Transportation Theory and Planning
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CHAPTER 1
TRANSPORTATION SYSTEM ANALISYS AND PLANNING PROCESS
1.1 Transportation system
The transportation system is defined as the set of components and their interactions whose
determine the travel demand between two different points and the transportation service offer to
supply.
1
To clarify the above statement, let us consider a city. We can identify two relevant systems for
our analysis within it: the activities system and the transportation one. The first is characterized
by the following elements
2
:
- the families and their residences, which can be classified through certain criteria such as
the income bracket, composition, etc…;
- the economic activities;
- the available surfaces in the various zones of the territory, classified on the base of their
use destination (apartments, offices, shops, ecc…).
The above listed components are correlated. Indeed, the family distribution on the countrywide is
strictly related to the job-opportunity locations. Moreover, several economical activities
settlement is determined by the family distribution. Lastly, the presence of families and
economical activities in the different areas of the city significantly influence the surface
availability and the related prices.
It has also to be highlighted the role played by the relative accessibility between zones, on which
the transportation service characteristics are relevant. Generally, the residence choice accounts
for its active accessibility to work areas and to areas in which family services are located.
Moreover, the activities settlement is also based on the passive accessibility, with respect to
potential clients, of the alternative zones. Thus, it is worth to notice that the transportation
demand is a derived demand: a movement does not produce utility but it is done in order to
perform a certain activity at the travel destination.
3
And the transport system strongly interacts
with the land-use, which regards all the activities and their special distribution on the territory.
1
Lupi, Marino. La Domanda di Trasporto (Appunti dalle lezioni di Tecnica ed Economia dei Trasporti). DISTART
- Trasporti, Bologna.
2
Catalano, Mario. La Pianificazione dei Sistemi di Trasporto. Corso di Tecnica ed Economia dei Trasporti, Prof.
Corretti Vincenzo, a.a. 2003-2004.
3
Cascetta, Ennio. Transportation System Engineering: Theory and Methods. UTET, 1998.
Transportation Theory and Planning
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Looking more carefully at the transport system definition we can immediately notice that it is
constituted by two sub-systems: a) the demand (sub-system), formed by the users (people and/or
goods), which is usually represented through origin/destination matrix, and b) the offer / supply
sub-system, represented by the physical (infrastructures) and organizational components, and
regulations.
The interaction between the demand and the offer causes the flows distribution on the network;
then, the flows allow the evaluation of the transportation systems’ performances and impacts,
that can be used significant indicators for the short-term planning mostly. In order to study the
interaction demand-offer it is necessary to build up the following models:
- Supply model: it is a mathematical model used to represent the real transport network.
The model is defined through the specification of the geometrical and operational
characteristics of the infrastructures, and the link flows, and provides costs and time spent
of links and nodes.
- Demand model: this model is used to describe the movements (destination, transport
mode, route) of people or goods. To define the model and compute its output (O/D matrix
of movements, transport modes and routes), socio-economical and transportation systems
attributes are necessary.
- Assignment model: it is the model used to assign the demand to the network. So it needs
the output provided by the previous two models and allows to calculate the vehicular
flows of the network links.
When we design these three models, different approaches, characterized by different
assumptions, can be used.
A first assumption when we study these models, regards the transport demand which can be
assumed to be rigid or elastic. In the first case, this means that the interventions that we will
propose for the supply model will change the flows distribution on the network only, and so the
route choice. On the other hand, elastic demand can be assumed: in this second case, both rout
choice and transport mode sharing can be affected by interventions.
In general, the assumption of rigid demand can be considered to be valid when:
1) we are dealing with not deep and short-term interventions;
2) transportation analyses are performed with reference to the peak hour of the average
weekday and the average demand value is assumed.
A second assumption regards the model used to represent the demand: we can distinguish two
different types of models. The descriptive models, characterized by the fact that no explicit
hypothesis on the users behavior are made; o the other hand, if explicit hypothesis on the users
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behavior are specified, we have the so-called behavioral models. In the first case we will talk
about deterministic models, whereas in the second case we will treat stochastic ones.
