Fusing probe speed and flow data for robust short-term congestion front forecasts

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Fusing Probe Speed and Flow Data
for Robust Short-Term Congestion Front Forecasts
Felix Rempe
BMW Group
Munich, Germany
Email: felix.rempe@bmw.de
Lisa Kessler, Klaus Bogenberger
Munich University of the Federal Armed Forces
Munich, Germany
Email: lisa.kessler@unibw.de
Abstract—In this paper a robust and flexible method is
proposed that combines the strengths of detector as well as
Floating Car (FC) data in order to provide short-term congestion
front forecasts. Based on the high spatio-temporal resolution of
FC data, congested regimes and according congestion fronts are
identified accurately. Subsequently, the flow data provided by
loop detectors are utilized in order to predict these congestion
fronts for a time horizon of up to ten minutes. Three variations of
the method are presented which focus the difficulty of estimating
traffic density in congested traffic conditions with given data.
The evaluation is based on real FC as well as loop detector
data collected during a congestion on the German Autobahn
A9. Comparisons of the variants of the proposed method and
a naive predictor emphasize the advantage of combining both
data sources and point out the strategy that results in the most
accurate front forecasts.
I. INTRODUCTION AND STATE -OF-THE-ART
Short-term traffic forecasts are fundamental for various
traffic-related applications [1]. In-vehicle systems such as
accurate travel time predictions as well as ‘tail of congestion’
warnings increase the calculability and safety of individual
transportation. The overall efficiency and safety benefit from
accurate short-term traffic speed forecasts through effective
control strategies such as Variable Speed Limits (VSL) or ramp
metering [2].
Many methods have been proposed that estimate and predict
traffic conditions for a short time horizon. Most approaches ap-
ply a first or second order Lighthill-Whitham-Richards (LWR)
model on loop detector data and apply data assimilation
techniques such as Kalman filters [3]–[6]. Another approach
called ASDA/FOTO identifies three traffic phases in space and
time and subsequently forecasts congestion fronts using the
shock-wave equation of traffic [7].
A rather new data source that provides great potential for
traffic state estimation and prediction is Floating Car (FC)
data. Compared to loop detectors, which are costly to install
and maintain and which only provide data for pre-determined
locations, FC data potentially covers an entire network and can
provide high-resolution traffic information. Due to the large-
scale availability at low costs FC data plays an increasing role
for traffic state estimation and prediction. Several approaches
focus on traffic estimation with (mainly) FC data [8]–[10].
Future traffic applications are expected to access a mix of
several data sources, each providing different types of data
with different accuracies. [11] gives a detailed overview of the
state-of-the-art in fusion of data in Intelligent Transportation
Systems (ITS) and its advantages. Though, data is usually
noisy, sensors are sparse in space and time and prone to
outages. This limits the applicability of many published ap-
proaches in practice. One method commonly applied is the
Generalized Adaptive Smoothing Method (GASM) that proved
to be accurate, efficient, robust and flexible with respect to the
input data [12]–[14]. It smooths data in time and space in a
sophisticated way and can be applied to extrapolate congestion
into the future. However, it does not allow to combine several
types of data such as traffic flow and speed, which limits its
capabilities of predicting congestion fronts accurately.
This paper proposes a new method to forecast jam fronts
based on FC data fused with detector data for a short time
horizon (up to 10 min). In contrast to other methods which
usually require data to be collected at fixed positions in fixed
time intervals, the proposed method allows data to be sparse
in time and space. The fusion of FC with detector data seeks
to combine the strengths of both data sources: The high
spatio-temporal coverage of FC data that provides accurate
traffic speed estimates and the flow data collected by loop (or
other stationary) detectors that is used for congestion front
prediction.
The paper is structured in a classical way. The following
section describes the prediction model. Next, a quality metric
that measures the prediction accuracy is proposed. An evalua-
tion using real data collected by FCs and loop detectors during
a traffic congestion on German freeway A9 is conducted.
Results are discussed and summarized in the last section.
