A Combined DTA Approach for Road Network Robustness Analysis
Minwei Li
1
, Henk J. van Zuylen
2
and Huimin Wen
1
1
Beijing Transportation Research Center, Liu Li Qiao Nan Li No. 9, Fengtai Disctric, Beijing, P.R. China
2
Department of Transport and Planning, Delft University of Technology, Delft, The Netherlands
Keywords: Combined DTA, Road Network, Robustness.
Abstract: In this paper a DTA model with two components is described: a user equilibrium (UE) model and an en-
route model. The UE model is called MARPLE (Model for Assignment and Regional Policy Evaluation)
that uses an iterative process to achieve equilibrium (deterministic or stochastic) (Taale et al., 2004). In each
iteration a network loading model is used to determine travel times. MARPLE en-route is developed based
on the MARPLE model, which runs one-shot simulation starting with the equilibrium assignment results. It
updates the path sets and path costs after each evaluation interval during the simulation. Travellers will
update their path choice according to the instantaneous path costs at the end of each interval using some
heuristic rules. A systematic framework for the robustness study of road networks is built up by combining
both DTA approaches, in which the results of UE approach are used as references and en-route approach is
used to simulate the network response for non-recurrent and short-term disturbances. The results for a
hypothetical network show that for evaluating the network performance after such disturbances, the en-route
assignment approach based on UE assignment results shows its capability and advantages in appropriately
representing dynamic drivers’ route choice behaviour when facing unfamiliar or unexpected situations on
the route.
1 INTRODUCTION
Network robustness, defined as the ability of a
system to continue to operate correctly under a wide
range of operational conditions, and to fail
gracefully outside of that range (Gribble, 2001), has
been widely developed in large-scale networks such
as electronics and internet. It also became an
important topic for transport networks. In that
context robustness can be considered as the ability
of the system to keep a certain capacity level to
handle traffic demand under abnormal situations.
Dynamic Traffic Assignment (DTA) models play an
important role in almost all the network robustness
studies, because they take into account the reaction
of drivers concerning route choice. Two approaches
of DTA, user equilibrium (UE) assignment and en-
route assignment, are separately implemented for
different categories of network robustness and/or
reliability studies. Basically, UE assignment models
are used by many researchers when considering
random changes in supply or/and demand of a
transportation network. En-route assignment models
are normally used to evaluate the effectiveness of
certain traffic management schemes or measures for
emergency situations or a short-term disturbance in
the network. But, so far, little work has been done to
develop a combined DTA model, to realize both UE
and en-route assignment approaches, with the aim to
be able to do a complete network robustness study.
A main task of network robustness studies is to
assess whether an existing transport network system
is susceptible to random failures (i.e. severe
accidents) and destructive events (i.e. earthquake or
terrorist attack). More important, we would like to
know which parts (so-called hot or weak spots) of
the network are most fragile, or vulnerable to the
external disturbances, so that both infrastructure and
control schemes could be improved in such a way
that the deterioration of the network caused by those
disturbances is mitigated.
Network robustness is rather new in the
transportation domain and a limited amount of
literature references could be found, such as Chiu
and Mahmassani (2002) and Kaysi et al. (2003).
Most of the methods implemented in these studies
are borrowed from network reliability studies, which
is in fact a quite different concept from robustness.
Network reliability is defined as the probability of a
device or a system performing adequately according
315
Li M., J. van Zuylen H. and Wen H..
A Combined DTA Approach for Road Network Robustness Analysis.
DOI: 10.5220/0004055803150320
In Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH-2012),
pages 315-320
ISBN: 978-989-8565-20-4
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)
to its purpose for the period of time intended under
the operating conditions encountered (Henley and
Kumamoto, 1981; Wakabayashi and Iida, 1992). It
means that reliability studies are generally
concerned with probabilities only. And reliability
problems are rooted in the uncertainty of traffic
conditions. In most of the existing reliability studies
of road networks, stochastic user equilibrium (SUE)
assignment models are implemented representing
choice behaviour, especially route choice behaviour
of travellers, to get the values of some chosen
performance measures, such as the work of Bell and
Iida (1997), Chen et al. (1999), Chen et al. (2002)
and Du and Nicholson (1997).
