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Advanced traffic data for dynamic OD demand estimation: The state of the art and benchmark study


Abstract and Figures

In this paper, the use of advanced traffic data is discussed to contribute to the ongoing debate about their applications in dynamic OD estimation. This is done by discussing the advantages and disadvantages of traffic data with support of the findings of a benchmark study. The benchmark framework is designed to assess the performance of the least square dynamic OD estimation methods using different traffic data. Results show that despite the use of traffic condition data to identify traffic regime, the use of unreliable prior OD demand has a strong influence on estimation ability. The greatest estimation ability occurs when the prior OD demand information is aligned with the real traffic state or omitted using information from AVI measurements and thus reinforces the necessity of establishing appropriate and meaningful values of OD demand. A common feature observed by various methods indicate that advanced traffic data require more research attention and fundamentally different approaches than those used today to turn them into usable information.
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Advanced traffic data for dynamic OD demand estimation: The1
state of the art and benchmark study2
Tamara Djukic3
Delft University of Technology, Department of Transport and Planning, The Netherlands4
+31 15 278 1723 email:t.djukic@tudelft.nl5
(Corresponding author)6
Jaume Barcel`
Universitat Politcnica de Catalunya BarcelonaTECH, inLab FIB, Spain8
Manuel Bullejos10
Universitat Politcnica de Catalunya BarcelonaTECH, inLab FIB, Spain11
Lidia Montero13
Universitat Politcnica de Catalunya BarcelonaTECH, Departament dEstadstica i Investigaci14
Operativa, Spain15
Ernesto Cipriani17
Universit Degli Studi Roma Tre, Department of Civil Engineering, Italy18
Hans van Lint20
Delft University of Technology, Department of Transport and Planning, The Netherlands21
Serge P. Hoogendoorn23
Delft University of Technology, Department of Transport and Planning, The Netherlands24
November 14, 201426
Word count:27
Number of words in abstract 153
Number of words in text (including abstract, first page and excl.ref) 5526
Number of figures and tables 6 * 250 = 1500
Total 7179
Submitted to the 94rd Annual Meeting of the Transportation Research Board, 11-15 January 2015, Wash-31
ington D.C.32
In this paper, the use of advanced traffic data is discussed to contribute to the ongoing debate about their2
applications in dynamic OD estimation. This is done by discussing the advantages and disadvantages of3
traffic data with support of the findings of a benchmark study. The benchmark framework is designed to4
assess the performance of the dynamic OD estimation methods using different traffic data. Results show5
that despite the use of traffic condition data to identify traffic regime, the use of unreliable prior OD demand6
has a strong influence on estimation ability. The greatest estimation occurs when the prior OD demand7
information is aligned with the real traffic state or omitted and using information from AVI measurements8
to establish accurate and meaningful values of OD demand. A common feature observed by methods in this9
paper indicates that advanced traffic data require more research attention and new techniques to turn them10
into usable information.11
With advanced real-time simulation tools that are able to integrate data from many different sensors both2
traffic operators and travelers can be provided with up-to-date and even projected travel and traffic infor-3
mation. Thorough calibration and validation procedures with sufficient data and granularity are critical in4
establishing the credibility of simulation tools for these different (real-time and planning) purposes. How-5
ever, unreliability and lack of knowledge about the projected OD demand makes prediction with advanced6
simulation models simply impossible, regardless of how well these models have been calibrated. In this7
respect, the estimation of dynamic OD demand has received a lot of attention in the last decades.8
Dynamic OD demand estimation methods have been proposed since the 1980s and since then a great9
evolution of these models have taken place. It started with the use of link traffic counts at intersection (1) that10
were translated into a practical generic optimization problem by (2). This OD demand problem formulation11
has received a lot of attention in the literature and has been continuously improved and extended. However,12
the methods and tools used in this area are still largely based on data that have been around from the early13
1980s and onwards, such as traffic counts and questionnaire data. As a result these methods are, to use a14
euphemism, ”assumption rich and data poor”.15
In the last decade the amount of empirical traffic data becoming available for both on-line and16
off-line use has increased, particularly in terms of the wide range of sensor technologies developed and17
applied to collect traffic data. New emerging data collection methods, such as large scale revealed travel18
itineraries and route patterns from GPS, Bluetooth and WiFi scanners, and cameras to name just a few, offer19
tremendous opportunities to extract more detailed and more valuable information about (origin-destination)20
demand patterns and travel behavior, than ever before. The literature intensively explores application of21
advanced traffic data for dynamic OD demand estimation, but a lot is yet to be done to extract sensible and22
valid information from these new data sources.23
In this paper, we present detailed literature review of different traffic data sources used in dynamic24
OD demand estimation. In addition, each of these traffic data has been independently applied to estimate25
dynamic OD demand, but to the authors’ knowledge, a deeper comparative analysis of their advances has26
not yet been performed. Although many methods have been proposed to solve the dynamic OD estimation27
problem using more traffic data, much fewer efforts have been reported to actually evaluate and cross-28
compare these methods under different circumstances (e.g. different network structures, different sets of data29
available in different qualities) (3), (4). In most cases where new OD estimation method is proposed, also a30
sensitivity analysis to demonstrate different properties of the method (5), (6), (7) is performed. The purpose31
of this paper is to contribute to a better understanding of traffic data advances by presenting a comparative32
analysis of the advantages and disadvantages of four least square dynamic OD demand estimation methods33
using different traffic data.34
The next section introduces the traffic data used in OD demand estimation process. The benchmark35
study is based on urban large-scale network and focuses on the suitability of each method to estimate dy-36
namic OD demand under different input data. Further, discussion about their advantages and disadvantages37
from points of view of theory and application is presented. Finally, conclusions and recommendations for38
future research are provided.39
Since OD matrices are often not directly observable, they have to be estimated from any available relevant41
data. Sensors typically measure traffic characteristics, which are the result of not just OD demand, but42
also of route choice and of traffic operations. Although data from traffic sensors come in many forms and43
qualities, they can essentially be subdivided into three categories depending on the source of information on44
OD flows and traffic operations.The types of input data that are used in literature for dynamic OD estimation45
and prediction are subdivided as depicted in Figure 1(a): (1) OD flow data; (2) link flow data; and (3) traffic46
condition data. The first type of input data, OD flow data, represent direct observations of OD flows obtained47
Djukic, et al. 4
from surveys or probe vehicles. The second type of input data, link flow data, are determined by the travel1
behaviour process. This process describes travel choices: when to depart, which mode to use, which route2
to choose. The third category of input data, traffic condition data over network, is determined by traffic3
operations. These data describe traffic state on a network: travel speeds, travel times, densities, etc. The4
sources of input data and their application in dynamic OD demand estimation and prediction process are5
discussed below.6
OD flow !
