1. science
2. mathematics
3. statistics

Agent-Based En-Route Diversion: Dynamic Behavioral
Responses and Network Performance Represented by
Macroscopic Fundamental Diagrams
Chenfeng Xiong †, Xiqun Chen §, Xiang He k, Xi Lin ††
, Lei Zhang*
‡‡
April 6, 2015
PrePrint Accepted for Publication in Transportation Research - C
Submitted on: May 15, 2014
Revised on: December 6, 2014; April 6, 2015
Abstract
This paper focuses on modeling agents’ en-route diversion behavior under information provision. The behavior model is estimated based on na¨ıve Bayes rules
and re-calibrated using a Bayesian approach. Stated-preference driving simulator
data is employed for model estimation. Bluetooth-based field data is employed
for re-calibration. Then the behavior model is integrated with a simulation-based
dynamic traffic assignment model. A traffic incident scenario along with variable
message signs (VMS) is designed and analyzed under the context of a real-world
large-scale transportation network to demonstrate the integrated model and the
impact of drivers’ dynamic en-route diversion behavior on network performance.
Macroscopic Fundamental Diagram (MFD) is employed as a measurement to represent traffic dynamics. This research has quantitatively evaluated the impact of
information provision and en-route diversion in a VMS case study. It proposes and
demonstrates an original, complete, behaviorally sound, and cost-effective modeling
framework for potential analyses and evaluations related to advanced traffic information system (ATIS) and real-time operational applications.
En-route diversion, agent-based simulation, dynamic traffic assignment, Macroscopic
Fundamental Diagram
†
Department of Civil and Environmental Engineering, University of Maryland, College Park, MD
20742. [email protected]
§
College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, China 310058, [email protected]
k
International Aviation Division, Institute of Air Transport, China Academy of Civil Aviation Science
and Technology, [email protected]
††
Department of Civil Engineering, Tsinghua University, Beijing, China 100084. [email protected]
‡‡
Associate Professor, * Corresponding Author. [email protected], phone: +1(301)405-2881
Department of Civil and Environmental Engineering, 1173 Glenn Martin Hall, University of Maryland,
College Park, MD 20742
1
1
Introduction
En-route diversion is a significant travel behavior that occurs frequently in every-day
travel. Recurrent congestion, non-recurrent incidents, work zones, etc. are likely to
trigger drivers to change route. Drivers usually make this decision based on their own
spatial/temporal knowledge. They identify alternative route(s), extract and compare the
likely travel conditions on both the downstream links and the alternative route(s) using
their knowledge and subjective beliefs formed from prior experiences. More recently, information provision alters this situation a great deal. With technical improvement, Advanced
Traffic Information System (ATIS), smart-phone applications, and GPS devices with enroute information become readily available in daily travels. Drivers can easily acquire
pre-trip and/or en-route information when any diversion decisions are to be made. For
instance, when traffic incidents take place in the downstream roadway segments, variable
message signs (VMS) can convey real-time traffic information and encourage diversion.
This arouses new research questions that need to be better addressed:
• to what extent do travelers comply to en-route information?
• how do we effectively evaluate information provision schemes and measure the network performance changes?
The authors are thus motivated to develop a useful analysis tool to accurately model enroute diversion, predict behavioral responses, and quantify the impact on transportation
network. With enhanced computational power and the exploration of new paradigms,
transportation modelers’ ambition to go “microscopic” and “dynamic” has never been
greater. This paper proposes a comprehensive analysis tool which integrates a calibrated
agent-based en-route diversion model and a simulation-based dynamic traffic assignment
(DTA) model. In order to answer the aforementioned first research question, this paper
focuses on microsimulating agent behavior and gauging the model parameters based on
calibration and solid empirical evidence. In order to answer the second research question,
the behavior model is dynamically linked with a simulation-based DTA model. This integration is completely agent-based and produces time-space trajectories for each simulated
agent. Moreover, it estimates time-dependent network conditions for quantifying the network performance. In order to demonstrate the applicability of the proposed model, a
case study using a subset network for Washington/Baltimore region is presented in this
paper.
The remainder of the paper is organized as follows. Section 2 presents a literature
review on behavior modeling and network performance measures. The integrated modeling
framework of the agent-based model and operational applications is proposed in Section
3. Section 4 introduces the behavior model and calibration method. The network model
and various performance measures are presented in Section 5. The integration and results
are interpreted in Section 6. Conclusions and discussions on future research directions are
offered at the end of the paper.
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2
2.1
Literature Review
Behavior modeling
Drivers’ en-route diversion behavior has been traditionally modeled by the econometric
theory of random utility maximization. In 1990s, a great deal of research efforts have
been spent on this line of research. Bivariate and multinomial probit models have been
used to model joint pre-trip departure time and en-route diversion behavior in response
to real-time information (Khattak et al., 1995; Mahmassani and Liu, 1999). Logit models were also developed to capture the effect of information provision when drivers were
en-route (Abdel-Aty et al., 1997). Stated preference and revealed preference data were
typically applied to estimate these types of models. More recently, mixed logit, which can
incorporate more heterogeneous taste variations, has been broadly employed in modeling
diversion behavior (Ben-Elia and Shiftan, 2010; Gan and Ye, 2014). Gao et al. (2010)
developed non-linear utility functions based on cumulative prospect theory (CPT) to consider the flexibility towards risk when real-time traffic information is provided. In these
recent advances, information on travel time and travel time reliability on the original route
and the diverting route plays a crucial role in influencing drivers behavior. Ben-Elia et al.
(2013) then analyzed how different information accuracy would influence behavior.
One obvious limitation for random utility maximization models is the assumed perfect
rationality. In these models, it is assumed that drivers know the probabilistic distribution
of link travel time and can make a rational decision (under risk in some cases). This
limitation is especially evident when modeling en-route diversion behavior, as the en-route
diversion is a decision triggered by impulsion and governed by uncertainty. Rather than
acquiring the real-time information, processing the information, comparing the original
route with the diverting route, and reaching a decision, drivers’ knowledge is more likely
to be biased and their en-route diversion is more likely to be governed by certain heuristics
or rules (Paz and Peeta, 2009). Rule-based computational process models were explored
by researchers to look at various behaviors including activity-scheduling (Ettema et al.,
2005) and mode choice (Janssens et al., 2006). Bayes’ Rule is believed to be among
the most prominent behavioral rules to represent decision-making under uncertainty (ElGamal and Grether, 1995). In the field of travel behavior modeling, Bayes’ Rule has been
employed to update model parameters (e.g. Amador et al., 2005; Janssens et al., 2006;
Xiong et al., 2015). Travelers’ day-to-day perception evolution has been modeled using
Bayes updating (e.g. Jha et al., 1998; Xiong and Zhang, 2013b). And there are studies
using Bayes’ Rule to infer drivers’ behavior and innate emotional status (e.g. Malta et al.,
2011). The application of rule-based approach in en-route diversion modeling is coarse
except one research to model and recalibrate the if-then diversion rules based on fuzzy
logics and weight factors (Paz and Peeta, 2009). The behavioral foundation and flexibility
of the Bayesian method can be quite substantial for modeling en-route diversion before any
pertinent new theories are devised to accommodate those apparent violations of perfect
rationality.