The supply model is represented by a graph, characterized by nodes and links. The graph
represents, generally, the real network. However, to properly model the transport network,
quantitative features, called cost functions, has to be associated to the links. The cost functions
are empirical relations that allow estimating a link cost based on its geometrical, functional, and
traffic characteristics. Since the cost function represent a generalized cost, in the sense that both
monetary and temporary link cost are considered, the flows can represent an important variable
in the link cost estimation, since the can heavily affect the link travel time. On the base of the
investigated transport network (highways, urban network, etc…) we can assume that:
- the cost functions are constant, and independent with respect to links flows;
- the costs functions depends on links flows (congested network): in particular, if we
assume link cost is a function of the flow on it only we talk about separable cost function,
whereas if the link cost depends also on flows on other links we have no-separable cost
functions.
Lastly, when also the assignment model can be studied with two different approaches:
- we can assume a no-congested network and talk about Network Loading models, or
- we can assume a congested network. In this second case, if we assume that demand is
constant in time, we have the so-called Static approach (User Equilibrium models), or we
can assume that the demand varies over time (Dynamic approach).
-
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Fig. 1.1 (a): Transportation analysis framework
On the base of the possible assumption that can be made, we can classify the assignment model
as follows:
Assignment Model
chart
Deterministic Path Choice
Model
Stochastic Path Choice
Model
No-congested Network
Deterministic Network
Loading (DNL)
Stochastic Network Loading
(SNL)
Congested Network
Deterministic User
Equilibrium (DUE)
Stochastic User Equilibrium
(SUE)
Deterministic Dynamic
Process (DDP)
Stochastic Dynamic Process
(SDP)
The table above shows that during the schematization process of a transport network various
assumptions can be made. These assumptions inevitably lead to different models to assign the
transport demand on the network. However, these models can be all used in both the cases of
rigid and elastic demand. Assuming rigid or elastic demand causes affects the demand mode
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share: using rigid demand the mode share is assumed to be fixed, whereas using the elastic one
the mode share becomes a variable of the problem which as to be computed in the analysis.
Obviously, the results obtained under the assumption of rigid demand are different from the once
obtained assuming elastic demand since the route choice, and consequently the flows, depend on
the considered mode.
Generally the interaction between transport demand and transport offer is immediate, whereas
the interaction between the transport system and land use is often regarded as a long-term
process.
4
1.2 Planning process scheme
The planning process in the Transportation trade can be classified in relation to the reference
country level (national, regional, local) and to the planning period (short- , medium- , long- term
periods). We will deal with the last case in the next paragraph.
The actual planning process in Transportation engineering can be split in six phases. The first
phase is a political crime essentially. It consists into define the interventions objectives and
fixing economical, temporal, and environmental constrains. The second one deals with the
creation of a mathematical model which describes the transport and the socio-economical
systems as a function of the objectives defined in the previous phase. This model has to be
calibrated through the study of the actual situation and made transferable. In the third phase
challenger projects have to be compared with the defender, the actual situation. Challenger
projects are usually defined by applying changes to the supply model. In the subsequent phase,
phase four, quantitative simulations of the challenger plans are performed through the
assignment model and economic analysis. Then, in phase five, the alternative plans are compared
and the in the last phase, phase six, the intervention to be realized is chosen based on the weight
assigned to the objectives identified in phase one. Generally, in the last phase both the
engineer(s) and the politician(s) are involved.
4
Schweizer, Joerg. Conventional transport planning-Basics. Sustainable Transportation Engineering class handout.
Bologna University, 2010.
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Fig. 1.2 (a): planning process scheme
In the last decade, a different approach raised in the planning process: government methods
which allow formally private investors, that do not hold any institutional position, to participate
in the decisional process of public programs related to the environment transformation are taking
place (de Luca, Rallo, 1995). The need of introducing private investors in the transport sector is
clear if we consider the impact that they have at the productive, economical, social,
environmental, etc… level and it’s becoming crucial since public funds alone does not supply
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what’s needed to operate and maintain the infrastructures. Indeed, more and more often federal
and local governments, especially in Europe, are turning to the private sector for help into
maintenance and improvements of transportation infrastructures.