II. PREDICTION MODEL
Let V(t, x)be the macroscopic traffic velocity at time tand
at position xon a road segment of length Lobserved during
time interval [0,T], such that t∈[0,T]and x∈[0,L].We
define the positions of the Ground Truth (GT) upstream jam
fronts Xup
GT (t)as the positions where traffic velocity undergoes
a critical velocity of vthres:
Xup
GT (t):={x:V(t, x)=vthres,dV (t, x)
dx <0}(1)
Accordingly, the downstream fronts are defined as:
Xdown
GT (t):={x:V(t, x)=vthres,dV (t, x)
dx >0}(2)
31

The goal of the proposed forecast method is to process all
given data that is available up to the time t−tpand provide an
estimate of all upstream jam fronts Xup
E,i(t, tp), where index i
denominates the i-th front in ascending order of x.tpis the
predicted time, i.e. the time that has passed since front ihas
been initialized with the GT:
Xup
E,i(t, tp)=Xup
GT,i (t−tp)+t
t−tp
˙
Xup
E,i ˆ
t, ˆ
t−(t−tp)dˆ
t
(3)
This Ordinary Differential Equation (ODE) is valid as long
as it holds that:
Xup
E,i(t, tp)<X
down
E,i (t, tp)(4)
If for any ithe condition is violated, both, Xup
E,i and Xdown
E,i
are removed from the sets. The propagation speed of a front
are computed with the well-known shockwave formula [15]
[16] [4] [3]:
˙
Xup
E,i(t, tp)= Qdown
i(t, tp)−Qup
i(t, tp)
Kdown
i(t, tp)−Kup
i(t, tp)(5)
Using the formulas (3) and (5) to forecast jam fronts
requires to set four quantities: (a) the outflow Qdown
i, (b) the
inflow Qup
i, (c) the downstream density Kdown
iand (d) the
upstream density Kup
i. Though, data is only available up to
time t−tp, such that all of these quantities constitute predictive
values.
Let us assume that available data consists of speed measure-
ments provided by FCs that have been processed into a conti-
nuous velocity estimate V(t, x),t∈[0,t−tp],x∈[0,L]using
a state-of-the-art traffic speed estimator [13] [17]. Flow data
provided by e.g. loop detectors is represented as a set of tuples
Q={(t, x, q)1, ..., (t, x, q)Nq:tj≤t−tp,j ∈1, ..., Nq}.
According density values (usually determined as q/v) follow
the same notation: K={(t, x, k)1, ..., (t, x, k)Nk:tj≤
t−tp,j ∈1, ..., Nk}.
Given a sufficient penetration rate of FCs, the resulting
speed estimate V(t, x)has a high spatio-temporal resolution
[8] [18], which usually exceeds the sparse placement of fixed
detectors. Therefore, the velocity estimate is well suited in
order to estimate the boundaries between traffic phases up to
the time of model initialization t−tp. The identification of
traffic phases subsequently allows for assigning sparse flow or
density measurements to the phases. This in turn is helpful
for the estimation of the aforementioned quantities required
for the front propagation.
Let PC(t, x)∈[0,1] be the probability that traffic in (t, x)is
in congested state. It is defined as a standard sigmoid function
with turning point vthres and parameter λ:
PC(t, x)=1−1
1+exp(−λ·(V(t, x)−vthres)) (6)
The estimation of the flows and densities from given data and
phase assignment is based on the following considerations. At
the time when the upstream front of a jam is detected, the
propagation of this front depends on the traffic conditions up-
and downstream of the front (i.e. in the congested regime).
Fig. 1. Fundamental diagram and corresponding space-time regions with
phase fronts and front propagation speeds (compare to [15])
The congested regime is characterized by a high density of
vehicles, whose velocities are synchronized among different
lanes [16]. Shockwaves in this congested regime propagate
upstream with a relatively low velocity of vC≈−15km/h
[19] [16] [13]. Although some traffic theories state the exis-
tence of a wide scattering of potential flows and densities in the
synchronized flow phase [16], during the prospective time ho-
rizon of ten minutes the current conditions inside a congested
regime are not expected to change significantly. Therefore,
we assume that for a prediction of the upstream fronts, the
flow and density values Qdown
i(t, tp)and Kdown
i(t, tp)are
sufficiently well approximated by setting them to best-known
value at the time of initialization.
On the other hand, the dynamically changing inflow
Qup
i(t, tp)definitely impacts the propagation of the front. If
the inflow is great, the front propagates upstream faster and
the congested regime grows. With greater flow in free flow
conditions also the density increases, though only slightly
(compare Fig. (1)). Compared to relatively slow shockwaves
in congested traffic, shockwaves in free flow propagate with
a greater velocity of vF≈80km/h downstream [20] [16]
[14] [15]. With respect to these empirical observations and
traffic theories based on a fundamental diagram (FD), in the
proposed method flow and density quantities are propagated
downstream with a velocity of vFin order to forecast flows
and densities in free flow conditions.
