ARIMA Model for Forecasting Short-Term Travel Time due to Incidents in Spatio-Temporal Context (TRB Paper )

Transcription

1 ARIMA Model for Forecasting Short-Term Travel Time due to Incidents in Spatio-Temporal Context (TRB Paper ) R. M. Zahid Reza Graduate Student of Civil & Environmental Engineering Department The University of North Carolina at Charlotte 9201 University City Boulevard Charlotte, NC , USA Tel.: ; rreza@uncc.edu Srinivas S. Pulugurtha (Corresponding Author) Professor & Graduate Program Director of Civil & Environmental Engineering Department Director of Infrastructure, Design, Environment, & Sustainability (IDEAS) Center The University of North Carolina at Charlotte 9201 University City Boulevard Charlotte, NC , USA Tel.: ; sspulugurtha@uncc.edu Venkata R. Duddu Assistant Research Professor of Civil & Environmental Engineering Department The University of North Carolina at Charlotte 9201 University City Boulevard Charlotte, NC , USA Tel.: ; vduddu@uncc.edu Total Word Count: 5,257 (Text) + 10 (Figures/Tables) * 250 = 7,757 Transportation Research Board 94 th Annual Meeting January 11-15, 2015, Washington, DC

2 Reza, Pulugurtha, & Duddu ABSTRACT This paper focuses on an application of Autoregressive Integrated Moving Average (ARIMA) model to incorporate traffic information from neighboring links in forecasting short-term travel time along a corridor due to an incident. The model was developed using 181 Vehicle Accident type incidents that occurred along ~19-mile freeway segment in the city of Charlotte, North Carolina. The spatio-temporal context based data was combined and analyzed with the ARIMA model using pre-whitening of the cross-correlation function alongside lagged regression. Results indicate that the travel times for consecutive segments are highly correlated and, both, upstream and downstream segments of a target segment on a corridor will influence the current state of target segment. However, upstream segments are observed to have a higher effect than downstream segments. The mean absolute percent error (MAPE) and mean absolute deviation (MAD) of the developed lagged regression model for every segment was mostly less than 10%. Moreover, the results obtained from the validation of models at both segment- and corridor-level indicate that the estimated effect of incidents on travel time is almost equal to and close to the real-time observations. MAPE and MAD computed from validation data (26 incidents) are observed to be less than 10% for 95% of samples indicating an accurate estimation of the effect of incidents on travel time using the proposed method. Keywords: Short-term, Traffic, Forecasting, Pre-whiten Cross-correlation, Spatial, Temporal, Freeway, Speed, Lagged Regression, Incident, Travel Time