Link flow !
Traffic condition
(a) Clasiffication of input data for dynamic OD demand estimation.
>( >(
>( >(
4( 4(
6<?( 6<@(
6<=( 6<?( 6<@(
(b) Examples of some traffic data and their sources.
FIGURE 1 Types of input data used in dynamic OD demand estimation.
To illustrate on a very simple network example, suppose there are four OD flows going from A to7
C, A to D, B to C and B to D (see Figure 1(b)). Figure 1(b) gives some examples of different traffic sensors8
and the spatio-temporal semantics of the traffic variables, which can be observed with those sensors. We9
will use this figure as a reference to explain the most important sources of OD flow data, and their features10
for dynamic OD demand estimation.11
OD flow data12
Observations of OD flow data are rare. The practical and theoretical limitations of survey OD generation13
techniques have led to an exploration of how such data could be derived from equipped vehicles with in-14
vehicle traffic sensors which act as probes by transmitting their origin and intended trip destination when15
Djukic, et al. 5
they initiate a trip.1
Automatic vehicle location (AVL) data are receiving attention for their potential to provide a large2
sample of OD flow data. The observation of OD flows from in-vehicle traffic sensors (e.g., GPS and GSM)3
allows the detection of vehicles in multiple locations as they traverse the network. This feature makes the4
re-identification and tracking of these probe vehicles possible, which in turn may (under certain conditions)5
provide information on particular OD pairs (e.g., OD pair AC in Figure ??). In an ideal case, if data on OD6
flows are collected from all vehicles equipped with in-vehicle traffic sensors, full information on OD flows7
over all OD pairs can be extracted. Today, probe vehicles constitute only a fraction of the total number of8
vehicles in a network. Several models have been developed for the estimation of OD flows using AVL data9
((8), (9), (10)). (9) introduced the notion of direct measurements for the incorporation of AVL data into the10
solution of the OD estimation and prediction problem.11
Automatic vehicle identification (AVI) data represent another OD flow data source of growing im-12
portance for estimating dynamic OD demand flows. The observation of OD flows from AVI sensors (e.g.,13
electronic-toll collection devices, infrared cameras, Bluetooth, WiFi, etc.) depends on: a) the location of14
these traffic sensors on a network, as depicted in Figure 1(b) and b) the sample of tagged vehicles. In an15
ideal case, if cameras are located on links connected to origin and/or destination nodes on a network, they16
can provide under some assumptions total demand that departs from origin B or arrives at destination C. If17
only a subset of vehicles is equipped with transponder tags or only a subset of vehicles is correctly identified18
by the AVI readers, then these OD flow data need to be explicitly considered in order to infer OD flows over19
all OD pairs. Several models have been developed for the estimation of OD flows using AVI data ((11), (12),20
(13), (14)). In brief, these models require estimating the sample rate (either market penetration rates or iden-21
tification rates) so as to relate the AVI samples to the OD demand. The estimation of sample rates, however,22
is a difficult problem in its own right, as these rates are essentially time-dependent and location-dependent23
random variables. Moreover, the inclusion of sample rates in the OD demand estimation problem could24
dramatically increase the number of unknown variables and impact the reliability of OD demand estimates.25
To circumvent primary difficulties associated with estimating sample rates, (15) developed an OD demand26
estimation model using partially observed AVI data.27
Link flow data28
Traffic link flow data collected from loop detectors at specific locations on a network are the most common29
type of input data used in dynamic OD demand estimation. The traffic link flow data could either be collected30
in the middle of a roadway segment, at entry or exit ramps on highways, or across a screen-line in an urban31
area. The number and position of loop detectors on an urban or highway network plays an important role,32
since traffic link flow data from these detectors can provide different information on OD flows. In an ideal33
case, if link flow data are collected on road segments belonging exclusively to routes used to serve one34
particular OD pair, they can provide information on OD volume for that particular OD pair. In addition, if35
loop detectors are located on links connected to origin or destination nodes on a network, they can provide36
under some assumptions total demand that departs from origin B or arrives at destination C, as represented in37
Figure 1(b). The traffic link flow data observed by loop detectors located on links between nodes 1 and 2 in38
Figure 1(b) are comprised of contributions from several OD flows (i.e., OD pairs: AC, AD, BC, BD). Thus,39
such link flow data require adequate specification of relation and mapping with OD flows. This procedure40
describes the most critical issue in OD matrix estimation, that is the relationship of the observed link flow41
data and traffic condition data with the unobserved OD flows.42
Traffic condition data43
Apart from traffic link flow data, loop detectors are able to detect speeds and turn fractions at bifurcations44
in the network. The available speed or derived density measurements can help to identify whether traffic45
link flow data represents a congested or uncongested traffic state on a network. As such, they can facilitate46
Djukic, et al. 6
correct interpretation of traffic link flow data, and identification of OD flows that need to be adjusted, and1
in which direction. The simplest approach to including this type of input data is to include speed or density2
measurements in the goal function of the dynamic OD estimation problem ((16), (17), (18)). Turn fractions3
data collected at bifurcations in the network may provide constraints on the route choice patterns ((19)).4
New technologies for probe vehicle re-identification and tracking (e.g. AVI systems and AVL sys-5
tems) might provide traffic condition data, such as partial point-to-point travel times, route choice fractions,6
vehicle paths, and turning fractions. The data may come from cameras that capture and compare vehicle7
plates or from floating car data which may report the vehicle’s location at certain intervals to construct tra-8
jectories, as is depicted in Figure 1(b). The difficulty for the OD demand model formulation is to define the9
relationship between traffic flow data and OD flows. The identification of trajectories or link travel times10