A. Estimating Phase Flows
In order to determine current and predictive flow and density
quantities, a traffic-characteristic spatio-temporal smoothing
operation is applied. Originally proposed in [12] and refined
in [14] [13] [18], the principle is to determine the traffic state
in (t, x)from sparse data in time and space using smoothing
operations that weight data with respect to their possibility to
32

be part of the same shockwave as (t, x). The weight Φ(t, x)
is formulated in terms of a smoothing kernel:
Φ(t, x)=exp
t−x
vdir
τ
−
x
σ(7)
where τand σare parameters that regulate the decay of
the weight in space and time, and vdir is the velocity of
the shockwave. We denominate ΦF(t, x)as the kernel with
parameters τF,σ
Fand vF, and ΦC(t, x)as the kernel with
parameters τC,σ
Cand vC.
In order to determine the traffic state in (t, x)given data
(flow or density) is smoothed utilizing either the free or the
congested kernel. E.g. QC(t, x)represents a flow estimate
using flow data Qsmoothed with the congested kernel ΦC:
QC(t, x)=(t∗,x∗,q∗)∈Q ΦC(t−t∗,x−x∗)PC(t∗,x
∗)q∗
(t∗,x∗,q∗)∈Q ΦC(t−t∗,x−x∗)PC(t∗,x
∗)
(8)
PC(t, x)as the probability for a measurement in (t, x)to
be in congested traffic state, serves as a weight. Effectively,
data is only smoothed within the phase to which it is assigned.
Accordingly, QF(t, x)is determined as (with PF=1−PC):
QF(t, x)=(t∗,x∗,q∗)∈Q ΦF(t−t∗,x−x∗)PF(t∗,x
∗)q∗
(t∗,x∗,q∗)∈Q ΦF(t−t∗,x−x∗)PF(t∗,x
∗)
(9)
As motivated before, Qdown
i(t, tp)of eq. 5 is set to the flow
estimate at the time of initialization of a front:
Qdown
i(t, tp):=QCt−tp,Xup
E,i (t−tp,0)(10)
The upstream flow is set to the predicted flow at the position
of the front:
Qup
i(t, tp):=QFt, X up
E,i (t, tp)(11)
B. Estimating Phase Densities
Setting the density quantities is less obvious since density is
not measured. The usual way is to estimate traffic density from
loop detector data as the quotient of flow and speed. However,
while in free flow traffic conditions flows and speeds can be
measured with high precision, in congested traffic conditions
vehicle speeds are low and can be estimated less accurately.
Consequently, also the error of the estimated density is high.
In order to overcome that issue and compare some variations,
in the following three ways to estimate the densities are
contrasted.
The first variation, denominated as K-DET, smoothes den-
sity quantities Kdetermined from detector data in the same
way as flow data. The resulting smoothed and continuous
functions KF(t, x)and KC(t, x)are used to set the respective
density values for the wave propagation:
Kdown
i(t, tp):= KCt−tp,Xup
E,i (t−tp,0)(12)
Kup
i(t, tp):= KFt, X up
E,i (t, tp)(13)
The second variation, denominated as K-MAX is based on the
ASDA/FOTO model [7]. In that model the authors propose to
precompute a density which represents the maximal density
in congested traffic where vehicle velocities are very low. As
a consequence, the downstream density is a constant. That
approach is integrated into this framework by setting:
Kdown
i(t, tp):=kmax (14)
and Kup
i(t, tp)similar to (13).
The idea of the third variation, called K-FCD, is that great
part of the estimation error of the densities in the congested
flow regime possibly stems from the inaccuracy in the traffic
speed measurements. Since the velocity estimate V(t, x)obtai-
ned from dense FCs is expected to have a greater accuracy,
using this for the calculation of densities could increase the
overall accuracy. Thus, Kdown
i(t, tp)and Kup
i(t, tp)are set
as:
Kdown
i(t, tp):= QC(t−tp,X up
E,i(t−tp,0))
V(t−tp,Xup
E,i(t−tp,0))(15)
Kup
i(t, tp):= QF(t,X up
E,i(t,tp))
V(t−tp,Xup
E,i(t−tp,0))(16)
Downstream fronts can be estimated similarly. However,
many empirical studies have shown that downstream fronts
are either fixed at bottlenecks, or propagate upstream with an
approximate velocity of vC(with few exceptions) [20] [19]
[12]. For simplification, since upstream fronts present greater
hazards, no further distinction is made in the context of this
paper and it is assumed that all downstream fronts propagate
upstream. Future work could elaborate this issue.
