al.  applied because of the limited availability of data. The influence traffic flow data from 110 active sensors to study the in- of location on traffic incident duration can be further fluence of traffic conditions on the traffic incident dur- investigated with the support of more detailed data in ation time. The traffic flow data included speed, volumes the future. by vehicle class, and sensor occupancy information ag- gregated into 5-min intervals. 2.4 Duration time distribution We should note that, although this paper specifically The distribution characteristics of the traffic incident focuses on practical dataset, simulated datasets are an- duration time are critical for several analyses and predic- other source of data for traffic incident duration time es- tion models. If the duration time fits a known probabilis- timation and prediction . The relationship between tic distribution, then modelling the expected value of incident clearance time and roadway clearance time for future incidents will be convenient. Previous studies different traffic incident scenarios were explored on the show that the traffic duration time from different data- basis of micro-simulation VISSIM modelling . sets has different distribution characteristics. Several Post-incident traffic recovery time along an urban free- studies reveal that the traffic duration time meets the way was estimated via a simulation due to the lack of log-normal distribution [12, 13, 21] or log-logistic distri- practical datasets for post-incident recovery time . bution [9, 31, 36, 39, 41, 42]. Weibull distribution (or Simulations should be considered an optional source of with gamma heterogeneity or random parameters) pro- basic datasets for traffic incident duration time studies vides the best likelihood ratio statistics for the used data- when practical datasets are unavailable. set in some other studies [9, 23, 25, 28, 37]. Several other studies report that the generalized F distribution is 2.6 Significant influencing factors the best type for the traffic duration time distribution Prior studies have generally identified various factors [24, 26]. Several studies have investigated the distribu- that influence the incident duration time or clearance tion of different duration phases or incident types and time, including incident characteristics, environmental have determined that various distributional assumptions conditions, temporal factors, roadway geometry, traffic Li et al. European Transport Research Review (2018) 10:22 Page 4 of 13 flow conditions, operational factors and some other fac- duration time, such as the real-time traffic flow condi- tors, which are shown in detailed in Table 1. Table 1 pre- tions and the details in characteristic differences of inci- sents a summary of factors and their significant dent locations, cannot often be integrated into the contributions, as revealed in prior studies, to traffic inci- incident dataset. Thus, we must consider several unob- dent duration analysis and prediction. Factors in Table 1 served factors that are not included in the factor vector, can be considered as potential factors and predictors for which affect the durations and are referred to as un- traffic incident duration time analysis and prediction observed heterogeneity. Two approaches have been studies, respectively. adopted in the current traffic incident duration time Moreover, several studies reveal that the duration of analysis and prediction to examine the heterogeneity different incident types (i.e., crashes, hazards, or station- assumption, namely, applying the gamma distribution ary vehicles) respond to various influence factors . to incorporate heterogeneity and allowing parameters The duration of different duration phases (i.e., report to vary across observations based on a pre-specified time, response time, and/or clearance time) also respond distribution, which is known as the random-parameter to different influence factors [9, 30]. However, the con- duration model [9, 23, 30, 37, 52, 53]. clusion from different datasets from different countries or regions in the significant factor analysis is sometimes 3 Traffic incident duration analysis different. Hojati et al.  found no significant effects of The common objective of a traffic incident duration the infrastructure and weather on the incident duration, analysis study is to determine the significant influence which is different from the findings of many other stud- factors for the duration and/or severity of different types ies [9, 11, 25, 51]. In some cases, the same factor, such of traffic incidents, which can provide suggestions or as taxi involvement, has been determined to have an ad- recommendations for traffic incident management. The verse influence on the traffic duration time. description and key elements of previous studies are Some factors will influence the duration of traffic inci- listed in Table 2. dents, but incident datasets do not always record these When an incident occurs, both the traffic operators factors, for example, the location of emergency and re- and travellers are concerned about how long the inci- covery services. Some studies reflected these factors dent process will last given that it has already lasted for through other factors; for