From a practical point of view, another limitation of the existing behavior models
is that they are often not well-calibrated due to data limitation and other issues. The
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inherent bias of the stated preference data and driving simulator data have long been
argued as a major deficiency of the models (Bonsall and Parry, 1991). The simulation
experiment may reinforce the subject’s perception of the simulator as artificial. In practice,
drivers’ route knowledge and en-route diversion propensity differ on a case-specific basis.
For instance, in some cases, drivers may have strong preference to stay on the original
route due to inertia. And if applying the model estimated using laboratory-collected data
to analyze the diversion, one may get biased results. The information-sensitive behavioral
models may be context dependent and the transferability of the diversion model may be an
issue when the planning and operational applications of the model to a specific diversion
scenario are of interest. Koutsopoulos et al. (1994) further asserted that driving simulators
for en-route diversion analysis could be more useful if revealed preference data collected
from “actual en-route route choice behavior” and an appropriated designed calibration
became available.
2.2
Operations and network performance measures
Limited number of studies tried to consider en-route diversion and information provision
in operational applications. Xu et al. (2011) developed a probit model by employing realworld loop detector data and vehicle plate reader data to analyze the impact of VMS.
Their study emphasized the significant difference between field observations and stated
preference survey responses. However, quantitative evaluation of the impact on networklevel traffic conditions was lacking. Bustillos et al. (2011) embedded en-route diversion into
a real-world regional network to evaluate the impact of incident scenarios. The en-route
decision was modeled using a presumed delay tolerance threshold. The behavioral foundation of the model needs further empirical justification. Tsubota et al. (2013) explored
the impact of en-route behavior changes under information provision by employing the
Macroscopic Fundamental Diagram (MFD) as a measurement. Assumed network using
microscopic traffic simulation in AIMSUN was employed to simulate different diversion
ratios. These pioneer studies all seek linkages between en-route diversion and operational
applications. The use of micro/mesoscopic simulators and DTA to represent traffic is helpful because the temporal/spatial variations in dynamic traffic is critical to network performance and driver behaviors. However, a complete framework that integrates en-route
diversion, model calibration, network models and simulation, and performance measures
is yet to be developed and is in imperative needs.
Fully taking the advantages of emerging DTA and simulation techniques, one can
obtain quantitative measures to evaluate non-recurrent situations and diversion scenarios. Among various performance measures, MFD is recently widely used to evaluate the
macroscopic traffic state dynamics for a two-dimensional urban road networks or freeway
networks and draws our interest. The study of network-wide traffic flow relationships
can be tracked back to 1960s (Smeed, 1967). Mahmassani et al. (1987, 1984) further investigated the properties of MFD using micro-simulation and real-world data. Recently,
numerous and empirical and micro-simulation studies in the literature have observed the
existence of a reproducible and well-defined relation between network average flow and
density for urban and freeway networks (Daganzo, 2007; Geroliminis and Daganzo, 2008;
4
Geroliminis and Sun, 2011b). These studies link the details in individual links with the
description of the congestion level of networks and its dynamics.
Geroliminis and Daganzo (2008) observed a linear relation between the total outflows
(trip completion rates) and exit flows and network weighted average flow rates using a
field experiment in downtown Yokohama. Keyvan-Ekbatani et al. (2012) exploited the
relationship of the total traveled distance per hour and the total time spent per hour
obtained from emulated loop measurements of all vehicles in an urban network. Saberi
and Mahmassani (2013a) explored the effects of inhomogeneity of traffic distribution on
the network between average network flow, average network density, and the standard
deviation of the network density. The path-dependent hysteresis (i.e. a loop with higher
flows as the density increases and lower flows as the density decreases) in the freeway
networks was revealed using loop detector data. MFD could be further formulated to solve
the optimal perimeter control problem for urban networks (Aboudolas and Geroliminis,
2013; Daganzo, 2007; Geroliminis et al., 2013). To obtain a small variance of link densities
within a sub-network which increases the network flow for the same average density based
on the spatial features of congestion, Ji and Geroliminis (2012) designed a partitioning
mechanism for a large transportation network so that each sub-network had a well-defined
MFD.
Geroliminis and Sun (2011a) showed that the MFD of freeway networks was hysteretic
and path dependent at the aggregate level. The reasons of non-existence of well-defined
MFDs for freeway networks were identified as the spatial heterogeneity in vehicle density
in the onset and offset of the peak period and the synchronized occurrence of transient
periods and capacity drop phenomena in the offset of congestion. Saberi and Mahmassani
(2013b) characterized hysteresis and capacity drop phenomena, and quantified the size of
hysteresis loops in freeway networks using loop detector data from real networks.
According to the existing MFD studies, we note that the MFD provides a time-varying
relationship of space-mean flow, density and speed of an entire network. It can be used to
predict the capability of a roadway system, or its behavior when applying inflow regulation
or capacity drop due to incidents or infrastructure failures. The maximum capacity (i.e.
maximum throughput) of the network can be retrieved from the MFD. Compared to other
performance measures such as network-wide averages (e.g. vehicle hours traveled, average
delay, etc.) and congestion maps, MFD can supplement measures of the characteristics of
the network evolution, e.g. how much network capacity is reduced. Another merit of MFD
in network performance is that it can evaluate the overall performance of multiple corridors
by calculating the cumulative statistics of their roadway segments. While this is a relatively
less exploited area, some seminal work studying MFD characteristics under the scheme
of route choice has been observed (Haddad et al., 2013; Leclercq and Geroliminis, 2013).
MFDs under different routing assumptions were analyzed in Leclercq and Geroliminis
(2013). MFD values were integrated in a route choice model under the framework of
cooperative traffic control (Haddad et al., 2013). As a useful measurement that captures
network-level dynamics, MFDs are assessed in this paper under information provision
and en-route diversion. This provides a promising extension to the existing literature on
dynamic routing and operations/control and can be complementary to the MFD-related
studies on route choice.
5
3
Agent-Based Simulation Model
The framework of modeling agents’ en-route diversion behavior under information provision is illustrated in Fig. 1.