III. ACCURACY ASSESSMENT
Intuitively, an error estimate such as the RMSE of the
forecasted front positions seems to be a reasonable choice
for a quality estimator. However, since both, the GT and the
simulated fronts, may dissipate over time, there are not always
two front positions that can be compared. Instead, we apply a
metric that is supposed to penalize (1) if the simulated front
deviates more than xtol from the GT front, (2) if the simulated
front dissolved, but the GT front is still active (true negative),
or (3) if the GT front already dissolved, but the simulated
front is still active (false positive). For a front of index ithe
function:
Hiti(t, tp)=1if Xup
GT,i (t)−Xup
E,i(t, tp)<x
tol
0otherwise
(17)
compares the GT front and the simulated front of index i.
Tot
iindicates whether there is a GT front or a simulated
front active:
Tot
i(t, tp)=1if Xup
GT,i (t)=∅∨Xup
E,i(t, tp)=∅
0otherwise
(18)
The accuracy Aof the method for a prediction horizon tp
corresponds to the number of hits over all simulated time steps
compared to all phase front positions that have been predicted
or were measured for a front of index i:
A(tp,i)=
t
Hiti(t, tp)
Tot
i(t, tp)(19)
33

6
BERLIN
MUNICH
[km]
Interchange
Munich North
8
Exit
Garching South
11
Exit
Garching North
15
Exit
Eching
17
Interchange
Neufahrn
30
Exit
Allershausen
39
Exit
Pfaffenhofen
47
Triangle
Holledau
Fig. 2. Congestion scenario used for evaluation. Upper left: Normalized flow values collected by loop detectors. Upper right: Sketch of the A9 Autobahnin
northbound direction. Bottom left: Collected floating car data. Bottom right: Estimated traffic speed
IV. APPLICATION TO REAL-WORLD DATA
Test site is the German Autobahn A9 in the north of Munich
where a heavy traffic jam occurred on April, 30th, 2015 due
to an accident (Fig. (2) up). One-minute flow data of several
lanes are averaged and divided by the number of lanes. Figure
(2) bottom visualizes the raw trajectory data that was reported
by a fleet of vehicles during that day on this road segment.
Note that, due to privacy protection, vehicles do not report
their position continuously, but, simplified, only in congested
traffic conditions. On the right, the velocity estimate V(t, x)
is depicted that is computed using the Phase-based Smoothing
Method (PSM) [17].
The congestion pattern reminds one of Homogeneous Con-
gested Traffic (HTC) [21] upstream of the accident location at
kilometer 43 with very low traffic speeds and homogeneous
traffic conditions. Further upstream several moving jams ori-
ginated that propagated upstream over long distances. On this
road segment, traffic is in oscillating state [21] or, in terms of
the Three-Phase traffic theory, there are several Wide Moving
Jams (WMJ) [16]. At the time when the congestion occur-
red (approx. 5pm), the upstream congestion front propagated
upstream with about 15km/h until 6pm, where a significant
drop in the upstream flow was measured. Next, flow is on a
low level such that existing WMJs dissolve. At 8pm the last
WMJ of the congestion pattern dissolved. Afterwards, a few
more moving jams occurred in the downstream region between
kilometer 18 and 32.
A. Parametrization
In order to apply the described method and its variations, a
few parameters need to be set. We set vthres to 30 km/h, λto
0.5, similar to [13] [14] vFto 70 km/h and vCto -15 km/h.
The kernel parameters σFand σCare set to 800 m, τFto
50 s and τCto 25 s. kmax is set to 90 % of the maximal value
measured during this congestion, which results in a value of
approx. 90 vehicles/km. Time is discretized into intervals of
10 s, space into segments of 50 m.
In addition to the three variations, a naive predictor is
modeled. This one propagates any front with a constant
velocity of vCupstream. For accuracy estimations xtol is set
to 500 m.
