A Descriptive Bayesian Approach to Modeling and ... - IEEE Xplore

IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 14, NO. 4, DECEMBER 2013

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A Descriptive Bayesian Approach to Modeling and Calibrating Drivers’ En Route Diversion Behavior Chenfeng Xiong and Lei Zhang

Abstract—This paper presents a Bayesian approach for modeling and calibrating drivers’ en route route changing decision with behavior data collected from laboratory driving simulators and field Bluetooth detectors. The behavior models are not based on assumptions of perfect rationality. Instead, a novel descriptive approach based on naive Bayes’ rules is proposed and demonstrated. The en route diversion model is first estimated with behavior data from a driving simulator. Subsequently, the model is recalibrated for Maryland, based on Bluetooth detector data, and applied to analyze two dynamic message sign scenarios on I-95 and I-895. This calibration method allows researchers and practitioners to transfer the en route diversion model to other regions based on local observations. Future research can integrate this en route diversion model with microscopic traffic simulators, dynamic traffic assignment models, and/or activity-based/agent-based travel demand models for various traffic operations and transportation planning applications. Index Terms—Bayes’ rule, Bluetooth data, calibration, driving simulator, en route diversion.

I. I NTRODUCTION

D

RIVERS’ en route route choice under information provision has been traditionally modeled by the econometric theory of random utility maximization [1]. Mahmassani and Liu [2] adopted a multinomial probit framework to model the commuters’ joint pretrip departure time and en route diversion behavior in response to real-time information, based on data from a laboratory interactive driving simulator. The study suggests that commuters switch routes if the expected travel time savings exceed an indifference band, which varies with the remaining trip time to destination. Abdel-Aty et al. [3] developed logit models to capture the effect of real-time information on en route diversion, using stated preference data. Khattack et al. [4] estimated a bivariate ordinal probit model of drivers’ diversion and departure time choice when traffic information is available. Limitations exist in the en route diversion models. First of all, they are often not well calibrated due to data limitation

Manuscript received April 7, 2013; revised May 29, 2013; accepted June 3, 2013. Date of publication July 15, 2013; date of current version November 26, 2013. This work was supported in part by the National Science Foundation, by the U.S. Federal Highway Administration Exploratory Advanced Research Program, and by the Maryland State Highway Administration. The Associate Editor for this paper was H. Dia. The authors are with the Department of Civil and Environmental Engineering, University of Maryland, College Park, MD 20742 USA (e-mail: lei@ umd.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TITS.2013.2270974

and other issues. The inherent bias of the stated preference data and the driving simulator data has long been argued as a major deficiency of the models [5]. Koutsopoulos et al. [6] further asserted that driving simulators, for en route diversion analysis, can be more useful if revealed preference data collected from “actual en route route choice behavior” and an appropriate designed calibration become available. Moreover, unlike the decisions of departure time and pretrip route choice, en route diversion is a decision triggered by impulsion. When making en route diversion decisions, a driver usually has very limited reaction time to obtain the realtime traffic information from the sources, process the information, compare the original and diverting routes, and make a decision. Therefore, some researchers [7], [8] emphasized the need for rule-based computational process models since it has long been claimed that utility-maximizing models do not always reflect the true behavioral mechanisms underlying travel decisions (people may reason more in terms of “if-then” structures than in terms of utility-maximizing decisions). A Learning-Based Transportation Oriented Simulation System applies CHi-squared Automatic Interaction Detection decision trees to model the activity scheduling behavior [9]. Janssens et al. [10] developed a Bayesian network augmented tree approach to look at multifacet decision making processes. This approach took advantage of both the Bayesian network and the decision tree/rule induction method. Zhang [11] developed a positive theoretical framework [referred to as the Search, Information, Learning, and Knowledge (SILK) theory] for travel decision making analysis, which was subsequently applied to model route choices on a real-world transportation network in Twin Cities, Minnesota, USA. Xiong and Zhang [12] further explored the SILK framework and proposed a descriptive departure time searching and switching model. This model has been successfully integrated with a large-scale microscopic traffic simulation [13]. In modeling en route diversion behavior, few studies have been reviewed in this line of research. Paz and Peeta [8] employed aggregate behavioral if-then rules and calibrated weight vectors for these diversion rules, to match the estimated and actually observed network states. Other than rules that give only a simple classification, models that give probability estimates are favored in the field of practical data mining and artificial intelligence for their flexibility in applications when combining decisions and sensitivity analysis [14]–[16]. The naive Bayes model is one of the most efficient and effective algorithms that predict probability estimates. Although its underlying conditional independence assumption is rarely true in real-world applications, the correlation among variables does not affect the performance optimality of the