However, UE is only an ideal situation that never
appears in reality due to many uncertainties in both
demand and supply. So, it is mainly meaningful for
network planning purposes. But for the network
robustness problem that focuses more on the
evaluation of network performance and assessment
of its ability to handle unpredictable incidents, this
equilibrium assumption is no longer suitable for the
non-recurrent and short-term congestion. In order to
achieve more accurate and realistic values of
network performance measures after the occurrence
of such disturbances, appropriate dynamic traffic
assignment models, such as en-route assignment
models, must be developed to realise more accurate
description or simulation of the choice behaviour of
travellers.
The objective of this paper is to develop a
method based on a systematic framework for the
comprehensive evaluation of robustness of a road
network. The paper is organised as follows. Section
2 briefly describes the features and differences of
UE assignment approach and en-route assignment
approach, highlights the importance of en-route
assignment approach in network robustness studies.
Section 3 provides a simulation-based systematic
framework for network reliability and robustness
studies, founded on the combination of above-
mentioned two DTA approaches. In Section 4, the
framework proposed in this paper is illustrated with
a simple network. Section 5 summarises and
analyses the results.
2 DTA MODELS
A traffic assignment model, especially a dynamic
traffic assignment (DTA) model, is the core of any
model based reliability and robustness study of
transportation networks. A DTA model typically
describes route choice by an assignment sub-model,
and the way in which traffic propagates through a
network by a network loading sub-model. A realistic
DTA model should be able to capture "over-
capacity" queuing, because it follows the trajectories
in time and space of the vehicles. Basically, two
distinct approaches exist to model route choice and
network loading in DTA: equilibrium assignment
and en-route assignment.
2.1 Equilibrium Assignment
Wardrop (1952) was the first to propose the
following condition for a deterministic user
equilibrium (DUE): for each OD pair, the costs of
the paths actually used are equal, and they are less
than or equal to the costs of each unused path
(known as Wardrop's first principle). It assumes that
each traveller has perfect information and chooses a
route that minimises his/her travel time or travel
costs, such that all travellers between the same OD
have the same travel time or cost. A consequence of
the DUE principle is that all used paths for each OD
pair have the same minimum costs. Unfortunately,
this is not a realistic description of loaded and
congested traffic networks (Slavin, 1996).
The stochastic user equilibrium (SUE) was
(amongst others) detailedly illustrated by Daganzo
and Sheffi (1997). They defined the equilibrium
state of traffic flow on a network as a SUE when
every user chooses his/her path such that his/her
perceived travel time or cost between origin and
destination is minimal. But perceived travel time or
cost on a link varies randomly across users.
In the equilibrium assignment problem, only pre-
trip path choice and iterative process are considered.
It consists of two main components: a method to
determine a new set of time-dependent path flows
given the experienced path travel times in the
previous iteration, and a method to determine the
actual travel times that result from a given set of
path flow rates.
2.2 En-route Assignment
In the en-route assignment problem, the routing
mechanism consists of successive executions of a set
of behavioural rules, which determine how drivers
iteratively react to information received en-route.
Information may be available at discrete points in
time, discrete points in space, or continuously in
both space and time. Some information may only be
available to a certain class of vehicles. Typically, the
information strategy is an exogenous input. Drivers’
responses to information can be modelled by some
SIMULTECH 2012 - 2nd International Conference on Simulation and Modeling Methodologies, Technologies and
Applications
316
heuristic rules that may involve one or more
parameters, such as the ‘penetration rate’ or the
‘compliance rate’. Another input to this problem is a
suitable pre-trip assignment. An en-route assignment
thus only requires running a single dynamic loading
of the demand onto the network over the time period
of interest apart from the assignments need to
determine the initial route choice.
2.3 Roles of Two Assignment
Approaches in Robustness Study
If an equilibrium assignment model is available, it is
possible to find the equilibrium traffic pattern in a
transportation network, taking into account all kinds
of uncertainties. Network robustness studies use
these patterns, as well as certain aggregated network
performance measures, to perform comparisons and
analyses. But equilibrium assignment approach is
not possible to represent the network situation under
irregular and non-recurrent incidents, such as
accidents. Thus it can be used in the network
planning domain to analyse the impact of repeatable
and long-term network changes, like introducing
new measures of intelligent transportation system
(ITS) or adding a new link to the network.
