A Road Provision Model Using System Dynamics
by
Khaled A Abbas
Department of Civil Engineering
University of Newcastle upon Tyne
Newcastle upon Tyne NEl 7RU, U.K.
ABSTRACT
One of the most difficult tasks facing highway administrators is how to
efficiently manage the allocation of road funds. In this paper a
comprehensible, easy-to-use, highway management tool is presented. This tool
takes the form of a computer simulation model which is intended to assist
managers of a network of highways to make better decisions concerning the
allocation of scarce funds. It mainly simulates the effects of different
investment strategies and maintenance options on the road network. This is
done by tracing the life-cycle costs of the major activities of providing and
maintaining the road system, and by considering the effects that these
activities have on the state and performance of the road network.
1. INTRODUCTION
The continued development of the road network is looked upon as a necessity
that contributes to the prosperity and wellbeing of a country. Construction,
maintenance and upgrading of roads constitute a large portion of the transport
budget in many countries, yet the growing conflict between the requirements
of the road network and the available financial resources is one of the most
serious problems that highway authorities have to deal with. There is a need
for simplified planning techniques that are capable of testing alternative
strategies for investing in the road network system.
This financial stringency requires the development of road management systems
to provide support for highway decision-makers so that they can make more
rational, informed decisions. These decisions should be targeted towards
achieving a better management and control of the road network system.
Road management systems can be described as computerised, analytic tools that
consider the whole life-costing of alternative strategies for the road
network. These tools enable the testing of alternative management and planning
programmes for the highway sector.
2. PURPOSE AND APPROACH
The main purpose of this study is to construct a dynamic, simulation model
that describes the structural, feedback interactions of the road network
system. The model is meant to analyse the impacts of proposed changes in the
funding levels, as well as in the structure of the priorities involved in the
allocation of road funds.
The System Dynamics methodology, (Forrester 1968), is used in this study as
the modelling framework within which the road management model is developed.
System Dynamics '90
The model simulates the effects of different road investment strategies. This
is done by tracing the life-cycle costs of the activities which are necessary
to develop and maintain the road system, and establishing the impacts that
these activities have on the condition and performance of the road network.
The main objectives of the model are as listed below.
(1) To model the process involved in the allocation of road funds. This
allocation process is meant to satisfy, (in a relative sense), the
financial requirements of the changing physical condition of the road
network. The two main constraints that are considered in this process
of allocation include: the level of available funds and the priorities
for allocating road funds to the main activities of the road network.
(2) To provide better insight and understanding of the dynamic, feedback
nature of the road system.
(3) To act as an experimental management tool for assessing the short- and
long-term consequences of different road strategies on the physical
development of the road system. A road strategy involves the
determination of; road funding levels, priorities for allocating road
funds and time intervention criteria for performing maintenance
activities.
(4) To assist in management and control of the road system.
(5) To provide a set of performance indicators that describe the state of
the road system at any point in its lifetime.
3. MODEL DESCRIPTION
The road provision model consists of two main parts, as shown in Figure 1.
The first, is the user interface module, the second is the System Dynamics
road provision module, see (Abbas 1990).
In this section, the System Dynamics conceptual model is introduced. The
feedback interaction between demand and supply of the road network system is
explicitly considered. The main assumptions and some of the important
variables of the model are explained. Causal diagrams are considered to be
an advanced and comprehensible step of the System Dynamics modelling
procedure. This paper presents the fundamental, causal mechanisms underlying
the structure of the System Dynamics road provision model.
3.1 Managing the Process of Allocation of Road Funds
Each time interval of the simulation, road funds are allocated among five
road system activities. Referring to Figure 2 the main activities of the road
provision model include:
(1) road administration activity;
(2) routine road maintenance activity;
(3) road construction activity;
(4) road rehabilitation-reconstruction, i.e. restoration activity; and
(5) periodic road maintenance activity.
This investment allocation process is performed in a dynamic fashion so as
to be relatively consistent with the competing priorities and the changing
demands of the road network system. The priorities for the allocation of
System Dynamics '90 3
road funds are set by the modeller to be in accordance with the most commonly
practised management of road funds in developing regions. The priorities are
as shown in Table 1.