example, the response time x minutes, where x ≥ 0. Thus, the length of time that can reflect the location of emergency service to an ex- elapsed from the beginning of incident detection until tent. Other studies found that response time influenced the end (i.e., duration time or clearance time) is note- the incident duration or clearance time [6, 30, 42]. In worthy in the traffic incident duration analysis. Table 2 many previous studies, however, this kind of information shows that many researchers applied various is not included due to the limited availability of the hazard-based models in their previous studies on traffic dataset. incident duration analysis. Most of these models are parametric accelerated failure time (AFT) models, 2.7 Unobserved heterogeneity and randomness which can determine the significant variables that Limited by the data collection methods, the initial infor- affect the traffic incident duration time. As shown in mation of an incident obtained by a traffic management Table 2, the distribution of accident durations has centre (TMC) is commonly insufficient. Furthermore, been found to be different per study and is a basic several latent influencing factors for the incident problem in modelling accident duration analysis. The Table 1 Factors and their significant contributions to traffic incident duration Types of Factors Factors Incident characteristics Incident severity, incident type, towing requirements, type of involved vehicles, number of casualties, number of lanes blocked and incident location Environmental conditions Rain, snow, dry, or wet Temporal factors Time of day, day of week, season, month of year Roadway geometry Street, intersection, road layout, horizontal/vertical alignment, bottlenecks, roadway type Traffic flow conditions Flow, speed, occupancy, queue length Operational factors Lane closures, freeway courtesy service characteristics Vehicle characteristics Large trucks, trucks with trailers, taxis, special vehicles, compact trucks, number of vehicles involved Others Driver, special events, time that a police officer reaches the site, police response time, report mechanism, accident characteristics reported at accident notification Li et al. European Transport Research Review (2018) 10:22 Page 5 of 13 Table 2 Studies on traffic incident duration time analysis Method Category Methodology Researcher Data source Duration time phase Duration distribution Hazard-based AFT hazard-based Jones et al.  2156 accidents Response time + clearance Log-logistic duration model model time (HBDM) Nam, Mannering  681 incidents Detection/reporting, Response Weibull, Weibull, and time, and Clearance time Log-logistic Chung et al.  2940 accidents Incident duration Log-logistic Alkaabi et al.  583 accidents Clearance time Weibull Chung, Yoon  1815 accidents Incident duration Log-normal Ghosh et al.  32,574 incidents Clearance time Generalized F Kaabi et al.  504 accidents Response time Weibull with frailty Hojati et al.  4926 incidents Duration time Weibull Wang et al.  1198 incidents Incident duration time Log-logistic Chimba et al.  10,187 incidents Incident duration time Log-logistic b c Hojati et al.  430 incidents Incident duration time Weibull and log-logistic Ghosh et al.  32,574 incidents Incident clearance time Generalized F Chung et al.  3863 accidents Duration time Gamma and inverse Gaussian Semi-parametric Hou et al.  2584 incidents Clearance time hazard-based model Shi et al.  7203 incidents Incident duration Regression and Log-linear models Golob et al.  525 accidents Incident duration Log-normal statistical tests Statistical tests Giuliano  512 accidents Response time + clearance time Log-normal Structural equation Lee et al.  3147 incidents Incident clearance time model OLS regression Zhang, Khattak  37,379 incidents Event duration Log-normal or log-logistic truncated regression distribution Analysis of variance Hojati et al.  4926 records Incident duration time Log-logistic and log-normal Mechanism-based Hou et al.  828 incidents Response time approach Association rule Lin et al.  999 accidents Incident clearance time learning algorithm Binary probit and Ding et al.  1056 incidents Response time and clearance time switching regression models Weibull AFT models with random parameters for crashes and hazards; a Weibull model has gamma heterogeneity for stationary vehicles The models include incident detection and recovery time as the components of incident duration Weibull with gamma heterogeneity for crashes; log-logistic with random parameters for hazards and stationary vehicles Event duration is defined as the “time elapsed from the notification of a primary incident to the departure of the last responder from the event scene after the removal of the primary and associated secondary incidents” Log-logistic distribution for hazards and stationary vehicles during weekdays; log-normal distribution for crashes differences may have resulted from several factors, 4 Traffic incident duration prediction including difference in sample size (from several hun- Traffic incident duration prediction modelling is considered dred to tens of thousands of accident records), differ- as a complex problem because of heterogeneity in input ence in the quality of accident