can help to identify or estimate route flows. Therefore, they provide constraints on the traffic conditions11
resulting from assigning the OD flows to the network. Estimating OD matrices only from link flow data can12
be rather challenging given the indeterminate relation between link flow observations and route flows ((20)).13
Hence, many researchers have tried to integrate traffic condition data into the dynamic OD demand esti-14
mation and prediction problem. Examples include: speed and density data (e.g., (21), ((16), (18)); turning15
fractions (e.g.,((19), (22)); travel times (e.g., (17), (16) ); and route flows (e.g., (23), (14)).16
In this section we will discuss the overall benchmark study and provide some more detail on the components.18
First, design and implementation of benchmark platform will be briefly described. Then, generation of input19
scenarios, varying in terms of network topology, traffic conditions, and data availability is provided.20
Overview of benchmark platform21
The benchmark platform used in this benchmark study has been developed within European Union COST22
Action MULTITUDE project (24). The main goal of this platform was to ensure equal testing conditions for23
various OD demand estimation methods that would support fair comparison and an understanding of their24
relative merits. The benchmark platform consists of two main elements:25
Traffic simulator: In this benchmark study we use the mesoscopic version of the Aimsun simu-26
lation model (25) as the common traffic model. The mesoscopic model with default set of parameters was27
used because it is substantially faster than the microscopic one.28
OD demand estimation algorithms: This element refers to selection and implementation of29
a single or multiple OD demand estimation algorithms to be compared. Note that more information on30
selected dynamic OD estimation methods is given in following section.31
For more detail description of the workings of benchmark platform, we refer to (3).32
Case study33
A key requirement for the task of evaluating an OD demand estimation algorithms, and for comparison of34
multiple ones, is to test the performance under a range of different conditions and scenarios and to ensure35
that these conditions are consistent across algorithms. For that purpose, in this benchmark study, we consider36
the following input scenarios:37
1. We will test on large size network from Vitoria, Spain, with route choice.38
2. We will consider different scenarios in terms of dynamic prior OD matrices, varying bias and39
random errors.40
3. We will consider different scenarios in terms of data availability (i.e. the number and location of41
sensors and the type of surveillance information).42
Djukic, et al. 7
Network topology1
Prior to methods evaluation, we define Vitoria network that consists of 57 centroids, 3249 OD pairs with a2
600km road network, 2800 intersections and 389 detectors presented with black dots in Figure 2(a). This3
network was chosen because of the availability and quality of the empirical detector data on network, and4
because a calibrated OD matrix was available in the mesoscopic version of the Aimsun (25). This network5
resembles a reasonable sized real-life network, and is representative for congested road networks, as found6
in many large urban areas. The true link flow on detectors is derived from assignment of true OD matrix7
in Aimsun for one hour peak-afternoon period reflecting the congested state at the network. The simulation8
period is divided in 15 minutes time intervals with additional warm-up time interval, T= 5. The trips9
between some of the OD pairs are not completed within one time interval due to congestion on network or10
the distance between OD pairs resulting in 4 lagged time intervals and very sparse assignment matrices.
(a) Loop detector sensor layout. (b) AVI sensor layout.
FIGURE 2 The Vitoria network, Basque Country, Spain
OD flow scenarios12
To estimate the dynamic OD matrix for a specific day and time period t, information on OD flows given13
by prior OD matrix ˜xij,t turns out to be an important source of information. Generally, the dynamic prior14
OD matrix provides the base OD matrix which is matched and scaled on the basis of additional information15
(e.g. link flow data and traffic condition data) using different methods. The demand level is a key element16
affecting the performance of dynamic OD estimation methods (24). We can simulate different prior OD17
demand patterns which capture various demand levels by randomly perturbing each entry in the ”true” OD18
demand matrix and for each departure time interval, t.19
The experimental design considers the following three prior OD demand scenarios:20
1. Low demand scenario (D7): This scenario addresses situations where the prior OD demand
might be a result of OD demand generated from out of date surveys. The low prior OD demand pattern is
generated for 85% of the ”true” OD demand level with random fluctuations over each OD pair and departure
time interval in range of +/- 15%, that is
ij,t =xij,t ×[0.7+0.3×αij,t]αij,t U(0,1) (1)
2. Random demand scenario (RD): This scenario is based on the assumption that the prior OD
matrix is the best estimate of the mean of the dynamic OD matrices. Any survey or off-line OD estimation
procedure will utilize data from several days, inherently smoothing out any day to day variation present in
Djukic, et al. 8
the flows. In this scenario, the prior OD demand pattern is generated for 95% of the ”true” OD demand
level and varied by adding uniformly random components in range of +/- 15%, representing the difference
between the smoothed historical OD demand estimates and the particular daily realization:
ij,t =xij,t ×[0.8+0.3×αij,t]αij,t U(0,1) (2)
3. High demand scenario (D9): This scenario addresses situations where the prior OD demand
reflects travel demand in peak-hours, when congestion occurs on network. The prior OD demand pattern is
generated for 105% of the ”true” OD demand level and varied by adding uniformly random components in
range of +/- 15%, that is
ij,t =xij,t ×[0.9+0.3×αij,t]αij,t U(0,1) (3)
Link flow and traffic condition data scenarios1
Sensors located on the Vitoria network can be divided into two main groups: loop detectors and AVL sensors.2
Loop detector sensors might produce local flows, densities, occupancies, etc. related to all vehicles at the3
detected loop. AVL sensors usually provide automatic signature identification for a subset of the vehicles;4
i.e., WiFi antennas to catch Bluetooth devices in discovery mode.5
Traffic data are collected from 389 loop detectors and also 50 AVI detectors located using the layout6
models in (26). Almost 90% of the trips are collected twice at least in the peak-afternoon demand scenario,7