Table 1: Priorities for Allocation of Road Funds
The Road Network Funds Priority
Road Administration Funds 1
Routine Road Maintenance Funds 2
Road Construction Funds (***) 3
Road Rehabilitation-Reconstruction
Funds (#**) 3
Periodic Road Maintenance Funds 5
(*#**) Both construction and restoration of roads have the same priority
regarding the allocation of road funds. This assumption is based on the fact
that both construction and restoration of roads will eventually lead to
kilometres of roads starting new life cycles. Absolute allocation is
determined using allocation factors. These factors are computed according
to the financial demand of the road construction activiy versus that of the
road restoration activity.
The stated structure, describing the priorities, considered in the allocation
of road funds may be varied to test the effects on road network performance
of alternative priorities for the allocation of road funds.
3.2 Main Assumptions and Definitions of the Model
In this section of the paper, the reader is advised to refer to the causal
diagrams describing the structure of the model and presented throughout
Figures 2 to 9. This section is meant to explain the main implicit assumptions
and definitions of the System Dynamics road provision model.
- Total Permitted Road Kilometres, (refer to Figure 5), is a parameter
that explicitly caters for the constraint of land use planning, taking
into account the following constants:
- maximum land area of the region;
= maximum allowed ratio of road area to land area; and
- average road width.
The constants are exogenously specified by the model user. On the
other hand, it is to be noted that another System Dynamics model is
System Dynamics ‘90
currently under development which is expected to explicitly model the
dynamics of demand for road cosntruction.
Recent field surveys, supplemented by the judgement of engineers of
the World Bank, suggest it is possible to distribute a country’s roads
among three classes of condition: good, fair, and poor. A road in good
condition requires only routine maintenance to remain that way. A road
in fair condition needs resurfacing , i.e. periodic maintenance. A road
in poor condition has deteriorated to the point that it requires either
partial or full reconstruction, i.e. restoration. (Harral 1988)
Good To Fair Road Kilometres Rate, (refer to Figures 7 & 8), is the
rate that dynamically determines the number of kilometres of roads
degrading from good to fair condition, over the incremental time
intervals of the simulation. Periodic road maintenance of a road is
considered necessary once the road condition degrades from good to
fair. It is vital to perform the periodic maintenance on time.
Periodic maintenance certainly betters the existing condition of a road
and prolongs its life-cycle. There are different views pertaining to
the exact extent of this betterment, but discussion of these views is
outside the scope of this paper.
Fair To Poor Road Kilometres Rate, (refer to Figures 6 & 8), is the
rate that dynamically determines the number of kilometres of roads
degrading from fair to poor condition, over the incremental time
intervals of the simulation. Restoration of a road is considered
necessary once the road condition falls from fair to poor. Once
restorated, the road kilometres restart a new life-cycle.
Good-Fair Condition Road Kilometres: Level, (refer to Figures 4 & 8),
represents the accumulation of road kilometres, which are in a good or
fair condition, over time, and hence requiring annual routine
maintenace.
To avoid double counting in the maintenance activities, Periodic Road
Maintenance Rate is subtracted from the Routine Road Maintenance Rate.
This avoids performing routine maintenance to road kilometres, which are
already expected to be periodically maintained, (refer to Figure 4).
Evaluation of different road strategies is mainly carried out by
comparing the output of the model which is mainly in the form of
performance indicators, against the user criteria. Some of the main
road performance indicators produced by the model are listed below.
(1) Number of Kilometres of roads in:
(a) good condition;
(b) fair condition; and
(c) poor condition.
(2) Efficiency and deficiency indices of:
(a) administration of roads;
(b) construction of roads;
(c) routine maintenance of roads;
System Dynamics ‘90 5
(d) restoration of roads; and
(e) periodic maintenance of roads.
(3) Expenditure and levels of:
(a) constructed roads;
(b) administered roads;
(c) routinely maintained roads;
(d) restorated roads; and
(e) periodically maintained roads.