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naive Bayes model, as quantitatively proved by Zhang [17]. Except for some research studies in mode choice modeling [18], [19], few travel behavior studies have explored this promising approach. Following this line of research, this paper develops a naive Bayes classifier to model drivers’ en route diversion behavior. Then, a Bayesian approach to calibrate the naive Bayes model is developed, in order to transform the naive Bayes prediction into more accurate estimates. This calibration approach is practical oriented and is demonstrated on a real-world en route diversion case study, where the Bluetooth-based testing data set is collected. The main contribution of this paper lies in the originality of the model and calibration in en route diversion behavior. The remainder of this paper is organized as follows. Section II presents the training data set, as well as the model development. Section III presents the testing data set and the Bayesian calibration process. Conclusions and discussions on future research are offered at the end of this paper.

II. M ODELING E N ROUTE D IVERSION B EHAVIOR A. Training Data From a Driving Simulator Experiment The data for developing the en route diversion classifier is collected from a driving simulator experiment designed by the Human Performance Laboratory at the University of Massachusetts Amherst, Amherst, MA, USA (see [20] for more details about the data). Sixty-three subjects were recruited in this driving simulator survey. In the driving simulator test, subjects were required to drive slowly at the beginning of each scenario to observe a route map of the entire network with travel times displayed for 10 s before arriving at the Divert Point, where a route choice decision had to be made. Subjects were shown three different types of route maps in the tests, as shown in Fig. 1. Each type of the maps appeared six times with different assigned travel times. Some social demographic information (i.e., gender, age, and years holding a driver’s license) has been also collected. In Fig. 1, each map contains one routine route with deterministic travel time tb and one risky diverting route using (m, n) to denote a random travel time with two ordered outcomes m or n (m < n), each with a probability of 50%. The risky diverting branch gets more complicated in topology from Map A through Map C. Map A contains one simple risk diversion, with possible low travel time tL and high travel time tH . In Map B, a bifurcation is added to the diverting route, where the safe detour has a deterministic travel time tH . The risky route has a low travel time tL and a prohibitively long delay tM , which could be due to an incident. At node i, a subject will receive real-time information on the realized travel time on the diverting route. Map C adds another bifurcation to the diverting route, upstream of the one in Map B, with two possible outcomes, namely, tb and tM . Again, real-time information is available at nodes i1 and i2 on the realized travel time. Similarly, the information at either node could help drivers avoid the extremely high travel time tM on the diverting route. A driver, while driving, takes into account the real-time traffic information to some extent in making en route diversion choice at the Divert Point.

Fig. 1.

Three types of maps in the driving simulator experiment.

B. Logit Model A binary logit model is first specified and estimated. There are two alternatives, which are denoted by + (i.e., not divert) or − (i.e., divert). In this model, expected travel time, i.e., Time, and travel time unreliability, i.e., UNR are employed as two major explanatory variables. Thus, individual n’s systematic utility function of choosing the routine route (i.e., not divert) is formulated as Vn (+) = β0 + β1 · Timen .