On the other hand, according to the features of
the en-route assignment approach, it can be used for
the analysis of unrepeatable and short-term
incidents, such as accidents or a natural disaster. But
if a DTA model is only capable of en-route
assignment, it is necessary to find the exogenous
input, especially the pre-trip assignment, from other
simulation tools or by other means. It is logical that
the results of a (dynamic) equilibrium assignment
can be used as the basic scenario, i.e. reference, for
the en-route assignment because it achieves an
‘ideal’ long-term equilibrium status for a chosen
transportation network.
3 FRAMEWORK FOR
ROBUSTNESS STUDIES
Based on the features of both assignment approaches
and the requirements of robustness studies of road
networks, a simulation-based two-stage systematic
framework is designed by integrating both an
equilibrium assignment model and en-route
assignment model (Figure 1). In this framework, the
equilibrium assignment model is a macroscopic
model named MARPLE (Taale et al., 2004). The en-
route assignment model, MARPLE-e, is developed
based on MARPLE, by using successively the
network loading model and the route choice model
for every pre-defined discrete interval.
Figure 1: Systematic framework for robustness studies of
road network.
In Stage One shown in the left part of the
framework, only the equilibrium assignment for the
basic situation is carried out. The results are used as
the reference of network performance for the
following robustness studies, as well as the initial
assignment input for the en-route assignment in
Stage Two. Several indicators are derived for
network performance comparisons as follows.
TTT: total travel time for the whole simulation
period [veh•h];
TTD: total travel distance for the whole
simulation period [veh•km];
TD: total delay for the whole simulation period
[veh•h];
NAS(t): equilibrium dynamic network average
speed within period t [km/h], defined as

(1)
Where υ
a
(t) is the average link speed and f
a
(t) is
the link flow of link a during period t in the
equilibrium situation;
NL(t): network load within period t [veh•h],
defined as

(2)
Stage Two
Reliability & Robustness Study
Stage One
Equilibrium Building
Network Building
Route Searching
Dynamic Equilibrium
Assignment
Demand
Control
ITS...
Equilibrium
Path Cost and
Path Flow
New Route Searching
Dynamic En-route
Assignment
External
Disturbance
Dynamic Equilibrium
Assignment
Network Rebuilding
Equilibrium System
Performance Z*
Demand
Control
ITS...
Long-term user
optimal Path Cost
and Path Flow
Short-term user
optimal Path Cost
and Path Flow
Long-term System
Performance Z
Short-term System
Performance Z
Network reliability and robustness study based on
1. Aggregated system performance indicator Z
2. Spatial-temporal effects of road network performance
3. Vulnerable links analysis
4. influence of traffic control strategy to network reliability and
robustness by bi-level method (M. Bell, 2000)
A Combined DTA Approach for Road Network Robustness Analysis
317
In robustness studies, random disturbances on
individual links will be introduced to the network in
Stage Two. Depending on the duration (long-term or
short-term) of the disturbance, either the equilibrium
assignment approach or the en-route assignment
approach could be used for the simulation
respectively. Besides the above-mentioned five
indicators, the loading multiplier NLM in equation (3)
is also used as a robustness indicator. The so-called
hot spots in the network are those arcs with the
smallest loading multiplier.
(3)
in which NL
equ
(t) is the result of equilibrium
assignment.
4 CASE STUDY
To demonstrate how the framework and related
assignment models works for robustness studies, a
simple, hypothetical network as shown in Figure 2 is
tested. The network consists of 10 nodes, 11 one-
directional links, and three OD pairs, in which origin
2 (O2) and destination 2 (D2) represent a town
centre.
Figure 2: Test network.
In Table 1, link characteristics are listed. Link 3 and
7 form a faster, but longer motorway, and link 11 is
a parallel, slower arterial. Links 4, 5, 6, and 8 are
urban links with lower speed and capacity, which are
the connectors between the motorway and the town
centre. There are in total 7 routes available for all the
OD pairs as listed in Table 2. Route 3 including Link
11 is not used under normal conditions.