data, difference in data and unobserved elements. In the past two decades, countries, and differences in other factors that affect many studies were conducted to investigate proper meth- accident duration. odologies to predict traffic incident duration time by using The other previous studies mainly employ various different datasets. Most of the previous studies on traffic in- regression methods, for example, ordinary least cident duration prediction are listed in Table 3. squares (OLS) regression model [11, 12, 31, 51]and statistical approaches [13, 36]intrafficincidentdur- ation analysis. For the time being, various HBDM 4.1 Prediction methods models have certain advantages in traffic incident Several approaches have been adopted to model the pre- duration analysis. diction of the incident duration/clearance time. These Li et al. European Transport Research Review (2018) 10:22 Page 6 of 13 Table 3 Traffic incident duration prediction studies Method Category Methodology Data source Duration time Accuracy phase Regression Time sequential method Khattak et al.  109 larger Duration time Not test without available model incidents dataset (truncated regression model) Regression model Garib et al.  205 incidents Incident duration 81% (adjusted R ) Linear regression (LR) Peeta et al.  835 crashes and Clearance time R : 0.234 for crashes; 0.362 1176 debris for debris OLS regression models Khattak et al.  59,804 incidents Incident duration Best MAPE: 37% A linear model with a stepwise Yu, Xia  503 records Incident duration Acceptable (77.8% predictions regression have an error within 60 min) Cluster-based log-normal Weng et al.  2512 accidents Accident duration Best MAPE: 34.1% distribution model Quantile Regression Khattak et al.  85,000 incidents Incident duration RSME: 57.49 min Fuzzy system Fuzzy system model Kim, Choi  2457 incidents Incident service Average error: 0.3 min time Fuzzy logic (FL) model Wang et al.  457 records Incident duration Average performance Fuzzy duration model Dimitriou, 1449 accidents Accident duration Best MAPE: 36%. Vlahogianni  Classification Tree Decision tree Ozbay, Kachroo  650 incidents Clearance time 60% less than 10 min Method (CTM) Non-parametric regression Smith, Smith  6828 accidents Clearance time Not good (correct rate 58%) and CTM CTM Knibbe et al.  1853 incidents Incident duration Theoretical reliability: 65% time Hybrid tree-based quantile He et al.  1245 incidents Incident duration MAPE: 49.1%. regression M5P tree algorithm Zhan et al.  2585 incidents Lane clearance MAPE: 42.7%. time CTM Chang, Chang  4697 cases Incident duration Accuracy of classification: 75.1%. Artificial neural FL and ANNs Wang et al.  695 vehicle Incident duration RMSE: about 20% networks breakdowns ANNs Wei, Lee  39 accidents Accident duration MAPE: 20%–30% ANN-based models Wei, Lee  24 incidents Incident duration MAPE mostly under 40%. A sequential forecast based on Lee, Wei  39 accidents Accident duration The MAPE value at each time two ANN-based models point is mostly under 29%. Multiple LR; DT; ANN; SVM/RVM; Valenti et al.  237 incidents Incident duration MAPE of the five models: K nearest neighbour (KNN) 34%–44%. Four adaptive ANN-based Lopes et al.  10,762 incidents Clearance time Model 4: 72% incidents: <10 models min error; 92%: <20 min error Topic modelling and ANN- Pereira et al.  10,139 Incident duration A median error of 9.9 min in based models accidents the best model ANN models Vlahogianni, 1449 accidents Accident duration Accuracy defined in the paper Karlaftis  is about 10% Bayesian ANNs Park et al.  13,987 incidents Incident duration MAPE: 0.18–0.29. Bayesian Bayesian networks Ozbay, Noyan  700 incidents Incident clearance Accuracy of approximately 80% networks times Probabilistic model based on a Boyles et al.  2970 incidents Incident duration Classification is correct half of naïve Bayesian classifier (NBC) the time. Bayesian decision model Ji et al.  1853 incidents Incident duration Theoretical reliability of 74% Tree-augmented NBC and a Li, Cheng  2973 incidents Incident duration The frequency of the correct continuous model based on classification is below 0.5. latent Gaussian NBC Bayesian network Shen, Huang  2629 incidents Incident duration Li et al. European Transport Research Review (2018) 10:22 Page 7 of 13 Table 3 Traffic incident duration prediction studies (Continued) Method Category Methodology Data source Duration time Accuracy phase overall classification accuracy is 72.6% hazard-based Time sequential procedure Qi, Teng  1660 incidents Remaining incident Accuracy increases with more duration model with HBDM duration information Log-logistic AFT model Chung  4869 accidents Accident duration MAPE: 47%. Log-logistic AFT model Hu et al.  5362 incidents Incident duration MAPE: 43.7%. Weibull AFT model Kang, Fang  1327 incidents Incident duration MAPE: 43%. KNN and Log-logistic AFT Araghi et al.  5362 incidents Incident duration MAPE: KNN: 41.1%; AFT: 43.7% model HBDM Ji et al.  24,604 incidents Clearance and 39.68% of incident: <10 min arrival time error Competing risk mixture HBDM Li et al.  12,093 incidents Incident duration MAPE: 45% for >15 mins G-component mixture model Zou et al.  2584 incidents Clearance time MAPE: 39% SVM Ordered probit model and SVM Zong et