(1)

The utility of choosing the alternative route (i.e., divert) is formulated as Vn (−) = β1 ·Timen +β2 ·UNRn +β3 ·Gendern +β4 ·Riskn . (2) The utilities are applied within the logit form to yield the probability of a given diversion observation that individual n chooses alternative C, i.e., Pn (C) = 

exp (Vn (C)) . Cn ={+,−} exp (Vn (Cn ))

(3)

The explanatory variables are defined as follows. • Time: the expected travel time. Time = tb in “not divert” alternative, and Time = (tL +tH )/2 in “divert” alternative.

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TABLE I B INARY L OGIT M ODEL FOR E N ROUTE D IVERSION

Fig. 2. Naive Bayes model structure. TABLE II C ONDITIONAL P RIOR P ROBABILITY E STIMATES FOR THE NAIVE BAYES C LASSIFIER

• UNR is specified as the 95% confidence interval of the random travel time duration. • Gender: a dummy variable, which is equal to one if the subject is male and zero otherwise. • Risk: a dummy variable, which is equal to one for Scenario Maps B and C and zero otherwise. Risk is a dummy variable reflecting the complexity (or risk) of the alternative route. Consider the situation when the diverting route involves bifurcation and possible huge delay tM (the situation in Maps B and C shown in Fig. 1). Even if, theoretically, the drivers can make the correct and strategic en route decision to avoid the huge delay penalty tM , with the guidance of the real-time information at the information point i (or i1 and i2 in Map C), drivers are less likely to divert considering the little reaction time in making this decision. Choosing this type of alternative route is considered as a diversion of high risk. The logit model estimates are presented in Table I. The estimated coefficients of the variables are all significant at 95% confidence level, except the constant, and are with the correct signs. The negative alternative specific constant β0 indicates that, under the driving simulation scenarios, the likelihood of diversion from the routine route has been positively affected by certain factors, e.g., the provision of travel time information. Travel time and travel time unreliability negatively affect drivers’ choice. Male drivers were more likely to divert from their routine routes. This finding conforms to previous en route diversion research [21]–[24]. The model estimates also showed that when the alternative route consists of more complex network topology and therefore represents higher risk, the drivers were less likely to divert. In this paper, evaluating the predicted responses versus the actual responses was used to compare between models. A withinsample tenfold cross validation is conducted for validating the en route diversion model. This validation technique is typically seen in most practical limited-data situations [25]. The aggregate cross-validation accuracy for the binary logit model is 91.3%.

Variables Fi used in this model include expected travel time (Time), travel time unreliability(UNR), gender (Gender), and diverting risk (Risk). Δ denotes percentage changes of the alternative route’s attributes from the attributes of the routine route. For each training observation F, the naive Bayes classifier is a function that assigns a class label to it. This method learns the conditional probability of each variable Fi , given the class C. According to Bayes’ rule, the probability of the example F = (F1 , F2 , . . . , Fn ) being class + is p(+|F) =

This paper then proposes a naive Bayes classifier (see Fig. 2) to model the en route diversion behavior based on the same data set. In Fig. 2, nodes represent a tuple of stochastic attributes (F1 , F2 , . . . , Fn ) and a behavioral classification variable denoted by C. There are two behavioral classes, which are denoted by + (i.e., the not divert class) or − (i.e., the diverting class). The directed arcs represent conditional dependence between variables.

(4)

For a training observation, the naive Bayes classifier assumes conditional independence of every other attribute, given the value of the classification variable p(F|+) = p(F1 , F2 , . . . , Fn |+) =

n 

p(Fi |+).

(5)

i=1

Thus, (6) shows the functional form of the naive Bayes classifier. The empirical observation is classified as + if and only if fnb (F) ≥ 1, i.e., p(+)  p(Fi |+) . p(−) i=1 p(Fi |−) n

fnb (F) = C. Naive Bayes Classifier

p(+)p(F|+) . p(F)

(6)

The estimated naive Bayes classifier model using the full training data set is presented in Table II. In the model, ΔTime and ΔUNR are estimated as normal distributed random variables. Their conditional prior probabilities are thus calculated as   1 (x − μx,C )2 √ exp − p(x|C) = (7) 2 2σx,C σx,C 2π