3 Reza, Pulugurtha, & Duddu INTRODUCTION Non-recurring congestion caused by incidents lead to significant delays on urban roads. Along with congestion, incidents have many effects such as secondary incidents resulting in increased delays, bottlenecking, and rubbernecking. Under free-flow or low flow conditions, travel time prediction can be easily made based on the free flow speed. The travel time is still very predictable, given available measurements and relationships of relevant traffic characteristics such as travel time, speed, volume and occupancy are available, if the traffic state remains stable over time as well as across space even though the traffic volume has increased. However, a complex traffic system is characterized by various time-dependent variables (flow, density, speed, travel time, etc.) and becomes non-linear in nature when traffic volume levels are close to the saturated condition (1). In this situation, dynamic travel time and non-stationary traffic state is no means proportional. Furthermore, incidents induce even more complexities to the traffic system, which reduces the preciseness of travel time predictions (1). Although there are many benefits in evaluating the effect of incidents on travel time, very few studies have considered the effect of traffic incidents on travel times due to the difficulty in obtaining reliable travel time data during incidents (2). This study aims at evaluating the effect of incidents on travel time to provide travelers with reliable and accurate travel time information in a timely manner, reduce incident time, and minimize the effect of incidents with an efficient Traffic Incident Management (TIM) system. LITERATURE REVIEW Travel time, a very important traffic characteristic, helps solve major operational problems along roadway facilities. These problems are associated to traffic signal timing control coordination, traffic assignment, and congestion management (5). Different multivariate methods have been applied for travel time prediction in the past. They include path-based estimation and link-based estimation. Park et al. (6) proposed Artificial Neural Network models for predicting freeway path/corridor travel time. Kwon et al. (7) adopted linear regression method with current and historical travel time information as predictors to forecast travel time during incidents. Zhang et al. (8) proposed a method to forecast freeway travel times using a linear model with departure time as a function of coefficients. Past studies incorporated various methods such as Kalman filtering, Markov Chain, the weighted moving average, cross correlation, and fuzzy logic theory to forecast travel times (9). Similarly, researchers have proposed statistical and machine learning techniques to evaluate the effect of incidents on travel time. Messer et al. (10) applied kinematic wave theory to forecast individual travel times due to an incident on freeway. However, the test results from their proposed theory inaccurately reported the wave speed. Koutsopoulos et al. (11) presented theoretical link travel-time estimation during an incident. However, the incident delay was estimated by using a deterministic model, thus producing same output for a given initial state. Al-Deek et al. (12) evaluated the benefits of a route guidance system, specifically in the case of incident congestion. However, the incident situation was assumed to be deterministic (12). Fu et al. (13) developed a travel time prediction model considering dynamic and stochastic nature of the traffic during incident conditions. The results indicate that the incident delay showed a high variance even when the expected delay was observed to be low (13). Sheu et al. (14) developed discrete non-linear stochastic model to forecast the real-time effects of traffic congestion when a lane is blocked. Zeng et al. (1) forecasted corridor-level travel time under incident conditions using various neural network approaches and showed that an extended state-space neural

4 Reza, Pulugurtha, & Duddu network (ExtSSNN) outperformed time delay neural network (TDNN) and traditional back propagation neural network (BP) (1). Different conventional and non-conventional techniques such as Artificial Neural Network (ANN), Genetic Algorithms (GA), approximate nearest neighbor, non-parametric regression, and time series modeling have been applied to forecast short-term or long-term traffic characteristics (3). In short-term forecasting (both for univariate and multivariate), the gist is to identify the fundamental pattern in the traffic data and utilize that same to forecast future traffic transformation. Various univariate methods such as smoothing, exponential smoothing, decomposition, and Kalman filtering can be applied for time series modeling for forecasting or to evaluate the effect of incidents. However, these univariate models consider only temporal factors for forecasting, neglecting the associated spatial factors. To address this limitation, multivariate forecasting methods are generally used to capture both temporal and spatial attributes of traffic. Popular multivariate methods are multivariate time series, multiple regression, state-space, and vector auto regression methods (4). However, each of these methods has their own limitations. For example, in case of Kalman filter method to address real-world problems, the stochastic errors in both state and observation processes are assumed to be known (15). In case of neural networks, the internal working process of network is defined as Black Box (1). ARIMA models are widely accepted for modeling stationary time series data owing to their accuracy in forecasting. Ahmed and Cook introduced ARIMA model to freeway traffic volume and occupancy forecasting in Levin et al. (16, 17) used this method as an alternative approach to model the stochastic nature of the traffic. So far, different types of ARIMA models have been developed to successfully forecast traffic characteristics such as traffic volume (or traffic flow), travel speeds, and travel time. Williams et al. (18) applied seasonal ARIMA model for short-term traffic flow prediction and reported a MAPE of 8.6%, outperforming the heuristic forecast benchmark. Gosh et al. (3) compared random-walk model, Holt-Winter s exponential smoothing technique, and seasonal ARIMA model for forecasting traffic flow for Dublin and concluded that seasonal ARIMA and Holt-Winter's smoothing technique provided competitively better forecasting results compared to random-walk model. Rui-min et al. (19) compared six short-term travel time prediction models i.e., moving average, exponential smoothing model, ARIMA model, Kalman filtering, Radial Bias Function Neural Network (RBFNN), and combined model for the major arterials in Beijing City. Statistical results showed that all the models performed almost similarly and better than RBFNN (19). Billings et al. (5) applied ARIMA to study the arterial travel time prediction problem for urban roadways using GPS probe vehicle data. The results for all the road segments were observed to be reasonably good (5). Swardo et al. (20) adopted ARIMA model to forecast the bus travel time and observed that moving average model clearly fit with the observed values for both directions (20). The effectiveness of a multivariate method enhances with the incorporation of surrounding traffic conditions. Vythoulkas revealed that traffic forecasting accuracy is closely related to the use of neighboring segments traffic information (21). Yang et al. (4) also showed spatio-temporal relationships of speed at consecutive segments are highly correlated under different traffic conditions. Not much has been done in the past to evaluate the effects of incidents by incorporating spatial and temporal variations in travel time. Moreover, very little has been done on developing time series models in forecasting travel time during incidents. This paper therefore addresses this