Traffic Simulator
Stimuli at time
period t
Behavioral
data
Field
observations
Traffic Simulator
Travel conditions
time period t
ATIS at t+1
Agents’ en-route
diversion model
Stimuli at time
period t+1
Travel conditions
time period t+1
ATIS at t+2
Agents’ en-route
diversion model
No
Divert
No
Divert
New route at time
period t+1
New route at time
period t+2
Figure 1: Structure of agent-based en-route diversion model
Routinely, travelers form a relatively stable travel pattern and route choice, especially
for their daily commute travels. A user equilibrium condition well represents this situation. When en-route traffic conditions change at time period t due to, for instance,
recurrent/non-recurrent congestion, incidents, and work zones, stimuli for the agents to
make en-route behavior changes, as well as the stimuli for operations strategy makers to
encourage diversion, becomes more significant. Various ATIS strategies can be employed
here to provide real-time traffic information. The travel conditions at time t for both the
congested original route and the diverting route will be conveyed to agents during the
period t + 1. While the response to ATIS can be modeled by a myriad of methods, we
employ an innovative Bayesian approach to empirically model and re-calibrate the agents’
en-route diversion by using behavior data collected from the driving simulator and field
observations collected by Bluetooth sensors deployed at two real-world diversion scenarios.
This agent-based model predicts the diversion decision for each individual simulated in
the model. Then the agent behavior is aggregated and fed back into the network traffic
simulator to obtain the traffic conditions for the next time period. The use of simulation modeling allows examination of the agents’ en-route diversion under various ATIS
scenarios.
4
Agents’ En-Route Diversion Behavior
The agent-based model includes these two components: (1) the Na¨ıve Bayes model is
employed to represent behavioral rules; (2) The Bayesian calibration is employed to recalibrate the model based on local observations. This paper aims at studying these two
6
tools’ applicability in the context of a real-world agent-based simulation and demonstrating
the superior transferability brought in by the Bayesian calibration. These two tools are
explained in this section.
4.1
Na¨ıve Bayes Model
Agents’ behavioral rules are represented by the Na¨ıve Bayes model developed in Xiong
and Zhang (2013a). This method is based on the more general Bayes’ Rule and data
mining techniques, which is believed to embed more reasonable behavioral foundation
without assuming random utility maximization. The study employs stated preference
data collected from carefully designed driving simulator scenarios. In the experiment,
subjects were required to drive slowly at the beginning of each scenario to observe a
route map of the entire network. A number of diverting points were built in the network,
where subjects were asked to make diversion choices. During the experiment, subjects at
each diverting point were shown different travel times and time ranges for their routine
route and diverting route(s) according to simulated traffic conditions. Three scenarios
were assigned to each driver and each scenario was repeated six times to make sure the
choices were stable. Drivers’ diversion decision has been denoted as two agent classes,
being the divert class and the not-divert class. A tuple of stochastic attributes (F1 , F2 ,
· · · , Fn ) affects the classification variable denoted by C, including travel time (Time) and
travel time unreliability (UNR) of the normal route and the diverting route, travelers’
socio-demographic information (e.g. Gender ), and diverting risk (Risk ). UNR is specified
as the 95% confidence interval of the travel time duration. Risk is a dummy variable
reflecting the complexity (or risk) of the diverting route. If the diverting route involves
bifurcation and possible huge delay, even if theoretically the drivers can make the correct
en-route decision to avoid the delay penalty with the guidance of the real-time information
at the VMS, drivers are less likely to divert. Diverting to this type of routes is considered
as a diversion of high risk.
For each training observation F, the na¨ıve Bayesian 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 not-divert class (denoted by C0 , while divert class is denoted by C1 ) is:
p(C0 )p(F|C0 )
(1)
p(F)
For a training observation, na¨ıve Bayes classifier assumes conditional independence of
every other attribute given the value of the classification variable. Equation (2) shows the
functional form of na¨ıve Bayes classifier, denoted by fnb (F). The empirical observation is
classified as C0 if and only if fnb (F) ≥ 1.
p(C0 |F) =
n
fnb (F) =
p(C0 )p(F|C0 )
p(C0 ) Y p(Fi |C0 )
=
p(C1 )p(F|C1 )
p(C1 ) i=1 p(Fi |C1 )
(2)
The estimated na¨ıve Bayes model using the stated preference data as the full training
dataset is revisited here in Table 1. These conditional priors, p(Fi |C0 ) and p(Fi |C0 ), can
7
be used to calculate the classifier (Equation 2) and thus constitute the agent behavioral
rules.
Table 1: En-Route Diversion Model’s Conditional Prior Probability Estimation Results
Classification:
Not Divert (C0 )
Variables
Conditional
Priors
Priors
Gender is male
Gender is female
low Risk
high Risk
∆Time
∆UNR
p(C0 )
p(male|C0 )
p(female|C0 )
p(low|C0 )
p(high|C0 )
p(∆Time|C0 )
p(∆UNR|C0 )
Divert (C1 )
Mean
(Std. Dev.)
0.53
0.403
0.597
0.504
0.496
0.022 (0.262)
0.452 (0.242)
Conditional
Priors
p(C1 )
p(male|C1 )
p(female|C1 )
p(low|C1 )
p(high|C1 )
p(∆Time|C1 )
p(∆UNR|C1 )
Mean
(Std. Dev.)
0.47
0.532
0.468
0.548
0.452
-0.163 (0.066)
0.304 (0.270)
In the model, ∆ denotes percentage changes of the attributes of alternative route from
those of the routine route. The high class prior for divert class (almost as high as the class
prior for not divert class) indicates that the likelihood of diversion from the routine route
has been positively affected by certain factors, e.g. the provision of travel time information.
Conditioned on the divert class, the probability estimates of ∆Time suggests that lower
expected travel time is one major incentive that shifts individuals off their routine routes.
On the other hand, the probability estimates of ∆Time conditioned on not-divert class has
mean value that is close to zero and has a relatively larger standard deviation. It indicates
that not-divert class is almost indifferent to expected travel time. Agents are generally risk
averse, given that the estimated p(∆UNR|C0 ) is positive and greater than p(∆UNR|C1 ).
Meanwhile, individuals take risk to some extent and have greater sensitivity to travel time
variability since p(∆UNR|C1 ) also has positive mean. Similar risk-seeking agent behavior
has been found by Ben-Elia and Shiftan (2010). The estimates on discrete variables (i.e.
Gender and Risk ) suggest that male drivers and drivers in lower-risk diversion situations
are more likely to divert. These empirical findings conform to previous research (Khattak
et al., 1993; Mannering, 1989).