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where C represents the classification; μx,C denotes the estimated mean of x, given class C; and σx,C denotes the estimated standard error of x, given class C. The estimates have similar model interpretation as the binary logit estimates. Conditioned on the behavioral class −, the probability estimates of ΔTime (i.e., mean value of −0.163 and standard deviation of 0.066) suggest that lower expected travel time is one major incentive that motivates drivers to divert. On the other hand, the probability estimates of ΔTime conditioned on behavioral class + have a mean value that is close to zero and has a larger standard deviation, which indicates that the not divert class is almost indifferent to expected travel time. The conditional probability estimate of ΔUNR for the diverting class has a positive mean value, which indicates that drivers take risk to some extent when making en route diversion decision. When travel time unreliability increases to a high level, drivers are more likely to stay with their routine route as p(ΔUNR|+) has higher mean than p(ΔUNR|−). The estimates on discrete variables (i.e., Gender and Risk) are also consistent with the estimates of the binary logit model, suggesting that drivers that are male and/or in lower risk diversion situations are more likely to divert to the alternative routes. With these prior probability estimates, the model predicts diversion probability for each empirical observation. For instance, consider the case that a male driver is in a low-risk diversion scenario with ΔTime = −10% (i.e., alternative route improves expected travel time by 10%) and ΔUNR = −10% (i.e., alternative route improves travel time unreliability by 10%). By employing (4), the model predicts that his diversion probability is 92.53%. A within-sample tenfold cross validation is conducted for validating this model. The aggregate cross-validation accuracy is 97.7%, which is slightly better than the binary logit model. When applied to predict diversion behavior, the predictive performance could dramatically differ from the actual observation. For planning and operational application purposes, this model needs to be further calibrated, as more field data become readily available. This issue is further discussed and studied in the next section of this paper. III. C ALIBRATING THE E N ROUTE D IVERSION M ODEL The driving simulator data are often criticized to be biased [6]. Certain features of the simulation experiment may reinforce the subjects’ perception of the simulator as artificial, although realism is clearly a goal when designing the scenarios. In other words, drivers in a simulator are more likely to behave overoptimistically and be biased toward en route diversion. Second, drivers route knowledge and en route diversion propensity differ on a case-specific basis, and the transferability of the diversion model may be an issue when the planning and operational application of the model to a specific region is of interest. Therefore, to supplement the driving simulator data, real-world field observations on an often-congested commuting corridor are collected as the testing data set, in order to recalibrate the en route diversion model. Then, a Bayesian calibration is performed to transform the naive Bayes classifier scores into more accurate probability estimates on local observations.

Fig. 3. I-95/I-895 en route diversion scenarios and Bluetooth sensor locations. (a) Scenario 1: simple risk diversion. (b) Scenario 2: high-risk diversion.

A. Bluetooth Detectors and Testing Data Set As shown in Fig. 3, I-95 and I-895 are two alternative routes that pass through the tunnels under the Baltimore Harbor and eventually rejoin at east Baltimore. They split approximately 5 mi prior to Baltimore City. The dynamic message sign (DMS) device has been installed prior to the split and is often used for displaying actual travel time, delay, and diversion messages with regard to these two alternative routes [26]. A number of Bluetooth sensors are deployed along these two routes to detect the actual travel time and the en route diversion behavior [27], as shown in Fig. 3. The Bluetooth sensors are capable of providing reliable and high-quality ground truth data on highways by detecting Bluetooth signals within a 300-ft radius [27]. While enormous traffic-related ground truth information was collected during the two-week Bluetooth sampling period, two real-world en route diversion scenarios were observed and extracted for the analysis. Scenario 1 is shown in Fig. 3(a). In