5 Reza, Pulugurtha, & Duddu need and focuses on adopting time series ARIMA model in forecasting the effect of incidents on travel time. The primary objective of this research is to forecast travel time of segments during incidents by incorporating the effect of characteristics of surrounding segments through the use of ARIMA model. It also aims at evaluating spatio-temporal relationships among the surrounding segments through pre-whitened cross-correlations function alongside lagged regression method during incident scenarios. STUDY CORRIDOR A mile long segment along southbound direction of I-77 in the city of Charlotte, Mecklenburg County of North Carolina (NC) was considered as a study segment for this research. The study segment extends from Traffic Message Channel (TMC) to 125N04792, consisting of 28 TMC codes. A description of selected TMC codes is shown in Table 1. From downstream to upstream, road links (TMCs) were designated as X6 to X34 based on sequence along the selected corridor of I-77 S i.e., downstream segment is designated as X6 and upstream segment is designated as Segment X34. The length of each segment is also shown in the table. Each segment shown in Table 1 is categorized as either internal (designated by N or P) or external path (designated by + or -). An internal path is the segment which starts at off-ramp and ends at on-ramp, while an external path is the road segment that leads up to the point of interchange or intersection (22). Figure 1 shows part of the study corridor. Pink triangle symbols in Figure 1 define the starting point of each TMC code that extends in the southbound direction. Incident data was obtained from North Carolina Department of Transportation s (NCDOT) Traveler Information Management System (TIMS). The TIMS database recorded a total of 244 incidents along I-77 S from 2010 to This database consisted of attributes pertaining to each incident. They include incident type, start and end time of incident, location (mile marker and coordinates), the number of lanes closed, reasons of incident, severity, and directions of traffic, road name, and presence of special condition. The classification of severity of incident in the TIMS database is not same as KABCO groupings recommended by the National Safety Council. Instead it is classified into three simple groups: A, B, and C. According to TIMS, the type A severity incident indicate incidents resulted in blockage of lane/lanes, type B severity incidents are incidents with a shoulder blockage, and type C severity incidents are incidents with no lane blockage but congestion. TIMS recorded seven different types of incident. For this study only Vehicle Accident type incident was chosen along with its severity. A total of 181 Vehicle Accident type incidents were observed during the years 2010 to 2012 along the study corridor (I77 S). INRIX collects real-time (24 7) speed data using numerous probes for more than 260,000 miles of roads, including interstates and major roads, all over the United States. In the INRIX database, each segment is defined by a unique nine digit code (known as TMC code) created by Tele Atlas and NAVTEQ. For every TMC code, corresponding average travel times are computed by averaging the travel time of all the vehicles observed to pass the TMC code at one minute interval. Besides travel time information, INRIX also provides speed, average speed, reference speed, and confidence score (22). Travel time information for the study corridor was obtained from this database. It was used to evaluate spatio-temporal effect of incidents on travel time.