4.2
Behavioral Model Calibration
From the estimated class priors (0.53 for C0 v.s. 0.47 for C1 ), one can draw the conclusion
that individuals (in the driving simulator, of course) are almost indifferent between their
routine route and the alternative one, given other conditions equal. However, this may
be greatly different in real-world cases (Koutsopoulos et al., 1994). Drivers may react
differently when actually provided with real-time information. Drivers may prefer their
routines due to the inertia effect. Therefore, a recalibration process is necessary before
applying the agent-based model. A separate field observation data source collected from
Bluetooth detectors deployed in a real-world VMS scenario in Maryland is employed here
8
as calibration evidence. Bluetooth detectors were deployed to penetrate vehicles in routine
traffic flow and re-routing flow during normal traffic conditions as well as the periods
whence an incident occurred. If an incident was identified, VMS in the upstream was
functioning and displaying dynamic information about travel times and travel time ranges
for the routine route and the alternative route. The Bluetooth detectors actively collected
data for two weeks (in April 2011) and thus could penetrate sufficient vehicles that were
repeatedly using the routes. For instance, if a subject who routinely used I-95 (see Fig. 3
for the location of I-95) stayed in I-95 during VMS period, her/his decision was recorded
as “not divert”. Otherwise, her/his decision was recorded as “divert”. Let us denote the
vector of these Bluetooth data points as E.
The recalibration process employed here was developed by Xiong and Zhang (2013a). It
offers a mapping from the real-world behavioral data to a set of more accurate behavioral
rules. By directly applying the uncalibrated na¨ıve Bayes model to E, one can predict
divert probabilities ranging on [0, 1]. If we translate the probabilities using log-odds:
s(E) = log(p(C0 |E)) − log(p(C1 |E)), this measurement can range on a space [−∞, +∞].
Thus, we can model the probability density function (PDF) of the prediction score s(E)
(conditioned on the actually observed class) as a function of the log-odd score. This PDF
p(s|C = {C0 , C1 }) is then applied as the recalibration function and plugged into Equation
(3) using Bayes’ Rule and the class priors.
p(C0 )p(s|C0 )
C={C0 ,C1 } p(C) · p(s|C)
p(C0 |s) = P
(3)
More details of this Bayesian calibration method is given in Xiong and Zhang (2013a).
Applying this method to analyze the actual observations E, we can correct the dramatically
higher diversion propensity predicted by the uncalibrated model and match the predictions
to the low diversion rate. In Fig. 2a we show the reliability diagram estimated for the
en-route diversion calibration dataset. The x-axis shows the predicted probability of the
na¨ıve Bayesian classifier for the divert class. The y-axis shows the empirically observed
relative frequency of the divert class. If the classifier is well-calibrated, all points should
coincide with the diagonal line, which indicates that the predicted diverting probability
are equal to the empirical probability. The model’s prediction is too optimistic, predicting
diversion probabilities that are too close to 1. In actuality, the diversion percentage is
much lower than the estimated value. After performing the calibration, the reliability
diagram is illustrated in Fig. 2b. The Bayesian calibration successfully readjusts the
model prediction to match the low diversion rate observed by the Bluetooth detectors. As
shown in Fig. 2b, most of the predicted probabilities are in line with the observed relative
frequencies.
This section has revisited the Na¨ıve Bayes model of en-route diversion and its Bayesian
calibration approach. These tools are then applied to predict agent behavior based on
empirical observations collected from real-world Bluetooth sensors. The behavioral model
departs from the utility-based models in the way that it employs Na¨ıve Bayes rules to
predict behavior. The calibration approach is a practical and powerful tool to take the
advantage of any types of real-world diversion data. Data sources that are as aggregate
as diversion rates or as microscopic as individual-level Bluetooth/GPS/Smartphone data
9
1
0.8
0.8
Observed Relative Frequencies
Observed Relative Frequencies
1
0.6
0.4
0.2
0
0.6
0.4
0.2
0
0
0.2
0.4
0.6
Predicted Probabilities
0.8
1
0
(a) Reliability diagram for the uncalibrated
Na¨ıve Bayes en-route diversion model
0.2
0.4
0.6
Predicted Probabilities
0.8
1
(b) Reliability diagram for the calibrated
Na¨ıve Bayes en-route diversion model
Figure 2: Reliability diagrams for the behavioral model calibration
can provide useful prior information for this approach to produce more accurate posterior
probabilities. This approach is a consistent and theoretically sound parametric method to
model agents’ en-route diversion behavior. It is flexible and thus can be easily transferred
to other study areas to analyze diversion-related operations and management strategies,
such as ATIS, VMS, 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. This
unique advantage is demonstrated in this paper through the construction of an integrated
agent-based simulation model to analyze scenarios on I-95 corridor. The traffic simulator,
network performance measures, and the modeling outcomes are presented in the following
sections.
5
5.1
Simulation Model and Network Performance
Simulation study description
A case study is conducted on an extraction of the Metropolitan Washington Council of
Government (MWCOG) network. A mesoscopic traffic simulation model for the study
area is developed (Fig. 3) using DynusT package (DYNamic Urban Systems in Transportation, Chiu et al., 2010). The network includes around 2000 links, 500 nodes, over
300 signalized intersections, 201 TAZs, three major freeway corridors, and one tolling
highway. As one of the latest DTA analysis tool, DynusT is chosen as the simulator. It
simulates individual vehicle’s movement based on a mesoscopic traffic simulation model,
Anisotropic Mesoscopic Simulation (AMS), which reveals its agent-based nature.
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Figure 3: Mesoscopic traffic simulation network
Three scenarios are simulated in this analysis:
• The basecase scenario represents the original demand pattern and dynamic user
equilibrium (DUE) condition, which is calibrated using MWCOG demand model’s
extended morning peak (5:00 a.m. to 10:00 a.m.) origin-destination (OD) demand
as the base matrices. The total number of agents during the 5 hours of simulation is
625,389. Real-world signal timing plans, probe-vehicle collected corridor travel time
data, and over 60 traffic count stations are employed as calibration evidence. The
calibration is documented in Zhang et al. (2012) and Xiong et al. (2015).
• The incident scenario assumes an incident occurring at 5:30 a.m. and last until
6:30 a.m. on a major commuting corridor, I-95 South Bound (SB). Incident location
is marked by the triangle on I-95 in Fig. 3. A closure of two lanes on the affected
link is assumed in the incident scenario. Real-time information is not provided to
agents (agents take their habitual routes identified in the basecase).
• The diversion scenario. Four VMS devices (denoted by the four blue rectangles
along the freeway corridor in Fig. 3) deployed on the upstream links are assumed to
be responsive to the incident. Incident message, travel time and travel time range
on I-95, and the corresponding travel condition on the alternative corridor (US-29)
are displayed to agents. Rule-based agents learn the prior information from the
DUE iterations in the basecase scenario and make en-route decisions according to
11
the na¨ıve Bayes rules. The VMS devices are assumed to be active between 5:30 a.m.
and 7:30 a.m. (one hour after the clearance of the incident). Real-time information
is updated during each predefined time period (10 minutes in this case study).