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TABLE III E N ROUTE D IVERSION P ERCENTAGE B ETWEEN I-95 AND I-895

this case, the DMS device posted travel time messages about the congestion on I-95 and suggested drivers to divert to I-895. Scenario 2 is shown in Fig. 3(b), where the DMS device reported major delays on I-895 and diverted drivers to the I-95/ I-695 corridor. The date, duration, and traffic diversion rate of these two scenarios are reported in Table III. Only in certain periods of time were the diversion messages posted. During these diversion events, the diversion behavior is significant [26]. For instance, in Scenario 1, approximately 10% of I-95 users decided to switch to the I-895 corridor. A total number of 39 191 Bluetooth devices has been detected during this two-week study period. Then, the data have been processed as follows. By matching the Bluetooth machine access control ID, 1186 repeated Bluetooth devices, which have been observed during the time periods of Scenarios 1 and 2, were also recorded at least twice in Base Case (i.e., all other time periods). Thus, this data set recorded routine route information (the route decision in Base Case) and en route diversion decision about these Bluetooth device bearers. In other words, the testing data set consists of 1186 Bluetooth samples, with the routine route information and the actual en route diversion decisions during Scenarios 1 and 2 successfully extracted from the Bluetooth data. The expected travel time and the travel time reliability associated with the routine and alternative routes have been derived using the exact time information recorded by the Bluetooth detectors at the time when the devices passed by. When trying to apply the estimated en route diversion behavioral model to this Bluetooth-based field data, information on variables Gender and Risk is also needed for model prediction. Gender information cannot be observed by Bluetooth detectors and, thus, has been generated by using Monte Carlo simulation. For variable Risk, Scenario 1 represents the low-risk diversion case (i.e., Risk = 0) defined in the driving simulator experiment (Map A in Fig. 1) since the route network in Fig. 3(a) has only one simple risk diverting route. Scenario 2, wherein the downstream of the alternative route has a further bifurcation (i.e., I-695), represents the high-risk diversion case (i.e., Risk = 1). B. Bayesian Approach to Calibrating the Naive Bayes Classifier Then, the Naive Bayes model has been applied to the Bluetooth samples. The model assigned each testing example a score between 0 and 1 that can be interpreted, in principle, as a class membership probability estimate. However, it is well known that these scores are not well calibrated [28]. Here, this paper demonstrated the relatively low predicting capability of

Fig. 4. ROC curve for the naive Bayes en route diversion classifier.

the model on the field data and proposed a Bayesian calibration approach, which significantly improved the accuracy of the prediction. Various quantitative performance measures are summarized in the next subsection. In Fig. 4, we show the receiver operating characteristic (ROC) estimated for the en route diversion testing data set. An ROC curve is typically employed for evaluating data mining schemes [28]. The true positive (i.e., the predicted class and the actual class are the diverting class +) rate is plotted on the vertical axis against the false positive (i.e., the predicted class is −, but the actual class is +) rate on the horizontal axis. The perfect classification would yield a point in the upper left corner, representing 100% accuracy. The diagonal line represents a completely random guess. If the classifier is well calibrated, the ROC curve should be above the diagonal line. The figure demonstrates the effect of overoptimistic probability estimation. The model’s prediction is too optimistic, predicting very high diversion probabilities, and, thus, yields a high false positive rate. In actuality, the diversion percentage is much lower than the estimated value. As depicted in Table III, the reported average I-95/I-895 percentages suggest that roughly one out of nine vehicles decided to use the diverting route in Scenario 1 and roughly half of the vehicles decided to divert in Scenario 2. The Bayesian approach to calibrating the naive Bayes classifier is illustrated in Fig. 5. To differentiate from the training observations F, testing data points are denoted by E. The en route diversion classifier produces a prediction about an empirical data point E in the testing data set. In addition, it gives some confidence score s(E), indicating the strength of its decision that the empirical observation belongs to the not divert class. The log-odds [see (8)] of the classifier’s estimate are usually defined as s(E) for recalibrating a typical data mining classifier [26]. This measurement is useful because it scales the outputs from [0, 1] to a space [−∞, +∞], where Gaussian and other distributions are applicable. Thus s(E) = log

p(+|E) . p(−|E)

(8)