6 Reza, Pulugurtha, & Duddu Segment No. TMC TABLE 1 Description of Segments along I-77 S Length (miles) Direction Location Segment Type X6 125N Southbound Nations Ford Rd/ Exit 4 & I-77 Internal X Southbound Nations Ford Rd/ Exit 4 & I-77 External X8 125N Southbound Tyvola Rd/ Exit 5 & I-77 Internal X Southbound Tyvola Rd/ Exit 5 & I-77 External X10 125N Southbound Woodlawn Rd/ Exit 6 & I-77 Internal X Southbound Woodlawn Rd/ Exit 6 & I-77 External X12 125N Southbound Tryon St/ Exit 6 & I-77 Internal X Southbound Tryon St/ Exit 6 & I-77 External X14 125N Southbound Clanton Rd/ Exit 7 & I-77 Internal X Southbound Clanton Rd/ Exit 7 & I-77 External X16 125N Southbound Remount Rd/ Exit 8 & I-77 Internal X Southbound Remount Rd/ Exit 8 & I-77 External X18 125N Southbound I-277/Exit 9 & I-77 & I-77 Internal X Southbound I-277/Exit 9 & I-77 & I-77 External X20 125N Southbound Morehead St/ Exit 10 & I-77 Internal X Southbound Morehead St/ Exit 10 & I-77 External X22 125N Southbound Trade St/ Exit 10 & I-77 Internal X Southbound Trade St/ Exit 10 & I-77 External X24 125N Southbound Brookshire Fwy/ Exit 11 & I-77 Internal X Southbound Brookshire Fwy/ Exit 11 & I-77 External X26 125N Southbound La Salle St/ Exit 11 & I-77 Internal X Southbound La Salle St/ Exit 11 & I-77 External X28 125N Southbound I-85/ Exit 13 & I-77 Internal X Southbound I-85/ Exit 13 & I-77 External X30 125N Southbound Sunset Rd/ Exit 16 & I-77 Internal X Southbound Sunset Rd/ Exit 16 & I-77 External X32 125N Southbound Reames Rd/ Exit 18 & I-77 Internal X Southbound Reames Rd/ Exit 18 & I-77 External

7 Reza, Pulugurtha, & Duddu FIGURE 1 Study corridor and segments.

8 Reza, Pulugurtha, & Duddu METHODOLOGY The methodology adopted in this research is discussed in this section. 1. Database to Develop Models Travel time data obtained for every one minute interval from INRIX for years for I- 77 S was used to develop the database for modeling the effect of incidents on travel time. To evaluate the spatio-temporal effects of incident, the database was developed such that each TMC code has the corresponding travel time for the specific timestamp and cumulative distance from the centroid of the 1 st segment (X6) of the study corridor. However, the effect of incident sometimes lasts even after the clearance of the blocked corridor or shoulder (23). Therefore, travel time for all 28 segments in the study corridor was collected for all the corresponding timestamps from the start time of incident to five hours after the end time of the incident. All the timestamps for each segment were split into 10 minute intervals. The average travel time for each segment during each specific time interval (for example, :10:00 to :20:00) was computed as an average of all the samples within the respective time intervals. This database was defined as a Database with Incident (DWI). Similarly, another database was developed with travel times when there are no incidents observed and is defined as a Database without Incident (DWOI). To generate DWOI database, all the days without incident on the study corridor I-77 S were selected from TIMS database (a total of 112 days were identified). As mentioned earlier, the selected timestamps for corresponding segments were then split into 10 minute intervals excluding the date part (for example, 10:10:00 to 10:20:00 for all 112 days) to compute average travel times on each segment in case of no incidents. 2. ARIMA Model To fit a time series model, it is necessary to transform the raw data into stationary form (as statistical properties of the series do not depend on time) so that the mean and variance do not change over time and both series are not correlated (24). Simple initial time series plot will help to identify whether the series is stationary or not. If the series is observed as not stationary, then the series is transformed into new time series where the values are differences between consecutive values known as differencing (24). The term differencing is actually the change between consecutive observations in the original series and may be applied consecutively more than once giving first differences, second differences, and so on. The first differences ( ) of time series ( ) can be described as shown in Equation 1. (1) The differenced series will have (t 1) values for a time series of (t) values. Occasionally the first order differenced data will not appear stationary. It may therefore be necessary to difference the data multiple times to obtain a stationary series. The degree of differencing determines the d value of AIRMA (p, d, q) model, where, p is the number of autoregressive terms in the model, d is the number of non-seasonal differences, and q is the number of lagged forecast errors in the predicted equation (24). Different types of unit root test can be done to check the stationary condition. One of the most popular unit root tests is the Augmented Dickey- Fuller (ADF) test. The null hypothesis of this test is that the model is not stationary. When the time series is stationary, any autocorrelation that remains can be explained by orders of p and q (where, p is the highest order of the autoregressive polynomial and q is the highest order of the moving average polynomial) computed from autocorrelation function (ACF) and partial