An example VMS plate is illustrated in Fig 4. During each time period when the VMS
devices are active, the travel conditions of the previous time period on the routine route
and the alternative route are provided to agents for them to make an en-route diversion
decision.
INCIDENT AT EXIT 35
TIME TO I-495 WEST
I-95 SOUTH
15-18 MIN
US-29
13-14 MIN
Figure 4: An example of traffic information displayed on VMS plates
In these simulation scenarios, real-time information is updated in each time period
based on time-varying link travel time retrieved from the AMS model (Chiu et al., 2010).
AMS is a vehicle-based mesoscopic traffic simulation approach that explicitly considers the
anisotropic property of traffic flow into the vehicle state updated at each simulation period.
In Section 5, the incident scenario without real-time information provision and the incident
scenario considering en-route diversion under ATIS are quantitatively compared using
various performance measures. In particular, MFD, defined in Section 5.2, is employed to
investigate the before-and-after performance of the I-95 SB corridor.
5.2
Network performance: macroscopic fundamental diagram
(MFD)
MFD can potentially be an intuitive and quantitative performance measure for analyzing
the three scenarios. To implement the macroscopic traffic analysis on the corridor level, we
may investigate the relationship of the accumulation of vehicles in a network with the exit
outflows, and the equivalent relationship of the network-wide weighted average density
and flow rate.
We have:
X
Nt =
ka,t la λa
(4)
a∈A
where Nt is the time varying number of vehicles in a network denoted by A, each individual
link is a ∈ A; ka,t denotes the traffic density of link a at time t; la and λa denote the length
and the number of lanes of link a.
12
Nt
=
Kt =
L
P
a∈A ka,t la λa
P
a∈A la λa
(5)
where Kt is the space mean density (vehicle per mile per lane) at time t, L is the total
length (lane-miles) of the network. Analogously, we have Eq. (7).
P
a∈A qa,t la λa
Qt = P
(6)
a∈A la λa
where Qt is the space mean flow rate (vehicle per hour per lane) of the network, qa,t is
the traffic flow rate of link a at time t. Both empirical observations (Geroliminis and
Daganzo, 2008) and dynamic traffic assignment experiments on a real large-scale urban
network (Mahmassani et al., 2013) concluded that Qt was robust linear with the trip
completion rate that was the sum of finished and exiting trips for the whole network. The
network-wide weighted average speed is given by:
P
a∈A va,t ka,t la λa
(7)
Vt = P
a∈A ka,t la λa
where the weighted quantity is the number of vehicles on an arbitrary link a at time t.
According to the traffic variables relationship in the MFD, as well as Equations (4–7),
the network average speed is estimated by:
Qt
(8)
Kt
The spatial standard deviation of densities in the network and their coefficient of variation (CV) are formulated using Eq. (9a) and (9b). CV represents the spatial distribution
of link densities, which can be employed as a reliability measure and infers network flow.
sP
2
a∈A la λa (ka,t − Kt )
P
σt =
(9a)
a∈A la λa
sP
ka,t
2
σt
a∈A la λa ( Kt − 1)
P
CVt =
=
(9b)
Kt
a∈A la λa
Vt =
These measures together form four different types of MFD and will be computed using
simulated agents in Section 5. They are: (1) weighted density – weighted average flow;
(2) vehicle accumulation – vehicle outputs; (3) weighted density – weighted average speed;
(4) weighted density – CV of link densities.
6
Integrated Agent-Based Simulation and Results
In this section, the integrated agent-based simulation is performed. We first demonstrate
the computational performance of the integrated model. Fig. 5 illustrates the run time
under different configurations in terms of (1) total number of simulated agents (from 20%
13
of the original demand to 200%); (2) time intervals to update VMS information (from
5 minutes to 60 minutes). On a desktop with Intel i-7 2.5 GHz CPU and 8 GB RAM,
five replications are simulated to ensure the stability of the results. The simulation data
with their mean and error range are plotted. Although simulation runs with increased
demand and fine-grained time intervals inevitably require more run time, the computational efficiency remains in a reasonable range, which clearly shows the applicability of the
model.
40
38.5
Mean time (µ ± σ)
Growth trend
Simulation data
Mean time (µ ± σ)
Growth trend
Simulation data
35
Computational time (min.)
Computational time (min.)
38
37.5
37
30
25
20
15
36.5
10
36
5
0
2
4
6
8
# of simulated agents
10
12
14
0
10
20
30
40
50
60
70
Time interval to update VMS (min.)
5
x 10
(a) Computational time for simulations with
different number of simulated agents
(b) Computational time for simulations with
different VMS time intervals
Figure 5: Computational times of different configurations of the agent-based model
6.1
Agent-based en-route diversion responses
In this section, the empirically estimated and calibrated en-route diversion model is integrated with DynusT network model and MFD post-processing analysis. Agents’ diversion
behavior response to the assumed incident and VMS scenario is analyzed and simulated.
In order to reflect the dynamic nature of this operational applications while retaining the
simulation in a manageable computational time, the time period length is set to be 10
minutes. Ten replications for each scenario are simulated in order to verify the stability of
the results. This setup can be fine-grained whence there is an enhanced computational capability. Agent decisions are dynamically determined and provided to the DynusT model
wherein the diversion scenario is simulated. Fig. 6 illustrates the agent-based simulation
results.
Fig. 6 illustrates, by VMS locations, the integration results of the time-varying travel
time (the bar charts) and travel time range (error bars) on the normal route and the
diverting route, as well as the agents’ aggregated diversion percentage for each time period
and each VMS. The darker curve represents the percentage of upstream I-95 users who
have taken the off-ramps at each VMS location during basecase scenario, while the lighter
curve represents that diversion percentage during diversion scenario. The VMS devices
are active between 5:30 a.m. and 7:30 a.m. to provide real-time information. The results
14
indicate that the integrated model well captures the agents’ behavior response dynamically
and at different upstream diverting points. At the very beginning of the incident (around
5:30 a.m. to 6 a.m.), the traffic condition of the corridor is close to free-flow condition
and the incident does not cause too much congestion. The diversion response is minor.
During the peak-of-the-peak (starting from 6:30 a.m.), severe congestion can be observed
and more drivers decide to divert. For instance, nearly 15% of agents divert at VMS 1
between 6:30 a.m. and 7 a.m. in response to the higher congestion on the normal route
(I-95 SB).