which account for 95% of the number of OD pairs and 86% of the most likely used paths identified in a8
DUE assignment with the ”true” prior OD matrix. The procedure proposed by (26) returns simulated travel9
times on these predefined and stored routes. Figure 2(b) shows Vitoria’s network and subnetwork covered10
by AVI sensor layout.11
In this section we make a choice of dynamic OD demand estimation methods used within today’s dynamic13
traffic management systems for the benchmark study. Since the main goal of the study is to evaluate the14
expected improvements due to implementation of richer and more varied traffic data, in this benchmark15
study we will focus on dynamic OD estimation methods that share same performance measure, i.e. least16
square error measure. In addition, one of the key requirements for successful benchmark study is to ensure17
good understanding and experience with various dynamic OD estimation methods that would support fair18
First we provide definitions that will be used further in formulation of dynamic OD demand meth-20
ods. The traffic demand between origin node oand destination node dis stored in the origin-destination21
(OD) matrix, x.Iis the set of all OD pairs and the vector x={xi|iI}is the OD demand. The22
historical or prior OD matrix ˜x ={˜xi|iI}is a matrix defined in OD flow scenarios that needs to be23
updated. y={yl|lL}are the link flow data. Link flow data and traffic condition data (e.g., speed,24
density, occupancy) are available on links ˆ
LL. Thus, the observed link flows on those links are denoted25
as ˜y ={˜yl|lˆ
L}and observed traffic condition data are denoted as ˜c ={˜cl|lˆ
L}. Additional traffic26
condition data, such as travel times, collected from AVI sensors available on links ˜
LLare denoted as27
˜z ={˜zl|l˜
L}. The study period has Ttime steps, and is divided in time intervals t,t= 1,2, ..., T .28
The generic formulation of dynamic OD estimation methods considered in this benchmark study,
Djukic, et al. 9
TABLE 1 Properties of Selected Dynamic OD Estimation Methods
Input data
Method prior OD link flow link density travel times Objective function Solution algorithm
Method 1 + + least square (LS) LSQR
Method 2 + + + normalized LS SPSA AD-PI
Method 3 + + + + normalized LS SPSA AD
Method 4 + + + normalized LS SPSA CG-TR
combining observed link flow data and traffic condition data, can be expressed as
ˆx =argmin
[f1(x,˜x) + f2(y(x),˜y) + f3(c(x),˜c) + f4(z(x),˜z)]
subject to
where xis the unknown OD demand vector ˆx = [ˆx1, ..., ˆxT], for time intervals t1,2, ..., T . The four1
functions f1,f2,f4and f4expresses the performance as a function of different error measures. An intu-2
itive interpretation of the problem given in (4) is that it searches the vector ˆx that is closest to the a priori3
estimate ˜x, and, once it is assigned to the network produces the traffic data y(x),c(x)and z(x)closest to4
their observed values. At each iteration step or time interval, t,y(x),c(x)and z(x), could be extracted5
from inputs of the AIMSUN traffic simulator and could be calculated using traffic assignment of the DUE6
simulation (see subsection Benchmark platform). The set of constraints depends on application of the prob-7
lem as well as the desired level of accuracy, and it can include non-negativity constraints, initial condition8
constraints, lower and upper bound constraints to avoid infeasible solutions and restrict search space, etc.9
Traveler’s route choice or traffic assignment rules are often obtained by optimizing an objective function,10
which can be explicitly included in the set of constraints. This formulation results in a bi-level optimization11
and represents the solution framework for considered OD estimation methods in this benchmark study. The12
functional form of the four functions f1,f2,f3and f4for estimators considered in this benchmark study13
is given by least square formulation. Although, the use of least square approach to formulate the dynamic14
OD demand estimation model has been originally proposed by (27), many authors build-on their modeling15
frameworks by exploiting different traffic data. Since different traffic condition data contain very diverse16
values normalized least square functions are applied. The selection of normalized least square objective17
function indicates that considered methods belong to a common ”family” and ensures to get a better grasp18
of the algorithms performance and improvements due to application of richer traffic data on OD flows. Table19
1presents the main properties of selected dynamic OD estimation methods.20
Method 1: The LSQR method21
The least square approach to formulate the dynamic OD demand estimation model given in Eqn.(4) is used22
by (6). They build-on their modeling framework by exploiting (28) proposal of using deviation of OD flows23
as state variables and deviations of link flows. The main properties of the model are given as follows:24
input data: prior OD flow and link flow data25
solution approach: LSQR algorithm26
To estimate dynamic OD demand by solving Eqn.(4) given by least square functions f1and f2, Bierlaire27
(6) proposed the LSQR solution algorithm to get the computational performance required for very large28
networks. LSQR is an iterative method for solving the least square problem, analytically equivalent to a29
Djukic, et al. 10
conjugate gradient method, based on bi-diagonalization procedures (29). Key properties of LSQR approach1
are that assignment matrix (very sparse in large scale networks) does not need to be explicitly constructed or2
stored, only multiplications with vectors need to be implemented. This feature is attractive for large sparse3
problems, which is the network case in Figure 2. For more detail explanation of this algorithm we refer to4
the paper (6).5
Method 2: The SPSA AD-PI method6
Cipriani (30) formulate the dynamic OD demand estimation model by adding traffic condition data, i.e.,7
densities, providing additional information on traffic regime. The main properties of the model are given as8
input data: prior OD flow, link flow data and density data10
solution approach: SPSA AD-PI algorithm11
The solution approach to solve dynamic OD demand problem given by normalized least square functions f1,12
f2and f3in Eqn.(4), is modified SPSA (Simultaneous Perturbation Stochastic Approximation) algorithm13
proposed by (30). Different variants of the SPSA algorithm have been proposed in (30), (16), where the off-14
line dynamic OD demand estimation problem is formulated as a bi-level nonlinear optimization program and15
solved with an assignment-matrix-free method. The authors proposed solution approach that is modification16
of the gradient-based path search optimization method (SPSA) dealing with the Asymmetric Design (AD)17