9 Reza, Pulugurtha, & Duddu autocorrelation function (PACF) plots. The rule to identify p and q orders from ACF and PACF plots is (25): If the sample ACF tails off very slowly and the sample PACF cuts after lag 1, p will be 1 If the sample PACF decays very slowly and the sample ACF cuts after lag 1, q will be 1 Full ARIMA (p, d, q) model can be written as (24): p d ( 1 1B p B )(1 B) yt c (1 1B qb AR( p) d differences MA( q) 3. Cross Correlation Function and Pre-whitening In the relationship between two time series (y t and x t ), y t may be related to the past lags of the x- series. The cross correlation function (CCF) can identify the lags of the x-variable that might be useful predictors of y t (4). Yang et al. (4) successfully used CCF to identify the relationship of speed series of different road segments. The same principle was applied in this research to identify the correlations of travel time series for different road segments. CCF is the productmoment correlation between two time series of different time lags. The general form of CCF for upstream and downstream travel times is shown in Equation 2 (4). (2) where, μ s and μ s-1 are the means of T s and T s-1, s and s-1 are the standard deviation of T s and T s-1, and, is the time lag between two series. In general, the cross-correlation function can be described as lead and lag relationship (4). When > 0, T s-1,t leads T s,t and when < 0, T s-1,t lags T s,t. For instance, consider = h where h is a positive integer. CCF measures the relationship between upstream travel time at h minutes before and the downstream travel time at time. However, few CCFs reveal so many significant spikes which make it very difficult to find the most significant one to predict the variable. So, the series must be pre-whitened first to simplify this complicated autocorrelation process and to identify accurate patterns. The prewhitening process involves following steps (25): An Autoregressive model with minimum AIC is fitted to x t p and q are used to pre-whiten x t and y t by multiplying with θ -1 x (B)Φ x (B)(1-B) d and generate two pre-whitened series t and t The CCF is computed for the pre-whitened series t and t Figure 2 shows difference between regular CCF with many significant spikes and prewhitened CCF with few significant number of spikes such as k = 0, 1, -1 which can be used to predict y t. q ) e t

10 Reza, Pulugurtha, & Duddu FIGURE 2 CCF and pre-whitened CCF. 4. Lagged Regression In forecasting, the leading factors of one segment should be identified first from pre-whitening cross-correlation factors. From these leading factors, lagged regression identifies the variables that are statistically significant to predict the models by fitting and evaluating different number of upstream / downstream segments as predictor variables. For example, the lagged regression model for segment X7 can be expressed as follows: V V X 7, t s, k where, k is the time lag, s is the segment ID, and ɛ k is zero-mean uncorrelated error term. (4). RESULTS Incident duration has a significant effect on travel time and travel speed variation along the corridor. Queue starts dissipating during the incident clearance period. However, even after the clearance of the blocked lane and shoulder, the effect of the incident on the traffic flow may persist (23). To understand this effect, a sample spatio-temporal variation of travel time is shown in Figure 3. s, t k k FIGURE 3 Travel time vs. distance for (L) without and (R) with incident condition. From Figure 3, it can be observed that for with-incident condition, travel time is affected up to approximately 3 miles. Thereafter, travel times for both with-incident and without-incident condition follow almost similar pattern. Moreover, Figure 3 shows that maximum travel time