6:30 AM
7 AM
7:30 AM
25
20
15
15
10
10
5
0
5:30 AM
6 AM
6:30 AM
7 AM
25
6:30 AM
15
10
10
5
5
5
0
0
0
5:30 AM
6 AM
7 AM
7:30 AM
7:30 AM
25
15
15
10
10
5
0
7 AM
25
6:30 AM
7 AM
7:30 AM
30
Normal Route Travel Time
Diverting Route Travel Time
Basecase Diversion Percentage
Divert Diversion Percentage
25
20
20
15
15
10
10
5
5
5
0
0
7:30 AM
Travel Time (min)
20
6 AM
30
Diversion Percentage (%)
Travel Time (min)
5:30 AM
20
6:30 AM
7 AM
(b) Agent diversion at VMS 2
30
6 AM
6:30 AM
Time
Normal Route Travel Time
Diverting Route Travel Time
Basecase Diversion Percentage
Divert Diversion Percentage
5:30 AM
25
15
7:30 AM
30
25
7:30 AM
20
(a) Agent diversion at VMS 1 (the northmost)
6 AM
7 AM
30
Time
5:30 AM
6:30 AM
Normal Route Travel Time
Diverting Route Travel Time
Basecase Diversion Percentage
Divert Diversion Percentage
20
Travel Time (min)
20
6 AM
30
Diversion Percentage (%)
Travel Time (min)
25
5:30 AM
30
Diversion Percentage (%)
6 AM
Normal Route Travel Time
Diverting Route Travel Time
Basecase Diversion Percentage
Divert Diversion Percentage
0
5:30 AM
Time
Diversion Percentage (%)
5:30 AM
30
6 AM
6:30 AM
7 AM
7:30 AM
Time
(c) Agent diversion at VMS 3
(d) Agent diversion at VMS 4
Figure 6: Travel time and travel time variance for normal route and diverting route and
the agents’ diversion percentages for the Basecase and the Divert Scenarios
Overall, the model predicted diversion percentages are moderate (the highest diversion
percentage is lower than 15%; the average diversion percentage is 5.2%) and are consistent
15
with Bluetooth observations. And the percentages are highly fluctuating, since the road
traffic evolves dynamically and a higher diversion percentage during a certain period is
likely to improve the traffic condition on the route and thereby results in a relatively lower
diversion percentage for the next time period. It is worth noting that the travel time
reliability also plays an important role in en-route diversion, since VMS typically displays
travel time range. If the diverting route’s travel time is more uncertain, risk-averse agents
are less likely to divert and the integrated model yields a lower diversion percentage.
6.2
Network performance results
On the network level, the proposed model predicts that over all simulated agents, the
average travel time per trip increases from 16.31 minutes in the basecase scenario to 17.83
minutes (8.1% increase) in the incident scenario. The provision of real-time information
and en-route diversion can effectively mitigate the network-wide average travel time to
17.07 minutes. Simulation results for the three scenarios, including total vehicle hours
traveled (VHT), vehicle miles traveled (VMT), average travel time/delay, and average
travel distance, can be found in Table 2. Spatial/temporal performance measures for
the I-95/US-29 corridor, including congestion maps for the directly affected I-95 SB and
macroscopic fundamental diagrams for the corridor sub-network, are presented in the
following subsections.
Table 2: Simulation Results for the Three Scenarios
Scenario
Demand
(vehicle)
VHT
(hour)
Avg. Travel Time
(min./veh.)
Avg. Delay
(min./veh.)
VMT
(mile)
Avg. Trip Distance
(mile/veh.)
Basecase
Incident
Diversion
625,389
625,389
625,389
169,983
185,864
177,889
16.31
17.83
17.07
3.70
4.59
3.85
4,605,512
4,466,686
4,576,050
7.36
7.14
7.32
6.2.1
Congestion Maps
Fig. 7 shows the congestion maps using average speeds across all lanes of I-95 SB for each
1-minute interval in the time-distance plot. The warmer shades indicate lower speeds and
more congested traffic flows, while the cooler shades represent higher speeds and free-flow
states.
Fig. 7a shows the southbound traffic flow evolutions on a 13.6-mile highway segment
wherein the four VMS are implemented (see the detailed layout in Fig. 3). The period
analyzed is the morning peak hours under the baseline scenario. The segment of mileposts
8.0 mile through 9.5 mile formed a traffic bottleneck that triggered a heavy congestion
at around 7 a.m.. The traffic jam propagated upstream to the location of 5.0 mile. Till
9:15 a.m., the downstream queues began to dissipate and subsequently regained the free
flow speed. It is worthwhile to point out that a local congestion state was formed at
the location of 7.5 mile and continued to the end the simulation time. This was caused
16
by an increasing on-ramp demands merging into the I-95 SB mainline. Fig. 7b shows
the mainline heavy congestion caused by the downstream incident that lasted from 5:30
a.m. through 8:30 a.m.. In the scenario without any en-route information provision, the
incident occurring in the 8.0–9.5-mile bottleneck has reduced the highway capacity and
induced a spill-over congestion propagating to the most upstream of the freeway segment.
Distinguishing with the baseline scenario, the incident induced jam queue propagated
backwards in a faster speed indicated by the larger slope during 6 a.m. through 6:45
a.m. from the mileposts 8.0 mile to 3.5 mile. It was also found that the speeds suddenly
dropped from the approximate free-flow speed of 55 mph to the oscillating speed between
5 mph and 20 mph at the beginning of the incident occurrence. Though the congestion
dissipated at around 9:30 a.m. in the bottleneck, a two-mile length of congested queue
was still present at the end of the simulation, i.e. 10 a.m. The spatial impact length of
the incident was larger than 9.5 miles in the study corridor, and the duration of congested
states was as long as 4 hours.
I−95 SB Basecase Scenario
I−95 SB Incident Scenario
13.6
13.6
5 mph
5 mph
12.0
12.0
15 mph
15 mph
Distance (mile)
10.0
25 mph
8.0
35 mph
6.0
45 mph
4.0
5 AM
6 AM
7 AM
8 AM
Time (hour)
9 AM
25 mph
8.0
35 mph
6.0
45 mph
4.0
55 mph
2.0
55 mph
2.0
10 AM
5 AM
(a) I-95 SB Baseline Scenario
6 AM
7 AM
8 AM
Time (hour)
I−95 SB Diversion Scenario
5 mph
12.0
15 mph
10.0
25 mph
8.0
35 mph
6.0
45 mph
4.0
55 mph
2.0
5 AM
9 AM
10 AM
(b) I-95 SB Incident Scenario
13.6
Distance (mile)
Distance (mile)
10.0
6 AM
7 AM
8 AM
Time (hour)
9 AM
10 AM
(c) I-95 SB Diversion Scenario
Figure 7: Comparison of congestion maps for I-95 SB
17
Fig. 7c shows the effect of the en-route diversion scenario on the congestion mitigation.