3.3 Main Input Values by the Model User
The user interface module can be described as a computerised, friendly
dialogue, designed mainly to instigate creativity in constructing alternative
scenarios for the road network, and also to work as a medium to facilitate the
specifiction of the model exogenous parameters by the user. The following
presents the main input parameters of the model and describes the options
available to represent these parameters, through using the user interface
module.
- Initial unit cost of:
(1) Yearly Road Administration Cost Per Kilometre.
(2) Routine Road Maintenance Cost Per Kilometre.
(3) Periodic Road Maintenance Cost Per Kilometre.
(4) Road Construction Cost Per Kilometre.
CS) Road Rehabilitation-Reconstruction Cost Per Kilometre. (Refer to
Figure 10)
- Inflation/deflation rates of the previously stated unit costs. (Refer
to Figure 10)
- The user can choose from among several forms that are available for
inputing road funds. Road Funds can be generated using any of the
following options:
(1) Empirical function (linear or nonlinear).
(2) Deterministic function.
Cy Random Stochastic function (stochasticity assumed to be of the
Gaussian type, and randomness is based on the pseudo randomisation
process).
(4) Combination of any of the above i.e. at a time specified by the
user, the function of the road funds changes from one form to
another. The available combinations include:
(a) Empirical function with Deterministic function.
(b) Empirical function with Stochastic function.
(c) Deterministic function with Stochastic function.
S The life cycle of a road progresses through time from an initial state
of being in good condition, passing through a state of fair condition
and terminating at a state of poor condition, where the road is almost
unusable, due to radical structure failure, i.e. high surface roughness
values. The maintenance specifications of the model matches particular
System Dynamics ‘90
threshold times at which the condition of a road changes from one state
to another. The main two threshold times introduced to the model are
defined below.
Q)
(2)
(a)
(b)
(c)
Good To Fair Period, which represents the period of time the road
lasts in a good condition i.e. the time when road condition
changes from good to fair, and hence requires periodic
maintenance. Refer to Figures 11 (Harral 1988) and 12 (Bhandari
1988)
Fair To Poor Period, which represents the period of time over
which a road life cycle lasts i.e. the time when road condition
changes from fair to poor, and hence requires restoration. Refer
to Figures 11 (Harral 1988) and 12 (Bhandari 1988)
As mentioned above, both threshold periods are meant to provide
the times when the intervention criteria for performing periodic
and restoration maintenance activities are satisfied. The user
interface module provides several different forms for generating
these intervention times at which the above-stated maintenance
activities should be performed. These forms are described below.
Deterministically scheduled to occur at a time specified by the
model user. (*)
Stochasticly scheduled to occur at a time specified by the model
user. Time here is randomly generated, from a normal
distribution, with a mean and a standard deviation specified by
the model user. This option is introduced, to cater for the
relative uncertainty involved in determining the exact threshold
times. (*)
Condition responsive, according to the HDM III empirical,
aggregate model (Paterson 1987), that describes the progression
of roughness over paved roads. The HDM III equation is of the
following form:
RI(t) = [RIg+725[1+SNC]“*4-9NE, (t) ] e%-0153t
where
RECS); RIg = roughness at times t and t=0 respectively, in
m/km IRI,
SNC = modified structural number,
t = age of the pavement since restoration or
construction,
NE,(t) = cumulative equivalent standard axle loadings
until time t, using damage factor =4, in million
ESA/lane.
It is to be noted that surface roughness of roads is considered
to be the most representable performance indicator of the changing
System Dynamics '90 7
condition of paved roads over time. (**)
(*) Scheduled maintenance is made at a specific time of the life of
a road. Scheduled maintenance, sometimes called preventive
maintenance, is applied irrespective of the actual condition of
the road at the time of maintenance.
(**) Condition responsive maintenance is performed at a time when the
condition of the road has deteriorated to a prescribed threshold
level. This conditional level is specified by the user according
to his acceptable criteria regarding the performance of roads.
The model is structured to keep the input data to a minimum, yet to produce
a comprehensive output of the condition and expenditure of the road network.
This information enables a thorough examination by the model user, thus
rationalising the decision making, concerning road funding strategies and
maintenance combination options.
