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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`

o7

Universitat Politcnica de Catalunya BarcelonaTECH, inLab FIB, Spain8

jaume.barcelo@upc.edu9

Manuel Bullejos10

Universitat Politcnica de Catalunya BarcelonaTECH, inLab FIB, Spain11

manuel.bullejos@upc.edu12

Lidia Montero13

Universitat Politcnica de Catalunya BarcelonaTECH, Departament dEstadstica i Investigaci14

Operativa, Spain15

lidia.montero@tudelft.nl16

Ernesto Cipriani17

Universit Degli Studi Roma Tre, Department of Civil Engineering, Italy18

ernesto.cipriani@uniroma3.it19

Hans van Lint20

Delft University of Technology, Department of Transport and Planning, The Netherlands21

j.w.c.vanLint@tudelft.nl22

Serge P. Hoogendoorn23

Delft University of Technology, Department of Transport and Planning, The Netherlands24

s.p.hoogendoorn@tudelft.nl25

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

28

29

30

Submitted to the 94rd Annual Meeting of the Transportation Research Board, 11-15 January 2015, Wash-31

ington D.C.32

1

ABSTRACT1

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

INTRODUCTION1

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

TRAFFIC DATA FOR ESTIMATION OF DYNAMIC OD DEMAND40

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

Traffic

operations

Route

choice

OD ﬂow !

data!

Link ﬂow !

data!

Trafﬁc condition

data!

(a) Clasifﬁcation of input data for dynamic OD demand estimation.

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(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

BENCHMARK STUDY17

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

11

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

xLD

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:

xRD

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

xHD

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

SELECTION OF OD DEMAND ESTIMATION METHODS12

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

comparison.19

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|i∈I}is the OD demand. The22

historical or prior OD matrix ˜x ={˜xi|i∈I}is a matrix deﬁned in OD ﬂow scenarios that needs to be23

updated. y={yl|l∈L}are the link ﬂow data. Link ﬂow data and trafﬁc condition data (e.g., speed,24

density, occupancy) are available on links ˆ

L⊆L. Thus, the observed link ﬂows on those links are denoted25

as ˜y ={˜yl|l∈ˆ

L}and observed trafﬁc condition data are denoted as ˜c ={˜cl|l∈ˆ

L}. Additional trafﬁc26

condition data, such as travel times, collected from AVI sensors available on links ˜

L⊆Lare 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

x∈S

[f1(x,˜x) + f2(y(x),˜y) + f3(c(x),˜c) + f4(z(x),˜z)]

subject to

y=assign(x),

x≥0,

y≥0

(4)

where xis the unknown OD demand vector ˆx = [ˆx1, ..., ˆxT], for time intervals t∈1,2, ..., 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

follows:9

•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

32

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

41

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

RESULTS4

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

10

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.

5

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

CONCLUSIONS10

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

ACKNOWLEDGMENT5

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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