Diversion effectively reduced the incident-induced delays. Both the spatial and temporal
impacts of the incident were significantly decreased by the en-route diversion and information provision. Compared with Fig. 7b, the spatial impact length of the incident was 6.0
miles in the study corridor, and the duration of congested states was 3 hours. In addition,
drivers’ diversion behaviors also smoothed the transition from the free-flow state to the
congested state for the segment of 3.5 mile through 8.0 mile. The speed breakdowns were
relieved and the jam propagation was slowed down, e.g. the propagating time period was
from 7 AM to 8 AM which is longer than 45 minutes shown in Fig. 7b.
6.2.2
Macroscopic fundamental diagrams
The MFDs represent the dynamic development of traffic conditions (Geroliminis and Daganzo, 2008; Geroliminis and Sun, 2011a,b; Saberi and Mahmassani, 2013a,b). In a transportation network, if traffic is distributed heterogeneously, characteristics with regard to
the hysteresis and capacity drop could be observed. In this study, we analyze the 1-minute
interval MFDs for the subnetwork of I-95 and US-29 using simulation, as shown in Fig. 8.
I−95/US−29 Network MFD
I−95/US−29 Network Vehicle Accumulation − Outputs
800
60
600
Outputs per Min.
Weighted Flow (veh/hour/lane)
700
500
400
300
40
20
200
Basecase Scenario
Incident Scenario
Diversion Scenario
Basecase Scenario
Incident Scenario
Diversion Scenario
100
0
0
0
10
20
30
40
50
60
Weighted Density (veh/mile/lane)
70
80
0
90
500
1500
2000
2500
3000
Vehicle Accumulation
(a) Weighted density - weighted avg. flow
(b) Vehicle accumulation - outputs
I−95/US−29 Network Weighted Density − Weighted Avg. Speed
I−95 South Bound Coefficient of Variation
60
3
Basecase Scenario
Incident Scenario
Diversion Scenario
Basecase Scenario
Incident Scenario
Diversion Scenario
2.8
Coefficient of Variation of Link Density
Weighted Avg. Speed (mile/hour)
1000
55
50
45
40
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
35
10
20
30
40
50
60
70
Weighted Density (veh/mile/lane)
80
0
90
10
20
30
40
50
60
70
80
90
Weighted Density (veh/mile/lane)
(c) Weighted density - weighted avg. speed
(d) Weighted density – coefficient of variation
Figure 8: Macroscopic Fundamental Diagrams of three scenarios
18
Fig. 8a depicts the relationship between the space mean flow rate and the space mean
density. It can be seen that the MFD curves of three scenarios satisfy homogeneity conditions and exhibit smooth curves when the weighed density is low. When the density
reaches 24 veh/mile/lane, throughput drop caused by the incident can be observed in both
the incident scenario and the diversion scenario. These two scenarios thereby reach their
maximum flow rates under the circumstances of higher densities. Compared to the agents
in the incident scenario, those in the diversion scenario have access to en-route information and thus can better utilize the remaining capacity of the network. Hence a higher
throughput is achieved in the diversion scenario. The hysteresis phenomenon (higher flows
as the density increases and lower flows as the density decreases) is remarkable in each
scenario, indicating that the flow rate is lower during the recovery period compared to the
loading period. An interesting finding is that when agents possess en-route information,
the hysteresis effect is less dramatic (in other words, the loading curve and the recovery are
closer). The MFD hysteresis patterns conform to existing studies on arterial and freeway
networks (Geroliminis and Sun, 2011a; Saberi and Mahmassani, 2013a; Tsubota et al.,
2013). We can also observe that the densities are successfully reduced when information
is available after the incident.
Fig. 8b depicts the relationship between vehicle accumulation (i.e. the number of
vehicles remaining in the network at each time period) and outputs (i.e. the hourly rate
of exiting flows from the network, including all off-ramp flows and the mainline flow of
the ending links). Analogously, the performance of the diversion scenario lies between the
basecase and the incident scenario. Fig. 8c shows the speed-based MFD curves. The
network-wide average speeds are consistent and closely predicted. The diversion benefits
the network by maintaining a higher level-of-service during the incident and lower densities
after the incident. Finally, network reliability is measured by spatial distribution of link
densities, i.e. Coefficient of Variation (CV, as defined in Eq. 9b). As illustrated in Fig.
8d, the network CV indicates that the incident, no matter with or without information
provision, will result in a much more unreliable and spatially unevenly distributed traffic
condition. Omitting the initial demand loading period (which leads to unevenly distributed
traffic), the highest CV in the two scenarios can reach 1.5 and 1.3 in the incident and the
diversion scenario, respectively. The CV gradually reaches its maximum value in the
incident scenario. In the diversion scenario, a peak CV occurs at the beginning of the
incident and maintains on a stable level. In other words, some additional queuing and
congestion are inevitably induced as soon as agents are diverted and start to concentrate
in disperse places. This is an important measure of time-varying reliability for analyzing
the impact of incident and diversion and should be accounted for in any evaluation.
Notably, the MFDs of the basecase and diversion scenarios exhibit consistent patterns
during the recovery, maintaining similar critical weighted average density (as shown in
Fig. 8a). This is due to the topological and control characteristics of the network such
that agents can promptly divert to the alternative route via multiple diverting points and
the alternative route has unused capacity, few signals and limited access. Would the MFD
patterns persist if these characteristics differ? We use simulation studies to shed some light
on the answer and reserve more thorough analysis for future research. Two circumstances
are demonstrated, including: (1) in the diversion scenario, the capacity of the alternative
19
route is reduced by 20%; (2) in the diversion scenario, only VMS 3 and 4 are used to divert
agents. Other simulation settings remain the same. MFDs of density-flow relationship for
the two cases are illustrated in Fig. 9a and Fig. 9b, respectively.
I−95/US−29 Network MFD
800
700
700
Weighted Flow (veh/hour/lane)
Weighted Flow (veh/hour/lane)
I−95/US−29 Network MFD
800
600
500
400
300
Congestion offset
200
100
Congestion onset
600
500
400
300
200
100
The Diversion Scenario
Diversion with reduced capacity
0
The Diversion Scenario
Diversion with fewer diverting points
0
0
10
20
30
40
50
60
Weighted Density (veh/mile/lane)
70
80
90
0
(a) MFD when the alternative route has less capacity
10
20
30
40
50
60
Weighted Density (veh/mile/lane)
70
80
90
(b) MFD when the original route has fewer diverting
points
Figure 9: MFD of density-flow relationship when (a) the capacity of the alternative route
is reduced by 20% in the diversion scenario; (b) only VMS 3 and 4 are enabled in the
diversion scenario.