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function fits produced by these methods, versus the actual testing data. The actual testing data behaviors are illustrated as nonparametric fixed-width kernels. Quantitative performance measures of these calibration functions are offered in the next subsection. In general, the calibration results agree with the empirical observation. The average value for the naive Bayes log-odds is approximately −0.5, which is consistent with the low diversion rates empirically perceived from the testing data set. In other words, the optimistic prediction estimated by the en route diversion model is well captured and recalibrated by this Bayesian calibration process. For the diversion class (−), the test data curve plotted in Fig. 6 skews toward the left side, as the en route diversion model gives these observations higher probability estimates to divert. This is the opposite for the not divert class (+). Fig. 5. Bayesian approach to calibrating the naive Bayes classifier.

C. Performance Measures

Fig. 6. Estimated class conditional score densities versus the actual densities of the testing data set.

The confidence scores (i.e., the log-odds) and predicted diverting probabilities may not necessarily match the empirically observed probabilities. For recalibrating the classifier, a certain posterior function performing a mapping of the score s to the probability p(+|s(E)) is needed, in order to obtain better predicting accuracy. Here, this paper breaks down the problem to the two specific classes. An estimator for each of the classconditional densities (i.e., p(s|+) and p(s|−)) is produced for the diversion class and the not divert class. Then, Bayes’ rule and the class priors are used to obtain the estimate for p(+|s(E)), i.e., p(+|s) = 

p(+)p(s|+) . C={+,−} p(C) · (s|C)

(9)

For the calibration function of the class-conditional densities, a Gaussian and a generalized extreme value (GEV) are fit to each of the class-conditional densities using the usual maximum-likelihood estimates. The fits of these two functions represent a qualitative comparison between using symmetric distributions and using asymmetric distributions to approximate the class-conditional densities. Fig. 6 shows the calibration

The calibration function maps the estimated probabilities (i.e., log-odd scores) to the actually observed diversion rates. Now, the evaluation of the calibration results is of concern. There are at least two types of performance measures that have been typically used in data mining to assess the quality of the probability estimates, namely, log loss [29] and squared error [30], [31]. While actually meaning an overall improved prediction quality, a better score according to these rules, sometimes, has been loosely termed improving “calibration” [16]. The actual classification for an empirical observation E (with class C(E) ∈ {+, −}) in the testing data set is observed. Let δ denote the Kronecker delta function, which is equal to 1 if the two arguments are equal to each other and 0 otherwise. The log loss and the squared error, i.e., Error2 , are defined in (10) and (11), respectively, i.e., log loss = δ (C(E), +) log p(+|E) + δ (C(E), −) log p(−|E)

(10)

Error2 = δ (C(E), +) (1 − p(+|E))2 + δ (C(E), −) (1 − p(−|E))2 .

(11)

This paper first reports the average log loss and the mean squared error (MSE) for the performance measure of the calibration. The results are given in Table IV. Both calibration functions result in significant improvement for the model’s prediction accuracy, as the average log loss statistic has been improved from −1.9909 to −0.9750 and −0.4792, respectively. The MSE has been reduced from 0.2855 to 0.0921 and 0.0767, respectively. Overall, asymmetric distributions (for instance, GEV in this case) tend to be empirically preferable and outperform symmetric distributions in terms of prediction accuracy. After the calibration, the receiver operating characteristic curves for Gaussian and GEV functions are plotted again in Fig. 7 to visualize the enhanced calibration results. Area under the curve statistics are summarized in Table IV for a direct interpretation of the ROC curves.

XIONG AND ZHANG: BAYESIAN APPROACH TO MODELING AND CALIBRATING DRIVERS’ DIVERSION BEHAVIOR

TABLE IV R ESULTS FOR C ALIBRATING THE NAIVE BAYES M ODEL

Fig. 7.

ROC curves for the Bayesian calibration.