Table1: Link characteristics.
Table 2: Route information for the OD pairs.
In case studies, simple incident scenarios are
designed. In each scenario, one and only one link,
except for link 1 and 10, is deteriorated during the
peak hour. In this hour, the capacity of the chosen
link is set as the certain ratio (from 0.0 to 1.0) to the
designed capacity. Before and after the peak hour,
the network works properly. In all scenarios, 70% of
the travellers are assumed to get instant and perfect
knowledge about the network conditions and to
update their paths accordingly. The rest 30% stay on
their pre-defined paths.
For each scenario, a 3.5-hour demand profile as
shown in Figure 3 is used, representing a ‘warming-
peak-cooling’ loading procedure. The last half an
hour is designed with zero demand to clear up the
network
Figure 3: Profile of the demand ratio (related to peak-hour
value).
4.1 Aggregated Indicators
In table 3, the values of TTT, TTD and TD for the
scenarios that the link is 100% blocked are listed.
The values in the parenthesis are the ratios to the
equilibrium ones (when link 11 is blocked). The
highest TD values appear when motorway links (link
2, 3, 7 and 9) are blocked. For the arterial links, the
influence of off-ramps (link 4 and 5) is much higher
than on-ramps (link 6 and 8).
SIMULTECH 2012 - 2nd International Conference on Simulation and Modeling Methodologies, Technologies and
Applications
318
Table 3: Aggregated network performance indicators
when links are blocked
* means route 3 is used in that case
4.2 Dynamic Indicators
Since en-route assignment is just a one-shot
procedure, using indicators NAS(t) (Figure 4) and
NL(t) (Figure 5) can describe the dynamics of the
network performances more clearly. In two figures,
the equilibrium scenario and the scenarios with link
3, 4 and 9 completely blocked are presented. In
Figure 4, it is obvious that after blocking link 3 and
9, network speed drops much more and longer than
other scenarios. In Figure 5, the curve for the
scenario when link 3 is blocked shows that although
the blockage is removed after the peak hour (interval
72) and the link capacity returns to its desired value,
it takes about one hour (till interval 100) for the total
network load to recover to the normal value. This
indicates the remarkable after effect level of the
incident.
Figure 4: Changes of NAS for some scenarios.
Figure 5: Changes of NL for some scenarios.
4.3 Sensitivity Analysis
Sensitivity information provides the change of the
network loading multiplier calculated by equation
(3) with respect to the changes of service level of
each link capacity. Level of service is defined as the
remaining capacity of the link after the incident on
the link. Figure 6 shows the values of NLM of the
scenarios with different level of services when the
capacity on links 3, 7, 8 and 9 drops respectively.
The curve of link 9 drops first and also the fastest if
the service level decreases in those curves, because
link 9 is a common link for both OD pairs (O1, D1)
and (O2, D1). So to a certain extent, link 9 is one hot
spot in this network.
Figure 7: Changes of Network Loading Multiplier (NLM)
in relation with different level of service.
5 CONCLUSIONS AND
DISCUSSION
In this paper, we presented a new simulation-based
systematic framework for the study of robustness in
road networks and tested its feasibility by evaluating
several network performance indicators. It is the first
time that both equilibrium assignment and en-route
assignment approaches are integrated in the study of
A Combined DTA Approach for Road Network Robustness Analysis
319
robustness of road networks. This framework can be
considered as a complete structure. The reason is
simple: the equilibrium assignment model can
represent normal daily situations and describe the
effects of long-term disturbances, while the en-route
assignment model can represent network
performance after non-recurrent and short-term
disturbances. Neither model shall be neglected due
to the different functionality for different conditions.
In addition, several time-dependent network
performance indicators, next to some common
aggregated indicators, have been derived for both
DTA approaches. A simple hypothetical network,
which represents a typical city network with a
motorway and parallel low-level path bypass, has
been used for testing. After introducing incidents on
different links, numerical results demonstrated the
feasibility of the robustness evaluation procedure.