4. SUMMARY AND CONCLUSION
A simulation model for the dynamic provision of roads is presented. The
model simulates the effects of road investment policies on the development
of the road network system. The investments are allocated among the
construction, maintenance and administrative activities. The maintenance
activities involved are routine, periodic and restoration maintenance. The
model is a typical policy analysis tool and is meant to give information
about the structure and performance of the road network system. The road
provision model allows us to analyse the life-cycle costs of a road under a
variety of alternative road funding policies, maintenance options, initial
unit costs, inflation rates, etc.
System Dynamics, the modelling approach used in this study, seems to fulfill
a need, which is not met by the standard planning and programming approaches,
namely that of providing for the concept of controllability, (Coyle 1978).
System Dynamics is a very strong, policy-orientated modelling technique.
In attempting to present the road provision model, three main topics were
addressed. First, to indicate how available road funds would be allocated
into major appropriation categories. Second, to introduce a set of
uncomplicated, yet reasonably, comprehensive submodels of the road system.
These submodels when linked together form the structure of the System Dynamics
road provision module. Third, to show the main input parameters required by
the model and to explain the options available for inputing each parameter by
using the flexible user interface module.
The overall objective of the developed model is to serve as a management tool
for designing, testing and assessing strategies that support the decision
making process in the field of Highway planning. The model is to be used by
transportation system managers, in policy planning, and by government
decision-makers in making better decisions concerning the road network
system.
System Dynamics ’90
REFERENCES
Abbas, K. A. 1990. Simulation of the Eeffects of Transport Investment Policies
on the Development of Road Infrastructure. In Proceedings of Universities’
Studies Transport Group Annual Meeting. Hatfield Polytechnic, Hatfield, U.K.
Bhandari, A. S., and K. A. Sam. 1988, The Road Network Stabilization Programme
in Ghana. In Proceedings of the 16th PTRC Summer Annual Meeting, Road
Deterioration in Developing Countries, Seminar G, 28-41. Sussex, U.K.
Coyle, R. G. 1978. Management System Dynamics. A Wiley-Interscience
Publication,
Forrester, J. W. 1968. Principles of Systems. The MIT Press/Wright-Allen
Series in System Dynamics.
Harral, C., and A. Faiz. 1988. Road Deterioration in Developing Countries:
Causes and Remedies. A World Bank Policy Study. A World Bank Publication.
The World Bank, Washington, D.C.
Paterson, W. D. 0. 1987. Road Deterioration and Maintenance Effects, Models
for Planning and Management. The Highway Design and Maintenance Standards
Series. A World Bank Publication. The John Hopkins University Press
System Dynamics '90
The ! Specify Period and Time Increment of
Simulation (START, LENGTH, DT)
$
\ Input Unit Costs and Inflation Rates
USER | of the Road Activities
: 4
| Choose a Form to Generate the
INTERFACE Road Funds Values
|
| [Select a Form to Represent Cendition of
Module | & Time Intervention Criteria for Roads
The —
i ! Initialise Model Variables and Start
System i Simulation (TIME=START)
|
|
| Dynamics | Simulation in Progress
i
| Road ts TIME > LENGTH ?
i MO ES
Provision i
: End of Simulation (TIME*LENGTH)
Module : +
| Produce Output
Fig 1: Framework of the Road Provision Model
10
System Dynamics ‘90
Road
(See Fig. 41 Maintenance
Funds Final
— —
+104
Road
(See Fis. SI Construction
Funds
[See Fig. a1
Se
+
+/0
Periodic
Road
Maintenance
Funds
--t--
4 +/0
Road Funds
Saved: Level
+ +/0
Road Rehabilitation-
Reconstruction (See Fig. 61
Road Funds
—— —-
{See Fig. 7!