This section has developed and demonstrated a Bayesian approach, which can be employed to calibrate the naive Bayes probability estimates predicted by the naive Bayes en route diversion model. This approach is a consistent and theoretically sound parametric method to transform the predicted diversion probabilities to the actually observed probabilities. This approach is very flexible and, thus, can be easily transferred to other study areas to analyze diversion-related operations and management strategies, such as Advanced Traveler Information Systems (ATIS), DMS, the provision of real-time information, etc. It has the practical value that researchers and practitioners may potentially apply the en route diversion model to other regions based on recalibration using locally collected field observations. IV. C ONCLUSION The objective of this paper has been to study the en route diversion responses of drivers under real-time information. To achieve this objective, a naive Bayes model is developed for this binary en route diversion decision (i.e., switch to the diverting route or stay on the normal route). This method is believed to embed more reasonable behavioral foundation without assuming random utility maximization. In addition, the model is shown to be slightly improved when compared with the binary logit model by conducting stratified cross validation to both models. Stated preference data collected from carefully designed driving simulator scenarios have been employed in the model estimation. Due to the inherent bias from the simulator data and the model’s transferability issue, the prediction accu-

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racy of the naive Bayes model has been shown by this paper to be overoptimistic on Maryland I-95/I-895 diversion scenarios, where DMS and Bluetooth detectors are deployed. Then, this paper developed a Bayesian approach to calibrating the en route diversion model using the Bluetooth data. The first contribution of this paper lies in the originality of the model. As an effective alternative to the typical discrete choice models that assume perfect rationality and random utility maximization, the naive Bayes classifier model proposed by this paper takes a purely probabilistic perspective, which predicts the posterior diversion rates based on the class priors. However, as it stands, the probability estimation result has significant explanatory power on en route diversion behavior. In addition, the Bayesian approach used to calibrate the naive Bayes probability estimates provides a consistent and theoretically sound parametric method to transform the predicted diversion probabilities to the actually observed probabilities. This calibration approach is very flexible, and the parameters can be easily estimated on a case-specific basis, which allows researchers and practitioners to transfer the en route diversion model to other regions based on local observations. It indicates a promising application potential. This paper also remains as a first research effort that uses Bluetooth-based field data to evaluate and eventually recalibrate an en route diversion behavioral model. This actual observation is usually absent in previous research. This research successfully demonstrated its merits in helping understand the actual behavior. It bridges the gap between the real-world en route diversion situation and the simulated driving experiments and stated scenarios, which have been used in modeling travel behavior for decades. Given the ease of estimating the parameters of this model, as well as the calibration functions, the model is operational and ready to be integrated with traffic models (e.g., microscopic traffic simulators and dynamic traffic assignment models) or demand models (e.g., activity-based/microsimulation models). These can be used in various transportation operations and planning applications that require en route diversion analysis. The case study of I-95/I-895 diversion presented in this paper highlights the potential of applying this model to analyze en route diversion behavior in congested commuting corridors. In addition, it helps in evaluating DMS, ATIS, and other traffic operations strategies and in improving the aforementioned traffic/ demand models’ sensitivity to real-time traffic information and en route congestion. ACKNOWLEDGMENT Views and opinions herein do not necessarily represent the views of research sponsors. The authors are responsible for all statements in this paper. The authors would like to thank Dr. S. Gao, X. Lu, and H. Tian for designing the driving simulator experiment and providing the training data set and Dr. A. Haghani and Dr. M. Hamedi for providing the Bluetooth/ DMS data set for testing and model recalibration. The authors would also like to thank the two anonymous reviewers for their invaluable comments and suggestions for the authors to improve this paper’s quality.