al.  3914 cases Accident duration MAPE: 22% SVM Wu et al.  1853 incidents Incident duration Total accuracy: 70% Combined/ Ordered probit model and a Lin et al.  22,495 incidents Incident duration Duration less than 60 min is hybrid rule-based supplemental 82.25% (within 10-min error) module CTM and Rule-Based Tree Kim et al.  4 years’ worth Incident duration The overall confidence is more Model (RBTM), DCM of data than 80%. A hybrid model that consists Kim, Chang  6765 records Incident duration Performed satisfactorily for of a RBTM, MultiNomial Logit incidents that last from 120 model (MNL), and NBC to 240 min Combined M5P tree and HBDM Lin et al.  602 accident Accident duration MAPE: 36.2% for I-64 and records 31.87% for I-190. The best mean absolute percentage error (MAPE) is 37% for the incidents that lasted for approximately 15 min approaches can be divided into several groups based on 4.1.2 Sequential and one-time models the different classification standards. Many previous studies assume that all information is available when predicting the traffic incident duration 4.1.1 Single and combined models because these studies were conducted by utilizing a his- The majority of previous studies generally adopt one basic torical dataset. These models are called one-time technique to develop the traffic incident duration predic- models. In fact, obtaining all information when the traf- tion model. However, one method cannot suit all of the fic incident was reported to the centre is almost impos- incident duration time ranges, so several researchers com- sible. Thus, the traffic incident duration time prediction bined two or more methods to predict the traffic incident model must accommodate new information as it arrives duration. Lin et al.  predicted incidents with less than in its own time sequence. Several studies have consid- 60-min duration by utilizing the ordered probit model and ered this challenging problem. A time sequential meth- employed a rule-based supplemental module to predict in- odology was developed by Khattak et al.  to predict cidents with longer than 1-h duration, which is similar to the incident duration as the TMC receives the incident the method used by Kim et al. . Kim, Chang  information based on a dataset of 109 large-scale inci- developed a hybrid model that consists of RBTM, dents. Khattak et al.  developed dynamic incident MNL, and NBC. Lin et al.  constructed an duration models to predict the incident duration more M5P-HBDM (hazard-based duration model) model in accurately because additional information can be ob- which HBDMs are adopted as the leaves of the M5P tained as an incident progresses. Wei, Lee  devel- tree to improve the ability of the original M5P tree oped a time sequential traffic incident duration algorithm to predict the traffic duration time. Vlaho- prediction procedure utilizing ANN-based models and gianni, Karlaftis  applied a fuzzy entropy feature data fusion techniques. Lee, Wei  then employed selection methodology to determine the redundant ANNs and genetic algorithms to construct two models factors and Artificial Neural Network (ANN) models to provide a sequential prediction of accident duration to predict the incident duration time. from the accident notification to clearance. Qi, Teng Li et al. European Transport Research Review (2018) 10:22 Page 8 of 13  developed a time sequential procedure that included 5.1 How to combine multiple data resources different hazard-based duration regression models with Several previous studies [6, 15, 41] have revealed that different variables for each stage according to the spe- except for the observed factors, several latent factors can cific information available. Lopes et al.  developed affect the traffic incident duration. Thus, obtaining more four adaptive ANN-based models to be activated with detailed and various types of data is necessary for a more the incoming data to improve the predictive perform- accurate analysis and prediction of traffic incident ance. Pereira et al.  also developed sequential models duration time. to obtain more reliable predictions by using a radial First, although the incident databases in many coun- basis function network. tries are relatively extensive, they still have the limitation of no-data field that provides the exact occurrence time 4.2 Evaluation of prediction accuracy of the incident. In particular, we can only obtain the The prediction accuracy is generally evaluated by com- time stamp when the operator first recorded an incident paring the detected traffic duration time and predicted into the database. The incident detection/reporting time traffic duration time. The MAPE is the most frequently is an important phase in traffic incident duration and applied measurement to investigate the accuracy of the can affect the duration time of the following phases. predictions. Root mean squared error (RMSE) and mean Obtaining the incident exact occurrence time based on percentage error (MPE) are also used in some cases. The an intelligent vehicle system, such as the eCall system lower the RMSE and MAPE values are, the more accur- [59, 60] in Europe and the OnStar system of General ate the prediction model becomes. The MPE shows pre- Motors, is possible in the future. diction