for gradient computation and the Polynomial Interpolation (PI) of the objective function (4) for the linear18
optimization. SPSA AD-PI permits to reduce the computational efforts with respect to the usual gradient-19
based methods, that is a basic issue to deal with a simultaneous demand estimation for on-line applications.20
For more detail explanation of this algorithm we refer to the paper (16).21
Method 3: The BiLevel-DUE method22
An improvement of the previous Method 2, proposed in (16) has been studied assuming the availability23
of travel times between Bluetooth sensors along the main paths connecting them in the network (Figure24
2(b)). The previous research reported in (31) has proved that a suitable Bluetooth sensor layout allows the25
identification of the paths between sensors and therefore the measurement of the associated travel times.26
Consequently, to implement the proposed method, the lower level DUE conducted with AimsunMeso needs27
to generate also the simulated travel time estimates from Bluetooth antennas along the corresponding paths.28
The main properties of the model are given as follows:29
input data: prior OD flow, link flow data, density data and travel time data30
solution approach: SPSA AD algorithm31
Thus, the dynamic OD estimation problem is defined by normalized least square functions f1,f2,f3and f4
in Eqn.(4) and solved by modified SPSA AD-PI approach used in Method 2.33
Method 4: The Enhanced BiLevel-DUE method34
The computational experience showed that prior OD flow information had a twofold negative influence35
avoiding the estimated matrix to move away from the prior matrix on one hand, and a high computational36
cost on the other hand. (32) proposed framework by excluding information on OD flow data given in Eqn.(4).37
The main properties of the model are given as follows:38
input data: link flow data, occupancy data and travel time data39
solution approach: SPSA CG-TR40
Thus, the dynamic OD estimation problem is defined by normalized least square functions f2,f3and f4
in Eqn.(4). This case study considers solution approach for given OD estimation problem to reduce com-42
putational time of the experiments. First, the computation of the approximated average gradient that could43
be enhanced using a conjugate gradient strategy as suggested in (33). It is known that conjugate directions44
permit to reach faster the solution than using the basic gradient method. Second, the use of a trust region45
Djukic, et al. 11
scheme is included as in (34). The main idea of trust region is to set implicitly at each iteration, a neighbor-1
hood around the current solution. Avoiding replications of matrices outside of the trust region is essential to2
reduce the computational burden. For more detail explanation of this algorithm we refer to the paper (32).3
The performance of Method 1 using prior OD demand information and link flow data is presented in Figure5
3. The estimation ability of the Method 1 demonstrates good performance, since no traffic condition data has6
been included in estimation process. This result can be explained by definition of state variables in Method7
1, i.e., deviation of OD flows captures spatial and temporal deviations between prior and real OD flows.8
Although, the Method 1 shows no significant differences between considered scenarios when estimating9
OD demand (Figure 3(a) and 3(c)) for low (D7) and high (D9) demand level, link flow results indicate10
slightly worse estimates (Figure 3(b) and 3(d)). We could infer from the results that even a good estimates11
of OD demand can produce different link flow results, which is a proof of under-determinedness of OD12
demand estimation problem.13
(a) R2for OD flows scenario D7. (b) R2for link flows scenario D7.
(c) R2for OD flows scenario D9. (d) R2for link flows scenario D9.
FIGURE 3 Method 1 results: R2for prior demand scenario D7 and D9
In line with findings described in literature and from Method 1, traffic condition data should improve14
the estimation ability of dynamic OD estimation algorithms, especially in congested networks such as one15
considered in this case study. Figure 4(a) and 4(b) provides an overview of Method 2 considering a prior OD16
demand lower then the real one (scenario D7). Information from traffic condition data, i.e., densities, has17
Djukic, et al. 12
the potential to influence the improvements in OD demand estimation from prior OD matrix, but this is not1
always the case. Results indicate that the highest estimation accuracy of Method 2 is observed for estimated2
OD flows (Figure 4(a)) and the lowest is observed for estimated link flows and densities (Figure 4(b)).3
These results show that including information on traffic conditions, despite its importance, may not suffice:4
while density allows to capture correct traffic regime at link level, its contribution at area level lowers for5
increasing network size and complexity because many OD flows combinations generate same link solution.6
Moreover, experiments show that SPSA algorithm is largely affected by a set of parameters related to its7
stochasticity and accuracy of assignment phase. Thus, appropriate refinement of values of such parameters8
has been adopted for Method 3, where different random seeds and objective function specifications have9
been used.
(a) R2for OD flows. (b) R2for densities.
(c) Flow term evolution for Method 2 and 3, d) Method 3: real vs estimated total OD flows.
FIGURE 4 Method 2 and 3 results
When travel time information is included in estimation process, the progress of Method 3 is im-11
proved over all prior demand scenarios, especially when prior OD information is close to the real traffic12
demand (Figure 4(c) and (d)). In addition, if travel time information is not included, the worst performance13
occurs when prior demand is lower then real one. Figure4(c)(d) demonstrates improvement in estimation14
accuracy when travel time information is included in estimation process. These results imply the necessity15
of establishing new techniques to extract valuable information from AVI and AVL sensors.16
Since results indicate strong dependency on the demand level of the prior OD, Figure 5illustrates17
Djukic, et al. 13
performance of Method 4 without prior OD information. When prior OD information is not included in ob-1
jective function, solution approach without defined trust region needs more iterations to converge. However,2
when solution approach based on conjugate gradient and trust region techniques is applied, computation3
time is decreased. Figure 5demonstrates that estimation accuracy increase for both OD demand and link4
flows, when prior OD demand information is not provided.
FIGURE 5 Solution approaches for Method 4: a) OD flow term evolution, b) real vs estimated total
OD flows.