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[24] A. J. Khattak, J. L. Schofer, and F. S. Koppelman, “Commuters’ enroute diversion and return decisions: Analysis and implications for Advanced Traveler Information Systems,” Transp. Res. Part A, Policy Pract., vol. 27, no. 2, pp. 101–111, Apr. 1993. [25] R. Kohavi, “A study of cross-validation and bootstrap for accuracy estimation and model selection,” in Proc. Int. Joint Conf. Artif. Intell., 1995, vol. 14, pp. 1137–1145. [26] M. Hamedi, A. Haghani, R. L. W. Fish, and A. Norouzi, “Framework for evaluation of dynamic message signs using Bluetooth traffic sensors,” Univ. Maryland, College Park, MD, USA, 2011, Working Paper. [27] A. Haghani, M. Hamedi, K. F. Sadabadi, S. Young, and P. Tarnoff, “Data collection of freeway travel time ground truth with Bluetooth sensors,” Transp. Res. Rec., vol. 2160, pp. 60–68, 2010. [28] I. H. Witten and E. Frank, Data Mining: Practical Machine Learning Tools and Techniques. San Mateo, CA, USA: Morgan Kaufmann, 2005. [29] I. J. Good, “Rational decisions,” J. R. Stat. Soc. Ser. B, Methodol., vol. 14, no. 1, pp. 107–114, 1952. [30] G. W. Brier, “Verification of forecasts expressed in terms of probability,” Monthly Weather Rev., vol. 78, no. 1, pp. 1–3, Jan. 1950. [31] M. H. DeGroot and S. E. Fienberg, “The comparison and evaluation of forecasters,” J. R. Stat. Soc. Ser. D, The Statistician, vol. 32, no. 1/2, pp. 12–22, Mar.–Jun. 1983. Chenfeng Xiong received the B.S. degree from Tsinghua University, Beijing, China, in 2009 and the M.S. degree from the University of Maryland (UMD), College Park, MD, USA, in 2011. He is currently working toward the dual M.A. degree in economics and the Ph.D. degree in the Department of Civil and Environmental Engineering at UMD. He has coauthored more than 20 peer-reviewed journal and conference papers. His main research work is on travel behavior, transportation economics, and agent-based microsimulation modeling. Mr. Xiong has been a recipient of the UMD A. James Clark Engineering School’s Distinguished Future Faculty Fellowship, the International Road Federation Best Student Essay Award, and several other fellowship honors. Lei Zhang received the B.S. degree in civil engineering from Tsinghua University, Beijing, China, the M.S. degrees in civil engineering and applied economics from the University of Minnesota, Minneapolis, MN, USA, and the Ph.D. degree in transportation engineering from the University of Minnesota in 2006. He is currently an Associate Professor with the Department of Civil and Environmental Engineering, University of Maryland, College Park, MD, USA, where he also directs the Transportation Systems Research Laboratory, which employs interdisciplinary approaches to model the interdependency between transportation, land use, and economic systems, analyzing the full impact of engineering and planning decisions to ensure efficient resource allocation and sustainable development in the broad domain of transportation. He has published more than 90 peer-reviewed journal and conference papers on topics including transportation planning, transportation economics and policy, travel behavior, advanced travel demand modeling, transportation data and survey methods, and traffic operations. He has received external funding support from various U.S. Federal and State government agencies and private foundations, totaling $5.07 million. His research interests are in the areas of transportation systems analysis; transportation and land use planning; transportation economics and policy; mathematical, statistical, and agent-based modeling; and integration of transportation operations and planning. Dr. Zhang is a member of several Transportation Research Board (TRB) Committees (Transportation Economics, Travel Behavior and Values, and Travel Survey Methods) under the U.S. National Academy of Sciences. He has recently served as the Chair of the Transportation Science and Logistics Cluster of the Institute for Operations Research and Management Sciences and the Chair of the U.S. Department of Transportation Expert Panel on Multimodal Long-Distance Passenger Travel Demand. He is the Online Editor of the Travel Survey Manual published by the TRB Travel Survey Methods Committee and the Guest Editor of a Special Issue on Sustainable Megaregion Development of the American Society of Civil Engineers Journal of Urban Planning and Development. He has been a recipient of the National Science Foundation CAREER Award, the TRB Fred Burggraf Award for excellence in transportation research by a researcher 35 years of age or younger, and the Best Paper Award at several international transportation conferences.