bias. Notably, the MAPE has several drawbacks. Second, several studies [16, 17, 40] prove that the traf- For example, the MAPE increases when the observed fic flow condition can affect the traffic incident duration value is lower, and even has no upper limit to the per- time; thus, how to integrate the increasing data on traffic centage error. The mean absolute error and mean flow condition is also a critical topic in future studies on squared prediction error can also be employed . traffic incident duration analysis and prediction. Traffic Another frequently utilized measure of effectiveness in condition information was previously sourced from the traffic incident duration prediction is related to a certain section detector, and the parameters mainly included tolerance of the prediction error [15, 20, 43, 58]. Simi- traffic flow volume, average spot speed, and occupancy. larly, Qi, Teng  stated that an incident duration is Owing to the recent development of floating cars and correctly predicted if the percentage of the relative error smartphones, several traffic information service compan- tolerance of an incident is less than a given value. Park ies can now provide the travel time information, which et al.  defined the proportion of the underestimated can be considered as an information resource. prediction to reveal what percentage of incident has Third, new data resources, such as crowdsourcing tech- been underestimated. nology (e.g., Waze, Twitter and Weibo), can also provide information on traffic incident conditions. Gu et al.  5 Challenges and future work studied a method based on natural language processing to The challenges of traffic incident duration analysis extract incident information from tweets on highways and and prediction are summarized in Table 4 and ex- arterial roads. Kurkcu et al. determined that plained as follows. Web-based social media data can be applied for more Table 4 challenges of traffic incident duration analysis and prediction Challenges Potential methods Previous research Combining multiple data resources Intelligent vehicle system (for example, eCall) Sdongos et al. ; Oorni, Goulart  Traffic condition detection information Wei, Lee ; Lee, Wei ; He et al.  Crowdsourcing technology Gu et al. ; Kurkcu et al.  Time sequential prediction model Based on response term’s report Khattak et al. ; Pereira et al. ; Li et al.  Based information from social media Gu et al.  Outlier prediction Different models for different duration ranges Lin et al. ; Valenti et al.  A time sequential prediction model Qi, Teng ; Pereira et al. ; Li et al.  Improvement of prediction methods Machine Learning Zhan et al. ; Lin et al. ; Park et al. ; Ma et al.  et al. Updated HBDM Li et al.  et al. Combining recovery times Combine new data resource Hojati et al.  Influence of unobserved factors Randomness model Nam, Mannering ; Hojati et al. ; Li et al.  Li et al. European Transport Research Review (2018) 10:22 Page 9 of 13 effective real-time incident responses and obtain accommodate new information chronologically. Time time-critical incident-related information. Utilizing such sequential prediction models can predict the elapsed information involves several challenges, such as how to time of an incident more accurately in support of the ap- obtain more useful records and adopting such information propriate traffic management and traveller information accurately because they can be vague and limited by the services by using continually updated information. text size. Therefore, how to combine such emerging infor- mation sources with traffic incident duration analysis and 5.3 Outlier prediction prediction is also a challenging topic in future studies. Traffic incident duration prediction currently faces diffi- Text analysis tools, such as topic modelling and sentiment culties in predicting outliers accurately. Most previous analysis, show good potential for discovering useful infor- studies show that the probability distribution of incident mation for analysis and prediction. duration has a long tail, which prevents several duration Overall, the first important step for future studies in prediction (i.e., statistical) models from predicting ex- traffic incident duration analysis and prediction is to treme values properly. For example, the HBDM models combine extensive information from connected vehicles, are disadvantaged by their inability to predict extreme traffic information providers, and social media to in- values. The reason is that the statistical models tend to crease the amount of datasets available for study. Infor- capture the central tendency in the data rather than the mation from various sources should also be acquired outliers to a certain extent. For example, several studies from incidents and constantly updated to correct predic- [30, 32] show unreasonable predictions that are longer tion results. Prediction accuracy may be improved or shorter than the average range with the same predic- through the integration of more data. tion model. Valenti et al.  compared five different models for traffic incident duration time prediction and 5.2 Time sequential prediction model found that only the ANN-based model can predict an The traditional methods that analyse and predict the incident