34

Fig. 3. Comparison of Ground Truth fronts with predicted upstream fronts for several variations of the proposed algorithm and a prediction horizon of 5min
(left) and 10min (right)
Fig. 4. Accuracy of several variations of the proposed algorithm with respect to the prediction horizon. On the left, the accuracy for the prediction of the
most upstream congestion front; on the right the accuracy for all other fronts
B. Results and Quality
Figure (3) depicts the positions of the simulated upstream
fronts compared to the GT fronts after 5 min and 10 min
respectively. For conciseness, we refer to the upstream front
with index iasafirst order front, and refer to the remaining
upstream fronts as higher order fronts.
The first observation is that all predictors overestimate the
positions of the upstream fronts frequently. Especially from
6.30pm-8pm where the WMJs dissolve, fronts are propagated
too far. While that is an expected result for the naive predictor,
this one still performs significantly better than the K-DET va-
riation. The variation K-MAX seems to predict the first order
front most accurately. Fronts of higher order appear straighter
than the first order front. This matches the propagation rule of
the naive algorithm, such that this approach predicts relatively
accurately. Comparing the 5min and 10 min forecast shows
the expected result that a greater prediction horizon causes
higher deviations.
Fig. (4) visualizes the accuracies of the variations and the
naive algorithm with respect to the prediction horizon. A
distinction between the prediction of the first order and higher
order fronts is made. The reason for this distinction is the
effect that influences the front propagation: the first order front
is mostly influenced by the prediction of the upstream flow,
while the inflow of higher order fronts is given by the outflow
of the neighboring fronts (compare Fig. (1)).
The quantitative results support the conclusions drawn from
the visual exploration. For short prediction horizons of up to
2 min all predictors show a decent accuracy. Shortly after, the
accuracy of K-DET drops quickly. K-FCD performs signifi-
cantly better than K-DET and achieves accuracies comparable
to the naive method. K-MAX is significantly more accurate
than any other method. For higher order fronts, K-DET
performs worst, but K-MAX and K-FCD do not excel this
method significantly. Here, the naive predictor outperforms the
other approaches.
An analysis of the computed densities of K-DET and K-
35

FCD that influence the propagation speed reveals that these
variations underestimate the density of the congested regime.
Consequently, the upstream fronts’ propagation velocities are
overestimated such that WMJs do not dissolve as expected
from the decreasing input flow. Since K-FCD with a more
accurate velocity estimate performs better, we attribute the
errors made by K-DET to the inaccuracy of the velocity
estimate in the denominator of the wave equation.
Comparing the naive approach and K-MAX we notice that
K-MAX predicts more accurately regarding the first order
front, whereas the naive approach outperforms the others for
remaining ones. First, this shows the effectiveness of the
proposed approach as it achieves to produce a more accurate
front prediction than any other method in comparison. Second,
the only difference to K-DET is the fixed downstream density.
That proves that this is a sensitive component of the method,
which K-DET is not able to estimate correctly. Third, for
higher order fronts the naive algorithm is the most accurate
one. The reason is that a transition from a congested into a free
traffic state and back into a congested traffic state without any
additional in- or outflow can be explained well with a FD (Fig.
(1)). In this case, the front propagation can be deduced directly
from the FD. Potentially erroneous measurements effectively
reduce the accuracy of the prediction. As a conclusion a mixed
model should be considered for application: The first order
front is predicted using the K-MAX variation, while for higher
order fronts a naive predictor is the best approach.
For future work, further studies should be conducted that
focus the fusion of various types of data e.g. density and
flow measurements collected directly via vehicles [22]. Furt-
hermore, a prediction of the traffic flow as it is done in this
method does not account for greater traffic streams leaving
an intersection. In the future, when routes of individuals may
be reported to central servers, these can be considered for
enhanced flow prediction.
V. C ONCLUSION AND OUTLOOK
In this paper a robust and flexible method is proposed that
combines the strengths of detector as well as Floating Car
(FC) data in order to provide short-term congestion front
forecasts. Using the high spatio-temporal resolution of FC
data, congested regimes and according congestion fronts are
identified with high accuracy. Subsequently, flow data provided
by e.g. loop detectors is utilized in order to predict these
congestion fronts. An evaluation of the method on a severe
congestion on a German Autobahn reveals a clear winner
that outperforms other variations and a naive method. Still,
a combination with a naive algorithm in case of cascades
of moving jams is the best choice in this comparison. The
presented approach combines data sources in a robust, efficient
and flexible way using specific smoothing operations. This
allows to apply the method to various types of data in real-
time.
ACKNOWLEDGMENT
The authors would like to thank Autobahndirektion
S¨
udbayern for providing the detector data.
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