11 Reza, Pulugurtha, & Duddu was observed for corresponding segment along the corridor 30 minutes after the incident occurrence. Effect of Traffic Condition and Distance on Cross-correlations The general behavior of traffic is different from the behavior of traffic during non-recurring congestion condition in case of an incident (23). So, an event of an incident may result in varying travel times as well as travel speeds. Further, it can be inferred that the spatio-temporal correlation within traffic will change with traffic conditions. The pre-whitened cross-correlation method was performed on two selected consecutive segments (X19 and X18). This revealed inter-influence between the two selected segments. Figure 4 shows cross-correlation between segments X19 and X18. For segments X19 and X18, it is observed that cross-correlation is significant when = 0, 1, -1, 2, 5, 9, 34, and -34. Here k = 0 indicates that current travel time at downstream segment is closely related to the current travel time on upstream segment and reveals the similarity in traffic flow patterns. = 0, 1, 2, 5, 9, and 34 indicates that the past travel time on downstream segment (X18) influences current travel time on upstream segment (X19). This implies that past travel times on upstream segment (X19) can be used to forecast future travel time on downstream segment (X18). Similarly, = -1 and k = -34 indicates that past travel times on upstream segment (X19) will influence the travel time on downstream segment (X18) FIGURE 4 Cross-correlation between X19 & X18. Yang et al. (4) evaluated the effect of distance on CCF and reported that CCF values generally decrease with an increase in absolute distance. However, in their study, the authors did not discuss the effect of incident. Therefore, to study the effect of distance on CCF for nonrecurring congestion condition, segment X18 was chosen as the target segment with 12 segments in the upstream direction and 15 segments in the downstream. Pre-whitened CCF for all twenty nine travel time series were computed with respect to the target segment (X18). The distance is computed from target segment (X18) to the centroid of each segment. In this case, the positive value indicates downstream direction and negative value indicates upstream direction. The is the time lag ranging from -34 to 34. A 3-D plot between the three variables (distance, time lag, and CCF) is shown in Figure 5.

12 Reza, Pulugurtha, & Duddu FIGURE 5 (a) 3-D views of CCF values (b) contour of CCF values. Figure 5 supports the assumption of Yang et al. (4) that the CCF value decreases with respect to absolute distance in both upstream and downstream direction even in the presence of an incident. The following can be inferred from Figure 5.

13 Reza, Pulugurtha, & Duddu From the distance perspective, the effective influence range is (6.0, -4.5), which indicates that, 6.0 miles of traffic in the downstream direction and 4.5 miles of traffic in upstream direction have influence on the travel time of the target segment (X18). From the time lag perspective, time lags are within 10 minutes. This indicates that the dynamic interactions within segments are very active in a short time range. Developing Lagged Regression Model for Road Segment For lagged regression, significant CCF and corresponding variables and lag time were identified. Among the significant variables only those variables which showed ρ<0.05 (95 th percentile confidence interval) were selected to build the lagged regression model. For example, X13, X16, X17, X19, X20, X21, and X22 are found statistically significant predictor variables to forecast traffic condition on X18. Time lag is not more than 10 min (Figure 5). To calibrate the model for each segment, mean absolute percent error MAPE and MAD were used. R-squared for the regression model always increases as variables are added. Therefore, it is not an effective measurement for model comparison and was not used in this research. Significant leading factors for each segment in study area are shown in Table 2. Prediction of Corridor Travel Time at Incident Effect Location For model validation, 26 incidents with different severity types and different number of lane blockages were considered. The computed MAPE and MAD based on these incidents data are shown in Table 3. Almost all the segments considered for validation have MAPE values less than 10% except for segments X17 and X18. For these two segments, MAPE value is greater than 10%. Similarly, MAD values of these two segments were also high when compared to other segments. The length of segments X17 and X18 are 0.8 and 0.11 miles, respectively. It is hard to come up with meaningful estimates for such short segments. However, the overall errors in prediction still seem to be low. The developed modified ARIMA model was validated both for segment- and corridorlevel travel time estimation. Sample validation results are shown for one incident. The incident occurred at 5:00 PM on May 16, The severity type was B and the number of lanes blocked was one lane. Corridor travel time variation for 10 min, 20 min,, 80 min is shown in Figure 6. The travel times obtained from INRIX indicate that 20 minutes after the incident occurrence, the travel time on a segment reaches up to 7 min and thereafter it started decreasing. The forecasted model shows significantly close results to the observed travel times from the INRIX. Figure 6 also shows the spatial effect of incident on travel time occurred up to 4 miles from the point of incident occurrence. The developed model was also validated for segment-level travel time. For this purpose, a different incident was selected to compare the travel time obtained from INRIX and forecasted travel time on segment X18, X19, 20, and X21 along the study corridor. Figure 7 shows the comparison between observed and forecasted travel time. From Figure 7, one can infer that the travel times from both INRIX and forecasted model are very close even at the peak point of travel time.