longer than 90 min. Lin et al.  employed traffic incident duration time employ the historic dataset different models for different duration ranges; an em- of traffic incidents with or without other dataset types, bedded discrete model is utilized on incidents with a such as the traffic condition dataset. These methods as- duration of less than 60 min, whereas a rule-based sup- sume that when a model is employed to analyse or pre- plemental module is adopted for incidents that can last dict the traffic incident duration time, all the possible for more than 1 h. In reality, the longer the traffic inci- information has already been obtained. However, when dent duration time, the higher its influence on the traffic an incident is reported to the traffic control centre, in- system. Thus, predicting a longer outlier traffic incident formation on the incident (e.g., location, time, weather, duration as accurately as possible is important. Pereira and traffic conditions) is provided by the reporting per- et al.  reported that a time sequential model with sons with considerable limitations. After the traffic re- continuously updated information can be an alternative sponse team arrives at the incident location, further method to predict the longer traffic incident duration, information is sent to the traffic control centre , particularly through the incremental analysis of incom- which can help understand the traffic incident more ing textual messages. Qi, Teng  determined that the accurately. accuracy of the incident duration prediction increased as Two possible data types can provide sequential useful more information is incorporated into the models. Thus, information on an incident. One type is the report from a time sequential model can be a feasible prediction the incident response team, as previously mentioned. method for longer outliers. After the team arrives at the incident location, the inci- dent record is updated in several aspects, including af- 5.4 Improvement of prediction methods fected lanes, traffic condition, and size of rescue force. The appropriate method is key to the accurate predic- The other type is from crowdsourcing platforms. Trav- tion of the traffic incident duration time. The two main elers who pass through the incident site can post infor- types of utilized methods in the past are statistical and mation about the incident on Twitter or other data-driven methods. The former are mainly regression platforms, thereby providing useful information . and hazard-based models, whereas the latter are mainly Thus, determining appropriate methods to mine useful neural networks and decision tree models. However, the information from these different data resources, such as accuracy measurements (e.g., MAPE) show that the pre- text analysis technique and machine learning techniques, diction of most methods is only reasonable and few are can be a challenging subject of future studies. very good. A few methods are suitable partly because of A time sequential prediction model needs to be devel- the randomness of the traffic incident duration. Several oped based on various basic models, such as HBDM, studies investigate the combination of two or more various ANN models, and some other models, to methods, as previously mentioned, to overcome the Li et al. European Transport Research Review (2018) 10:22 Page 10 of 13 limitations of a single model. The results indicate a needs to consider heterogeneity, variation in time, and slight but insignificant improvement. Machine learning randomness in modelling. Furthermore, with the com- has recently developed rapidly and can provide a poten- bination of different data resources and larger datasets, tial direction to explore prediction methods for traffic more advanced machine-learning and other potential incident duration. Machine learning can conduct methods can be explored in the future to predict traffic data-driven predictions from sample inputs by con- incident duration (e.g., deep learning approach and structing an algorithm that can learn from the data. Sev- self-learning method). Several text-mining tools should eral machine learning methods, such as DT learning, be employed in data processing to deal with more useful, SVM, Bayesian networks, and genetic algorithms, have textual data resources from social media or from reports been applied in predicting traffic incident duration time of incident responders . [15, 17, 54, 57]. It needs to be noted that each of these approaches has its own advantages and disadvantages. 