A Combined DTA Approach for Road Network Robustness Analysis

Minwei Li

, Henk J. van Zuylen

and Huimin Wen

Beijing Transportation Research Center, Liu Li Qiao Nan Li No. 9, Fengtai Disctric, Beijing, P.R. China

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

 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

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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

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(1)

Where υ

(t) is the average link speed and f

(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

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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.

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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

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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.

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