Some general remarks on the robustness of such
kind of network can be made:
1. Common links that are used by multiple
OD pairs have more influence on the network
performance;
2. Disturbances on off-ramps have more
deterioration effects to the network, because they
will immediately influence the motorway traffic and
cause high delay;
3. Time-dependent indicators NAS(t) and
NL(t), and NLM derived from NL(t), can clearly
describe the changes of the network performance, as
well as the robustness of the network.
A potential research topic of road network
robustness is to incorporate robustness constraints to
the network design problem. Some researchers, such
as Yin et al. (2004) and Zhang and Levinson (2004),
have introduced the concept of robustness to
network design and upgrade. But due to the
simplicity of their static assignment models, the
understanding of the disturbances and their impact
on the robustness performance of a road network is
not suitable for describing the dynamics. Thus, our
framework can improve the quality of related studies
for network design and planning purpose.
REFERENCES
Bell, M. G. H., (2000) A Game Theory Approach to
Measuring the Performance Reliability of Transport
Networks, Transportation Research Part B, Vol. 34,
pp. 533-545
Bell, M. G. H., Iida, Y., (1997) Network Reliability,
Transportation Network Analysis, England, John
Wiley & Sons, West Sussex, pp. 179-192
Chen, A., Yang, H., Lo, H. K., Tang, W., (1999) A
Capacity Related Reliability for Transportation
Networks, Journal of Advanced Transport, Vol. 33(2),
pp. 183-200
Chen, A., Yang, H., Lo, H., Tang, W., (2002) Capacity
Reliability of a Road Network: An Assessment
Methodology and Numerical Results, Transportation
Research Part B, Vol. 36, pp. 225-252
Chiu Y. C., and Mahmassani H. S., (2002) Hybrid Real-
time Dynamic Traffic Assignment Approach for
Robust Network Performance, Transportation
Research Record, No. 1783: Transportation Network
Modelling, pp. 89-97
Daganzo, C. F., Sheffi, Y., (1997) On Stochastic Models
of Traffic Assignment, Transportation Science, Vol.
11, No. 3, pp. 253-274
Du, Z. P., Nicholson, A., (1997) Degradable
Transportation Systems: Sensitivity and Reliability
Analysis, Transportation Research Part B, Vol. 31, pp.
225-237
Gribble, S. D., (2001) Robustness in Complex Systems,
In: Proceedings of the 8th Workshop on Hot Topics in
Operation Systems (HotOS-VIII), May,
Elmau/Oberbayern, Germany
Henley, E. J., Kumamoto H., (1981) Reliability
Engineering and Risk Assessment, NJ, Prentice-Hall,
Englewood Cliffs
Kaysi I. A., Moghrabi M. S., and Mahmassani H. S.,
(2003) Hot Spot Management Benefits: Robustness
Analysis for a Congested Developing City, Journal of
Transportation Engineering, pp 203-211
Slavin, H., (1996) An Integrated, Dynamic Approach to
Travel Demand Forecasting, Transportation, Vol. 23,
pp. 313-350
Taale, H., Westerman, M., Stoelhorst, H. and van
Amelsfort, D., (2004) Regional and Sustain-able
Traffic Management in The Netherlands:
Methodology and Applications, In: Proceedings of the
European Transport Conference 2004, October 4-6,
Strasbourg, France, Association for European
Transport
Wakabayashi, H., Iida, Y., (1992) Upper and Lower
bounds of Terminal Reliability of Road Networks: An
Efficient Method with Boolean Algebra, Journal of
Natural Diaster Science, Vol. 14, pp 29-44
Wardrop, J. G., (1952) Some Theoretical Aspects of Road
Traffic Research, In: Proceedings of the Institute of
Civil Engineers, Part II, pp. 325-378
Yin Y. F., Madanat S., Lu X. Y., (2005), Robust
Improvement Schemes for Road Networks Under
Demand Uncertainty, In: CD-ROM of 84rd Annual
Meeting of Transportation Research Board, January 9-
13, Washington, D.C.
Zhang L., Levinson, D., (2004) Investing for Robustness
and Reliability in Transportation Networks, In:
Proceedings of 2nd International Symposium on
Transport Network Reliability, August 20-24,
Christchurch & Queenstown, New Zealand, pp. 160-
166
SIMULTECH 2012 - 2nd International Conference on Simulation and Modeling Methodologies, Technologies and
Applications
320