Fig 2: Management of the Road Funds
System Dynamics '90
11
matrations: ~ = ~ Adniaistretions: Road
Administration = ~ ~ Administration<= = = - = —
Funds Cost Required Kilometres: Level
7 \ N
1 N
7 | Ke
1 7 I Deficiency
Yearly Road index
Administration Cost 7 | Road —
Per Kilometre 7 I Administration
I 7
I - I |
oN 4 & |- ¢ I
Road Not Administered I
Administration = = - - -—»> Road 1
Rate ~ Kilometres Rate |
'
Efficien:
Index Oj
Road
Administration
+ +
Administered Not Administered
aC a
Kilometres: Level Kilometres: Level
Fig. 3: Road Administration Activity
Routine Road + Routine Road + Good-Fair
Maintenance = ~ — —Maintenance Cost«= = — = Condition Road
Funds Final Required Final Kilometres: Level
1 . *
I 7 oi “gx
| 7 I Deficiency
Routine Road LS I Index Of
Maintenance Cost Routine Road
Per Kilometre 7 I Maintenance
1 7 1
1 gt I aaa
va
Non | - I
Periodic Road Routine Road Not Routinely |
Maintenance = = = >Maintenance- = - ~ = --»Maintained Road 1
Rate Rate ~ Kilometres Rate |
Ly
Efficiency
Index Of
Routine Road
Maintenance
sad >
eeutingty Not Routinely
Maintained Road Maintained Road
Kilometres: Level Kilometres: Level
|_Fig. 4: Routine Road Maintenance Activity
12 System Dynamics ‘90
Road Road
Construction _—— Rehabilitation
Funds Allocation Reconstruction
Factor “\ Cost Required
| \N Not Constructed
! \ Road
+) Kilometres: Level
Road \ __ Road * Efficiency
Construction -— —— ———Construction Index Of
Funds Cost Required Road
Vand a Construction
7 t
Construction Cost | !
Per Kilometre 1
. ra | Deficiency
Road “¢ Not Constructed Index Of
Construction | -> Road Kilometres = — —> Road
Rate AN Rate Construction
Tan =
\ .10 | 7 _
20) see LL” —_—
\Balance Of , Road Kilometres Total
Kilometres:—— ——— = =» Roads Stille — — Requiring < == =Permitied
Level To Be Constructed Construction’ Road Kilometres
Fig. 5: Road Construction Activity
Road Construction = Road
Cost Required —= —— ——» Rehabilitation-
Reconstruction
Not Rehabilitated- Z, Funds Allocation
Reconstructed 7 Factor
Road Kilometres: 7 i.
Level $s
Efficiency . Road 7 Road
Index Of Road Rehabilitation-/ + Rehabilitation-
Rehabilitation- Reconstruction ——-—— —> Reconstruction
Reconstruction Cost Required, Funds
i} * +s
I ~ poad
Rehabilitation-
| Reconstruction
Cost Per
Kilometre,
N
‘ +
Deficiency Not Rehabilitated- | NO Road
Index Of Road <= — —Reconstructed <— t Rehabilitation-
Rehabilitation- Road Klometres + » Reconstruction
Reconstruction SS * 7 Rate
‘XN 1 O Z
™ Ng 72
Road Kilometres SN I GF =
Fair To Poor Requiring Balance Of Roads Rehabilitated-
Road ————» Rehabilitation- — — —» Still To Be <——-——— —— Reconstructed
Kilometres * Reconstruction: * Rehabilitated-— Road Kilometres:
Rate Level Reconstructed Level
|_Fig. 6: Road Restoration Activity
System Dynamics '90
13
Efficiency Not Periodically Periodic Road +Perlodic Road
Index Of Maintained Maintenance—— —— —> Maintenance
Periodic Road Road Kilometres: Cost Required Funds
Mahitersnce Level * *
+
Perlodic Road
| Maintenance Cost
Per Kilometre
NS
Deficiency, Not Periodically Ne
Index Of + — — Maintained <= Periodic Road
Periodic Road Road Kilometres
Maintenance Rate ite
Pi aN
NIN
Rosd Kilometres Balance Of Roads *
Good To Fair———» Requiring Periodic — —» Still To Be «<— —~ ——Perlodically
Road Kilometres +/- jaintenance: + Periodically — Maintained Road
Rate Level Maintained Kilometres: Level
Fig. 7: Periodic Road Maintenance Activity
> Good-Falr Condition™™ “~ —~ —~ ~]
———— > Road Kilometres: Level |
rn
Routine, Road Maintenance: I
ost Res
5Q 10) e™ 10 | |
Routine Road Maintenance
Funds I
Road 4 ~ ~—S
4 © Rehabilitation “Road |
Reconstruction Construction
Funds Funds I
| !