Consequently, results obtained using Method 4 are improved and also a significant reduction in6
the computational time is achieved. This is very important feature for on-line applications. For example,7
Method 2 requires 40 dynamic equilibrium assignments for each iteration, resulting in 7.5 minutes for each8
assignment on the Vitoria network, a total amount of 5 hours per iteration was needed.9
In this paper, results show that despite the potential of information from advanced traffic data to improve11
OD demand estimation, the information captured by these data are not fully explored by the available es-12
timation procedures. Traffic condition data may help to correctly interpret the traffic link flow data, and to13
identify which OD flows need to be adjusted, and in which direction. However, the main issue underling14
the OD estimation methods, is spatial and temporal OD pattern given by prior OD matrix, especially in15
congested networks. It is possible to infer from the results that even a good estimates of OD demand can16
produce different link flow and traffic condition data, which is a consequence of under-determinedness of17
OD estimation problem. In addition, the computational experiments presented in this paper prove the ro-18
bustness and quality of the OD estimates exploiting AVI measurements. The computational performance of19
the Enhanced Bilevel DUE method without prior OD information and using gradients and trust region has20
been substantially increased by significantly reducing the number of function evaluations and the number of21
iterations, converging faster in this way to better demand estimates. These OD estimation methods provide22
effective tools for off-line pre-processing of prior OD data for on-line applications.23
This paper did not intend to claim the superiority of one type of traffic data over the other but24
was intended to show the potential of different types of traffic data for dynamic OD estimation. The use25
Djukic, et al. 14
of advanced traffic data to model dynamic OD demand is relatively new, and the literature still show a1
lack of empirical experiments to validate their use for dynamic OD estimation clear. The benchmark study2
presented here indicates that advanced traffic data require more research efforts and new techniques to turn3
them into usable information.4
This research is partly funded by the ITS Edulab, a collaboration between TUDelft and Rijkswaterstaat.6
Also,this research is supported by the EU COST Action TU0903 MULTITUDE Methods and tools for sup-7
porting the Use caLibration and validaTIon of Traffic simUlation moDEls project and AIMSUN - Transport8
Simulation Systems.9
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... To solve these difficulties, the development of new and more advanced sensor technologies has made data collection more efficient and they provide more information than the simple vehicle count (Djukic et al. [39]). In this new field, Automatic Vehicle Identification (AVI) sensors come to collect data that allow for more accurate studies, because they collect a type of information that no other sensor can collect in addition to the simple fact of counting and classifying vehicles by groups. ...
... Note that despite having assumed a prior flow (dashed lines in the figure) very different from the real flow (continuous-filled curve), the model is able to reproduce the real shape (dashed-dot line) of the curve, even the important distortion due to the congestion produced by link 14 where the wave crests almost disappear and the flow intensity is quite constant from 11:00 to 18:00 h. Similar curves were derived for routes 2,13,14,15,19,27,33,34,39,40 and 43 (see Table 7). ...
Full-text available
The traffic flow on road networks is dynamic in nature. Hence, a model for dynamic traffic flow estimation should be a very useful tool for administrations to make decisions aimed at better management of traffic. In fact, these decisions may in turn improve people’s quality of life and help to implement good sustainable policies to reduce the external transportation costs (congestion, accidents, travel time, etc.). Therefore, this paper deals with the problem of estimating dynamic traffic flows in road networks by proposing a model which is continuous in the time variable and that assumes the first-in-first-out (FIFO) hypothesis. In addition, the data used as model inputs come from Automatic Number of Plate Recognition (ANPR) sensors. This powerful data permits not only to directly reconstruct the route followed by each registered vehicle but also to evaluate its travel time, which in turn is also used for the flow estimation. In addition, the fundamental variable of the model is the route flow, which is a great advantage since the rest of the flows can be obtained using the conservation laws. A synthetic network is used to illustrate the proposed method, and then it is applied to the well-known Nguyen-Dupuis and Eastern Massachusetts networks to prove its usefulness and feasibility. The results on all the tested networks are very positive and the estimated flows reproduce the simulated real flows fairly well.
... In this case, the sensitivity of SLPSSI and SLPSTR is evaluated in three probable scenarios, which are usually used in modeling the traffic demand [30]. e random coefficients in four modes are considered equal to θ � [5%, 10%, 15%, 20%] for each of these scenarios: ...
Full-text available
The origin-destination (OD) matrices express the number and the pattern of trips distributed between OD pairs. OD matrix structural comparison can be used to identify different mobility patterns in the cities. A comparison of two OD matrices could express their difference from both numerical and structural aspects. Limited methods, such as the mean structural similarity (MSSIM) index and geographical window-based structural similarity index (GSSI), have been developed to compare the structural similarity (SSIM) of two matrices. These methods calculate the structural similarities of two OD matrices by grouping the OD pairs into local windows. The obtained results from the MSSIM entirely depend on the dimensions of the chosen windows. Meanwhile, the GSSI method only focuses on the geographical adjacency and correlation of zones while selecting local windows. Accordingly, this paper developed a novel method named Socioeconomy, Land-use, and Population Structural Similarity Index (SLPSSI) in which local windows are selected according to socioeconomic, land-use, and population properties for SSIM comparison of OD matrices. The proposed method was tested on Tehran’s OD matrix extracted from cell phone Geographic Position System (GPS) data. The advantage of this method over two previous ones was observed in determining the new pattern of trips on local windows and more precise detection of SSIM of the weekdays. The SLPSSI approach is up to 10 percent more accurate than the MSSIM method and up to 5.5 percent more accurate than the GSSI method. The proposed method also had a better performance on sparse OD matrices. It is capable of better determining the SSIM of sparse OD matrices by up to 8% compared with the GSSI method. Finally, the sensitivity analysis results indicate that the suggested method is robust and reliable since it is sensitive to applying both constant and random coefficients.
... The reference mobility tableau, is compared with where = * ( + * [0,1]), in which is chosen from [0.6, 0.8, 1.05] and is chosen from [0.05, 0.1, 0.15, 0.2]. Here different represents different demand scenarios that are encountered in traffic demand modeling [45]. RRNSA is a robust metric if: • For the same , RRNSA decreases when increases. ...
Human mobility similarity comparison plays a critical role in mobility estimation/prediction model evaluation, mobility clustering and mobility matching, which exerts an enormous impact on improving urban mobility, accessibility, and reliability. By expanding origin-destination matrix, we propose a concept named mobility tableau, which is an aggregated tableau representation to the population flow distributed between different location pairs of a study site and can be represented by a vector graph. Compared with traditional OD matrix-based mobility comparison, mobility tableau comparison provides high-dimensional similarity information, including volume similarity, spatial similarity, mass inclusiveness and structure similarity. A novel mobility tableaus similarity measurement method is proposed by optimizing the least spatial cost of transforming the vector graph for one mobility tableau into the other and is optimized to be efficient. The robustness of the measure is supported through several sensitive analysis on GPS based mobility tableau. The better performance of the approach compared with traditional mobility comparison methods in two case studies demonstrate the practicality and superiority, while one study is estimated mobility tableaus validation and the other is different cities' mobility tableaus comparison.
... The recent literature has highlighted how the inclusion of FCD samples in the O-D demand estimation problem positively impacts the reliability of the result [62,65], also proving that travel times and route choice probabilities derived from FCD are effective when added as traffic measurements in the optimisation problem [47,66]. ...