5.5 Combining recovery times For example, DT learning may consider many possible Two previous studies [23, 50] show that longer traffic in- outcomes but the final decisions based primarily on ex- cident duration can result in longer recovery times, lead- pectations, which could lead to unrealistic results. SVM/ ing to severe congestion. Travelers must generally know SVR is powerful for solving problems of classification, how long the recovery time will be so that they can se- regression, but is more time consuming if dealing with lect the suitable route to their destination. Detecting the very large datasets. Bayesian networks can accommodate recovery time was previously difficult because of the lim- incomplete information but computing posterior distri- itations in the fixed traffic detectors; few studies con- bution may be extremely difficult. In traffic incident dur- sider the recovery time . The development of several ation prediction, genetic algorithms help to reduce the emerging traffic-condition detection techniques cur- input features but the time taken for convergence maybe rently provides an opportunity to detect or infer the re- longer. covery time duration. For example, INRIX or Baidu in The prediction methods need to focus on the follow- China can provide real-time traffic conditions mostly ing aspects in future practical applications: based on floating car data of taxis, trucks, coaches, and other vehicle types. Such information can be used to 1) The critical function of the traffic incident duration infer the recovery time duration of an incident, and time prediction model is to support real-time traffic sometimes the simulation dynamic traffic assignment management and traveller information service, so tool is also needed. One of the difficulties with this infer- the prediction model has to be run online and must ence is how to identify the congestion cause, that is, be less time-consuming. whether the congestion is due to the incident independ- 2) The prediction model must adopt incomplete ently or caused by other factors (e.g., recurrent conges- information because when an incident is reported, tion). Investigating the significant factors that influence only part of the information on the incident can be the recovery time are possible with the recovery time obtained for incident duration prediction and even data, which can be helpful in adopting appropriate traffic until the incident is cleared. Obtaining all the management strategies to reduce the incident influence. information that influences the traffic incident Thus, determining a proper method to infer or detect duration time is impossible. For example, if no the recovery time and corresponding method to analyse traffic detector is present near the incident location, and predict it can be a future topic. An appropriate traf- then obtaining the volume of traffic that passes fic theory model or method based on simulations may through the incident location is almost impossible. provide effective means to infer the recovery time of Thus, the traffic incident duration prediction model traffic flow conditions. to be developed should have the ability to consider incidents with incomplete information. 5.6 Influence of unobserved factors Many previous studies show that except for several re- In traffic incident duration estimation and prediction, corded factors, several unobserved factors affect the traf- both the traffic operators and travellers are concerned fic incident duration. The prediction model must deal with the length of time between detection and clearance with unobserved factors. Several researchers [9, 23, 52] of an incident; that is, how long the entire process will have recently investigated methods dealing with unob- last given that it has already lasted for several minutes. served heterogeneity, such as the duration model with The hazard-based duration model can provide effective random parameter. The reason for heterogeneity cannot techniques to estimate and predict traffic incident dur- be easily understood. For example, different response ation time as shown by previous studies. HBDM remains patterns will result in different traffic incident duration a significant, potential method for future work, but it times even for incidents with similar factors. Several Li et al. European Transport Research Review (2018) 10:22 Page 11 of 13 countries, including China, have deployed a quick clear- Acknowledgments This study was supported by the National Natural Science Foundation of China ance policy for minor accidents, such as those without in- under Grant No. 71361130015 and Beijing Natural Science Foundation under juries or vehicles that are still functional. In fact, drivers Grant No.8162024. who become involved in incidents can negotiate among Authors’ contributions themselves before the incident response team arrives at All authors read and approved the final manuscript. the scene. The drivers can also fill in the necessary insur- ance forms and take photos as evidence to reduce the inci- Competing interests dent duration. However, other drivers will stay at the The authors declare that they have no competing interests. incident scene and wait for the incident response team even for minor incidents, thereby resulting in a longer Publisher’sNote traffic incident duration time. This difference is related to Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. several characteristics of different drivers, such as psycho- logical traits, experiences, and knowledge, which are diffi- Author details cult to consider in the modelling. Thus, control for Department of Civil Engineering, Tsinghua University, Room 304, Heshanheng Building, Beijing 100084, China. Department of Management randomness, heterogeneity, and the time-varying variables Engineering, Technical University of Denmark, DTU Bygningstorvet 116B, in the traffic incident duration estimation and prediction 3 2800 Kongens-Lyngby, Denmark. 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