Compared to MFD of the originally assumed diversion scenario, the diversion curves
in these two cases exhibit inconsistent MFD patterns. This discrepancy is most significant
during congestion offset in Fig. 9a (where a significant hysteresis is observed) and during
congestion onset in Fig. 9b (where lower throughput is observed). It indicates that
diversion could have less effect on traffic recovery, when the alternative route has less
capacity to serve diverting vehicles. And similarly, less benefit can be expected for traffic
loading period if the original route has fewer diverting points.
Analogous to the dissimilarity between freeway networks with hysteresis phenomena
and arterial networks without hysteresis (Geroliminis and Sun, 2011a), diversion scenarios
with different topological and control attributes can lead to significantly different MFD
results. Circumstances can be generalized into fourfold: (1) the network has less redundant
capacity; (2) topologically, the network has fewer access points to the alternative route;
(3) traffic conditions between routes are highly correlated (e.g. diversion under severeweather situation); (4) on the demand side, the diversion has a very low compliance
rate. If any of these circumstances holds, the subnetwork may have significantly different
MFD patterns. It may not even have well-defined MFDs to describe a clear flow-density
relationship (Geroliminis and Sun, 2011a). While this paper represents one specific case
of network-level MFDs, a future study should deeply investigate and summarize MFD
performance under various circumstances.
20
7
Closing Remarks
The objective of this paper has been to study the en-route diversion responses of agents
under real-time information provision and to quantitatively analyze their impacts on network performance. In order to achieve this objective, an integrated agent-based simulation
approach is proposed. On the demand side, a na¨ıve Bayes classifier is developed to model
the decision-making. Stated preference samples collected from driving simulator scenarios
have been employed in the model estimation. Bluetooth-based field observations have been
employed in the model re-calibration. On the supply side, this integration has incorporated
a real-world large-scale mesoscopic traffic simulation model coupled with simulation-based
DTA to reveal interesting traffic dynamics.
The first contribution of this paper lies in the originality and completeness of the
integrated modeling framework. The rule-based behavior model serves as an plausible
alternative to the traditional discrete choice models. Individuals that are perfectly rational are replaced by Bayesian agents. Moreover, the rule-based model predicts agent
behavior probabilities in a highly efficient way, which especially useful when millions of
agents are simulated in the system. Secondly, the model’s operational application also
represents a first attempt to link agent behavior with large-scale network simulation. It
has demonstrated superior transferability of the agent-based model since less than five new
parameters are re-calibrated and the model predicts consistent diversion behavior which
matches the Bluetooth observations. The proposed framework is comprehensive. It models the agent behavior, calibrates the model, simulates network conditions, dynamically
applies the behavior model, deploys the diversion strategy in the simulation, and obtains
various performance measures.
This paper also remains as a first research effort that uses MFD measurements to quantitatively evaluate the information provision and en-route diversion in an assumed incident
scenario. Unlike typical averaged statistics, MFD measurements are time-dependent representations of traffic characteristics. The MFDs of the studied I-95/US-29 network have
confirmed that agents’ en-route diversion has an impact on network throughput, average
flow, speed, and density. Compared to the incident scenario, the diversion scenario indicates a more robust network which has less significant flow decrease and recovers with
weaker hysteresis. This is an important finding. Without real-time information provision,
an incident has the potential to make the network much more vulnerable and suffering
from severe breakdown. En-route diversion can help avoid the breakdown and maintain a
consistent traffic pattern to the normal traffic pattern of the network. Another interesting
finding regarding the corridor-level MFD is that according to the CV measure of link densities, some unevenly distributed local congestion is inevitable even if the overall weighted
average density can be well controlled. This finding suggests that when evaluating VMS
and diversion, the spatial distribution of link densities should be carefully accounted as
a measurement of reliability. Finally, it is worth noting that the simulation results are
case-specific and sensitive to the network topology. Diversion can be less beneficial if the
behavioral compliance rate is low, or if the network does not have an alternative route as
effective, e.g. the network is non-redundant or has fewer access points to the alternative
route. Another situation is that the traffic conditions between routes are highly correlated
21
(Lindsey et al., 2014). An extreme case can be the severe-weather situation where the
capacities of both routes are deteriorated. In order to fully evaluate VMS and diversion,
a future study needs to systematically examine situations under various uncertainty and
network scenarios.
As demonstrated in this paper, the en-route diversion model is easy to be estimated
and applied in computational processes and agent-based simulation. This model is highly
transferable if applying the proposed calibration functions to any available ground truth
data. The proposed framework is comprehensive and can be applied in operational analysis
(e.g. to evaluate ATIS strategies) and demand models (e.g. to predict more realistic
en-route diversion behavior). This approach meets the imperative needs in modeling enroute diversion and real-time information provision in demand modeling and operational
applications, especially when most commuting corridors in contemporary metropolitan
areas get increasingly congested and ATIS, such as VMS, becomes readily available.
Despite the promising applicability of the proposed modeling framework, it is acknowledged that much needs to be done theoretically to further extend existing understanding
on behavior under information provision and on MFD characteristics. MFD performances
under various uncertainty, control, and topological circumstances need to be investigated
in order to comprehensively assess the effect of information provision. On agent behavior
modeling, laboratory experiments have shown evidences that drivers can learn from their
prior experiences over time through a reinforced learning process (Ben-Elia and Shiftan,
2010; Lu et al., 2011). And the discrepancy between the information and the actual experience can influence agent learning and decision-making (Ben-Elia et al., 2013; Gao and
Huang, 2012). Behavioral parameters for learning processes have been calibrated using
surveys, experiments, and network simulation (Lu et al., 2014; Xiong et al., 2015). Following this line, more research is needed for modeling transportation as a complex system
that accounts for the combined effect of travel information, agent behavior, and network
dynamics. Another pitfall is that the framework only considers en-route behavior changes,
while other dimensions of behavior adjustments are not included. In reality, ATIS and
reliable traffic information could also encourage mode shifts, pre-trip route changes and
trip rescheduling (Sun et al., 2012), which should be included in a cohesive multidimensional framework. Optimal ATIS strategies can be explored using the framework such as
optimal VMS deployment (e.g. how many VMS devices, VMS locations, and durations)
and information penetration (e.g. percentage of agents possessing pre-trip/en-route information). Simulation-based optimization and meta models can be a powerful optimizer for
solving these types of decision-making problems (Chen et al., 2014).
Acknowledgment
This research is partially funded by Dr. Lei Zhang’s National Science Foundation CAREER Award, the U.S. Federal Highway Administration Exploratory Advanced Research
Program, and the Maryland State Highway Administration. The authors are responsible
for all statements in the paper. We are grateful to the three anonymous reviewers for their
valuable comments for us to improve the paper’s quality.
22
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