Full-text available
The increasing availability of historical floating car data (FCD) represents a relevant chance to improve the accuracy of model‐based traffic forecasting systems. A more precise estimation of origin–destination (O‐D) matrices is a critical issue for the successful application of traffic assignment models. The authors developed a methodology for obtaining demand matrices without any prior information, but just starting from a data set of vehicle trajectories, and without using any assignment model, as traditional correction approaches do. Several steps are considered. A data‐driven approach is applied to determine both observed departure shares from origins to destinations and static assignment matrices. Then the O‐D matrix estimation problem is formulated as a scaling problem of the observed FCD demand and carried out using as inputs: a set of traffic counts, the FCD revealed assignment matrix and the observed departure shares as an a‐priori matrix. Four different optimisation solutions are proposed. The methodology was successfully tested on the network of Turin. The results highlight the concrete opportunity to perform a data‐driven methodology that, independently from the reliability of the reference demand, minimises manual and specialised effort to build and calibrate the transportation demand models.
... Here, sensitivity of GSSI and GSTR are tested for four different cases of random scaling percentages i.e. ψ = [5%, 10%, 15%, 20%] over three types of demand scenarios. These demand scenarios are generally encountered in traffic demand modelling (refer Djukic et al. (2015)) and are as follows: ...
Full-text available
Most traditional metrics compare origin-destination (OD) matrices based on the deviations of individual OD flows and often neglect OD matrix structural information within their formulations. Limited metrics exist in literature for the structural comparison of OD matrices. One such metric is mean structural similarity index (MSSIM) that computes statistics on groups of OD pairs defined by local sliding windows. However, MSSIM can result in different values based on the choice of the size of the window. In literature, no clear consensus has been reported on the level of acceptability of the window size and the resulting MSSIM values. Addressing this need, we propose the concept of geographical window, and develop geographical window based structural similarity index (GSSI) that exploits OD matrix structure by computing statistics on the group of OD pairs that are geographically correlated. Compared to traditional sliding window based MSSIM, the advantages of GSSI technique identified from real case study application are (a) it preserves geographical integrity; (b) it compares results with physical significance; (c) it captures local travel patterns; (d) it compares large-scale sparse OD matrices; and (e) it is computationally efficient. A thorough sensitivity analyses suggest that GSSI is a robust statistical metric and has potential for practical applications such as, benchmarking different OD estimation methods; improving the quality of solution by maintaining structural consistency in the OD estimation process; and identifying gaps in the transit service by comparing local (within a geographical window) travel patterns of car and public transit.
... Ma and Qian (2018a) used the high-granular multi-source traffic data to estimate high-resolution dynamic OD demand. Emerging technologies such as AVI (Zhou and Mahmassani 2006;Antoniou et al. 2006;Djukic et al. 2015), probe vehicles (Cao et al. 2013), mobile phone location (Cascetta et al. 1993), and Bluetooth (Barceló et al. 2010) data were also employed to reconstruct dynamic O-D demands. ...
Full-text available
Two bi-level models to reconstruct origin-destination (O-D) demand under congested network are explored in terms of the observed link and route travel times, where one model inputs the known trajectories of observed route travel times and the other model uses both known and unknown trajectories of observed route travel times. The proposed models leverage both the link and route traffic information to determine the network O-D demand that minimizes the distances between the observed and estimated traffic information (O-D, link and route travel times) in the upper-level, and optimize the stochastic user equilibrium (SUE) in the lower-level. Meanwhile, the observed information of travel time can capture the relationships between traffic flow and travel cost/time in congested network. The K-means (hard assignment) and Gaussian mixture model (GMM, soft assignment) clustering methods are presented to identify the trajectories of observed route travel times. An iterative solution algorithm is proposed to solve the built O-D reconstruction models, where the method of gradient descent, the method of successive average and Expectation-Maximization (EM) algorithm are used to solve the upper-level model, lower level model, and GMM, respectively. Results from numerical experiments demonstrate the superiority of the travel time based model over the traditional flow based method in congested traffic network, and also suggest that using both the route and link information outperforms only using link information in the reconstruction of O-D demand.
... Here, sensitivity of NLOD and its structural component are tested for four different cases of random scaling percentages i.e. ψ = [5%, 10%, 15%, 20%] over three types of demand scenarios. These demand scenarios are generally encountered in traffic demand modelling (refer Djukic et al. (2015)) and are as follows: ...
Full-text available
Origin-Destination (OD) matrix is a tableau of travel demand distributed between different zonal pairs. Essentially, OD matrix provides two types of information: (a) the individual cell value represents travel demand between a specific OD pair; and (b) group of OD pairs provides insights into structural information in terms of distribution pattern of OD flows. Comparison of OD matrices should account both types of information. Limited studies in the past developed structural similarity measures, and most studies still depend on traditional measures for OD matrices comparison. Traditional performance measures are based on cell by cell comparison, and often neglect OD matrix structural information within their formulations. We propose a methodology that adopts the fundamentals of Levenshtein distance, traditionally used to compare sequences of strings, and extends it to quantify the structural comparison of OD matrices. The novel performance measure is named as normalised Levenshtein distance for OD matrices (NLOD). The results of sensitivity analysis support NLOD to be a robust statistical measure for holistic comparison of OD matrices. The study demonstrates the practicality of the approach with a case study application on real Bluetooth based OD matrices from the Brisbane City Council (BCC) region, Australia.
... Examples of such data sources included in demand calibration are, for example, speeds (Balakrishna, 2006;Lee and Ozbay, 2009;Cipriani et al., 2011;Frederix et al., 2011); link travel times (Ben-Akiva et al., 2012); speeds and densities (Antoniou, 2004;Huang, 2010); and link travel times and densities (Zhou et al., 2012). These additional measurements of link conditions can be obtained from conventional detectors (e.g., inductive loop detectors) and they pro- Yamamoto et al., 2009;Cao et al., 2013;Nigro et al., 2018), Bluetooth/Wi-Fi devices (e.g., Barcel6 et al., 2010Barcel6 et al., , 2012Djukic et al., 2015), roadside cameras (e.g., Asakura et al., 2000;Mishalani et al., 2002), and tag/plate readers (e.g., Dixon and Rilett, 2002;Eisenman and List, 2004;Zhou and Mahmassani, 2006;Antoniou et al., 2006;Sun and Feng, 2011;Cipriani et al., 2014). Reviews of heterogeneous traffic data used for calibration are presented in Djukic (2014) andTympakianaki (2018). ...