14 Reza, Pulugurtha, & Duddu Table 2 Performance Comparison of Fitted Model Target Segment for Forecasting Holdout Performance Segment Downstream Upstream MAPE MAD X6 3,4,5 7, 8,9, % 0.98 X7 4,5,6 8,9,10, % 1.29 X8 4,5,6,7 9,10,11, % 2.11 X9 5,6,7 10,11,12, % 2.62 X10 6,7,8,9 11,12,13, % 2.41 X11 7,8,9,10 12,15, % 1.26 X12 9,10,11 13, % 0.61 X ,15,16, % 0.96 X14-15,16, % 4.44 X15-16,17,18, % 2.98 X16-17,18,19, % 4.47 X17 15,16 18, % 1.56 X18 13,16,17 19,20,21, % 7.05 X19 16,17,18 20,21, % X20 17,18,19 21,22,23, % 1.08 X21 18,19,20 22,23, % 0.30 X22 21,20 23,24,25, % 0.83 X23 19,20,21,22 24,25,26, % 5.11 X24 22,23 25,26, % 0.75 X25 21,22,23,24 26,27,28, % 3.33 X26 23,24,25 27,28,29, % 9.94 X27 24,25,26 28,29, % 5.38 X28 26,27 29,30,31, % 1.00 X29 26,27,28 30,31,32, % 7.73 X30 27,28,29 31,32, % 8.56 X31 28,29,30 32,33,34, % 7.21 X32 30,31 33,34,35, % 7.34 X33 30,31,32 34,35, % 5.21 X34 32,33 35,36,37, % 3.19

15 Reza, Pulugurtha, & Duddu Table 3 Model Validation Target Model Validation Segment MAPE MAD X6 4.18% 1.80 X7 7.49% 3.77 X8 6.22% 3.95 X9 7.38% 6.18 X % 10.0 X % 5.42 X % 1.68 X % X % X % X % 4.85 X % X % X % 1.07 X % 0.81 X % 1.86 X % X % 1.12 X % 7.02 X % 4.34 X % 3.72 X % 0.52 X % 5.60 X % 5.32 X % 4.56 X % 7.81 X % 9.12 X % 3.32 X % 9.56

16 Reza, Pulugurtha, & Duddu FIGURE 6 Comparison of travel time from observed and forecasted model.

17 Reza, Pulugurtha, & Duddu FIGURE 7 Comparison of segment level travel time. CONCLUSIONS This paper presents the effect of incidents on travel time using modified ARIMA model. The study proposed a methodology to evaluate significant predictor variables by modifying crosscorrelation function through pre-whitening method along with lagged regression technique. The results demonstrate that the travel times on consecutive segments are highly correlated even with incidents. As expected, downstream segments to the target segment have higher effect when compared to the effect on upstream segments. The MAPE and MAD computed from validation data are observed to be less than 10% for 95% of samples indicating an accurate estimation of the effect of incidents on travel time by the ARIMA model developed in this research. Developing the models based on incident severity will help estimate their effect on travel time more accurately. This merits an investigation. ACKNOWLEDGEMENTS This paper is prepared based on information collected for a research project funded by the United States Department of Transportation - Office of the Assistant Secretary for Research and Technology (USDOT/OST-R) under Cooperative Agreement Number RITARS-12-H- UNCC. The support and assistance by the project program manager and the members of Technical Advisory Committee in providing comments on the methodology are greatly appreciated. The contributions from other team members at the University of the North Carolina at Charlotte are also gratefully acknowledged. Special thanks are extended to Ms. Kelly Wells of NCDOT and Mr. Michael VanDaniker of the University of Maryland (UMD) for providing access and help with INRIX data. DISCLAIMER The views, opinions, findings, and conclusions reflected in this paper are the responsibility of the authors only and do not represent the official policy or position of the USDOT/OST-R,

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