+ +
———== Rehabilitation- Road l
Balance Of === = = ==» Reconstruction Construction
Fonds Sul! iy Be + Rate i |
abilltated-
Reconatructed © Good Fait
+t — — Road <= 4
1 iliomeiree *Kilometres
Road Kilometres Difference
Requiring
Rehabilitation-
Reconstruction:
Level «Fair To Poor Road-+——Added —— Good To Fair Road
Kilometres Rate * Road Kilometres * Kilometres Rate
Fig. 8: Road Kilometres Starting New Life Cycles
14
System Dynamics '90
Road a Road + Routine Road
Administration Funds Maintenance
Rate Rate
| Road Routine Road |
Administration Maintenance
Funds Funds Final
1 10
Administration
Expenses Rate ——
— ——>Road
+ 20
Expenses Rate
+
Routine Road
Maintenance
Road
Road———= = ——=_ ——-> Saved: Level ,
Rehabilitation- = Construction
Reconstruction Expenses Rate
Expenses Rate t*
% +
Road + Road
| 4 O Rehabilitation- Construction 3 O | 16)
Reconstruction Funds
| Funds
Road Road
Rehabilitation- , + Construction
Reconstruction Rate
Rate .
Periodic Road +Periodic Road 4 Periodic Road
Funds
Fig. 9: Recycling of Saved Road Funds
Maintenance ———> Maintenance~ =~ > Maintenance
Rate
Expenses Rate
Yearly Road
Administration—= — —» Administration Cost
+
+ Road —— —— =» Yearly Road
Administration
Cost
Cost Average Increase Rate <—_ == == Per Kilometre
Inflation *
1@
Yearly Yearly Yearly Yearly
Periodic Road Rehabilitation- Road Routine Road
Maintenance Cost | Reconstruction Cost | Construction Cost | Maintenance Cost
Averagg Inflation Averaga, Inflation Average, Inflation Average inflation
1 1 ! 1
}- + }- J *
Perlodic Road Road Rehabilitation- Road Routine Road
Maintenance Cost | Reconstruction Cost | Construction Cost | Maintenance Cost
Increase Rate Increase Rate Increase Rate wee as
+t I I +t I
1s@! 40! | 130! 120!
I |. | | |
Perlodic Road Road Rehabilltation- Road il -_— sods
Maintenance Cost | Reconstruction Cost | Construction Cost | Maintenance Cost
Per Kilometre r Kilometre Per Kilometre Per Kilometre
Rates of the Road Activities
Fig. 10: Unit Costs and Inflation
System Dynamics '90 15
Ny
\
_ With axle loads
g ? 15 percene higher than normal With normal loading
Z0ub ;
2 ob if
rd Reconstruction or major rehabilitation required y
2 o9F (in absence of earlier strengthening) Zl
g osp
é 7
Piso Critical stage in life
SL cycle of paved road
gosh
Boat Pavement strengthening indicated o
g ”
a re :
2
ik
0 1 1 i 1 i 1 a i 1 1 1 1 1 1 j PRB OF i 1 1 |
0123 4 5 6 7 8 9 10 11 12 13 14 15 16°17 18 19 20 21 22
o-nr N OKADA N OO DC
Fig. 11: Deterioration of Paved Roads Over Time
Source : (Harrel 1988)
Surface Roughness (IRI)
[ Resurfacing or Reconstruction i
[goood FAIR "Poor
F CONDITION CONDITION CONDITION
[ Reseal or thin Overlay
=
L 1 1 f 1 1 es 1 J
ie} 2 4 6 8 10 12 14 16 18 20
Years
Fig. 12: Condition of Paved Roads Over Time
Source : (Bhandari 1988)
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