Full-text available
Computationally efficient offline demand calibration algorithms for large-scale stochastic traffic simulation models
... In the literature, the spatial pattern of traffic between origins and destinations is usually expressed by a trip distribution matrix based on the undirected graph model of traffic network and widely used in the traffic state estimation [28], traffic flow prediction [2] or traffic flow demand estimation [29] and so forth. To extend the trip distribution matrix to the digraph model, we propose the concepts of turning rate and traffic transition probability (TTP) which are capable of accurately capturing the traffic distribution among roads with road intersections. ...
... In the literature, the spatial pattern of traffic between origins and destinations is usually expressed by a trip distribution matrix based on the undirected graph model of traffic network and widely used in the traffic state estimation [13], traffic flow prediction [14] or traffic flow demand estimation [15] and so forth. To extend the trip distribution matrix to the digraph model, we propose the concepts of turning rate and traffic transition probability which are capable of accurately capturing the traffic distribution among roads with road intersections. ...
Conference Paper
Full-text available
One of the key traffic variables required for both ex post and ex ante evaluation of traffic management and policy measures are OD demand matrices. Since these are generally not measured directly, OD matrices are estimated on the basis of aggregate quantities (e.g. counts, travel times), prior OD information and many assumptions and (parameterized) physical laws relating these to the OD flows, such as traffic assignment models. Without ground truth OD information, however, it is difficult if not impossible to assess the quality of an OD estimation method, particularly since there are so many unknowns involved. One alternative indicator for the quality of an OD estimation method then is the sensitivity of the method to (and robustness against) random and structural perturbations of the input (data from sensors, prior OD matrices) on a few typical test networks. In this paper we propose such an assessment methodology based on the Latin Hypercube (LHC) method, which is an efficient alternative for Monte Carlo sampling and particularly suited for high-dimensional estimation problems. We demonstrate the methodology on a real urban corridor network for one well-known OD estimation method (the minimum information estimation method) to illustrate which results can be obtained and how these can be used to benchmark different OD estimation methods.
Full-text available
Origin destination (O-D) trip matrices that describe the patterns of traffic behavior across a network are the primary data input used in principal traffic models and, therefore, a critical requirement in all advanced systems supported by dynamic traffic assignment models. However, because O-D matrices are not directly observable, the current practice consists of adjusting an initial or seed matrix from link flow counts that are provided by an existing layout of traffic-counting stations. The availability of new traffic measurements provided by information and communication technologies (ICT) allows more efficient algorithms, namely for real-time estimation of O-D matrices that are based on modified Kalman filtering approaches to exploit the new data. The quality of the estimations depends on various factors such as the penetration of the ICT devices, the detection layout, and the quality of the initial information. The feasibility of real-time applications depends on the computational performance of the proposed algorithms for urban networks of sensitive size. This paper presents the results of a set of computational experiments with a microscopic simulation of the network of Barcelona's central business district that explore the sensitivity of the Kalman filter estimates in relation to design factor values.
Full-text available
The problem of estimating time-varying origin-destination matrices from time series of traffic counts is extended to allow for the use of partial vehicle trajectory observations. These may be obtained by using automated vehicle identification (AVI), for example, automated license plate recognition, but they may also originate from floating car data. The central problem definition allows for the use of data from induction loops and AVI equipment at arbitrary (but fixed) locations and allows for the presence of random error in traffic counts and misrecognition at the AVI stations. Although the described methods may be extended to more complex networks, the application addressed involves a single highway corridor in which no route choice alternatives exist. Analysis of the problem leads to an expression for the mutual dependencies between link volume observations and AVI data and the formulation of an estimation problem with inequality constraints. A number of traditional estimation procedures such as discounted constrained least squares (DCLS) and the Kalman filter are described, and a new procedure referred to as Bayesian updating is proposed. The advantage of this new procedure is that it deals with the inequality constraints in an appropriate statistical manner. Experiments with a large number of synthetic data sets indicate in all cases a reduction of the error of estimation due to usage of trajectory counts and, compared with the traditional DCLS and Kalman filtering methods, a superior performance of the Bayesian updating procedure.
Conference Paper
The paper presents an in-depth analysis of the bi-level gradient approximation approach for dynamic traffic demand estimation. Initially, a sensitivity analysis of the parameters of Simultaneous Perturbation Stochastic Approximation method (SPSA) with Asymmetric Design (AD) and Polynomial Interpolation (PI), firstly proposed by authors in 2011, is presented. Then, an adaptive method based on the second order SPSA AD-PI approach, is explored; finally, some new advances of the estimation method are proposed in order to keep under control traffic phenomena during the estimation.
This paper presents an in-depth analysis of the bi-level gradient approximation approach for dynamic traffic demand adjustment and the development of new adaptive approaches. Initially, a comparison between the simultaneous perturbation stochastic approximation (SPSA), asymmetric design (AD), polynomial interpolation (PI) method, which was first proposed by authors in 2010–2011, and its second-order development is presented; then, a sensitivity analysis of the parameters of the SPSA AD-PI is reported; finally, some new advances of the estimation method based on an adaptive approach are proposed and evaluated on a real test network.
Estimating origin-destination trip matrices from link traffic counts has been a subject of substantial research. It is well known that the accuracy of the resulting estimated origin-destination (O-D) matrix largely depends on the employed estimation approach itself, errors of the input data, and an appropriate set of links from which flow information should be collected. Previous studies have overwhelmingly focused on the development of various estimation models, while paying very limited attention to the traffic counting location and error bound issues. Recognizing their interdependence, this study makes a joint investigation of the traffic counting location, estimation method, and error bound in an integrated manner, while taking into account the effects of various route choice assumptions made in the traffic assignment models and the levels of traffic congestion on the network. A few useful properties of the counting location rules and error bound measures for the O-D matrix estimation problem are demonstrated theoretically and numerically.