1.3 Planning level
As we told previously, we can distinguish three planning levels based on their temporary effects:
a) Strategic planning: it is the wider level, used in the large scale interventions; it produces
decisions which can strongly affect the transport in the long-term period. It needs of
relevant investments and modifications.
b) Tactic planning: it refers to decisions regarding the re-organization of the supply system.
It produces medium-term effects and it is characterized by local interventions and limited
investments.
c) Operating planning: it counts limited interventions in space and time (2-3 years) and
regards the functioning of the single transport modes. It is based on the re-organization of
the existing infrastructural and human resources. The investments are extremely limited.
It appears to be clear that the transport system simulation is fundamental to compare alternative
plans quantitatively. Since the transport system simulation makes use of three models (demand,
supply, and assignment models) we will start analyzing them from the next chapter.
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CHAPTER 2
TRANSPORTATION NETWORK REPRESENTATION
As every other engineering system, the transportation system has to be modeled though a
mathematical model in order to be analyzed. The use of mathematical model is fundamental to
describe quantitatively the actual or the future behavior of the investigated system. When we
build up a mathematical model we have to identify all the variables which significantly affect the
system and it has to be determined the functional relation between these variable. However, in
order to treat the problem with mathematical tools, each model used to represent a real system
does not contain the entire possible variables that affect it, and generally models are built up
under certain reasonable assumptions that unavoidably lead to an error. That’s why when we
deal with mathematical model we talk about the accuracy of its results. In general, when we creat
a model of a real system three steps must be followed:
- model specification: all the significant system variable has to be identified and the
mathematical relations between these variables have to be found;
- model calibration: all the unknown coefficients of the model have to be estimated;
- model corroboration: system simulations have to be performed and their results must be
compared with the real ones in order to estimate the model capacity to reproduce the reality.
This cycle should be generally iterated until the required accuracy into reproduce the real system
is reached.
2.1 Study hypothesis and phases for transportation system modeling
The transport demand can be defined as the number of users with determined characteristics
which utilizes the transport system in a certain time period (hour, day, ecc…).
5
The demand unit
measure is users/time. In particular:
- private road transport: vehicles/hour;
- railroad transport: passenger/hour;
- public road transport: passenger/hour.
However, in general we can assume a reference time interval different from hour (i.e. 15’, 30’, a
day, etc…). The choice of the reference time interval depends on the study objectives: for
5
Gallo, Mariano. Appunti di Tecnica ed Economia dei Trasporti. Università degli studi del Sannio, 2002.
Transportation Theory and Planning
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example, the year is assumed when we want to perform the intervention cost/benefit, whereas a
15’ time interval is used in designing the signalized cycle. In any case, the transport demand is
the result of the single movements which affects the transport system in the considered period.
The demand study is important to evaluate the transport system loads. Consequently, once we
have performed transport demand estimation we can verify the network functioning or design a
new transport system.
The transport system is generally analyzed with a mathematical model based on the following
hypothesis regarding the transport demand:
1) the transport demand is assumed to be rigid and equals to its average value;
2) the system is assumed to be stable: the transport demand average value is considered
constant within sufficiently wide intervals such that the system can reach a stable
condition in which its significant features (flows, performances, impacts, etc…) are
constant and independent with respect to the particular moment in which they are
measured. Making this assumption the transport system is analyzed through a static
approach, since the system does not change in time. Moreover, we can distinguish two
different stationary conditions:
- within-a-period stationary: proper stationary conditions are considered within a
reference interval (i.e., peak hours);
- between periods stationary: proper stationary conditions are considered for all the
intervals characterized by similar functioning (i.e., the peak hours of all the
weekdays).
Then, each mobility-studio regarding a transport system is performed following these steps:
a) study area boundary has to be defined;
b) the initial continuous problem has to be changed in a discrete one (zoning process) ;
c) a graph which represents the real network has to be built up;
d) definition of the supply model through the assignment of a cost function for each link
(chapter 3);
e) an estimation of the demand has to be performed (we treat this topic later in chapter
6);
f) demand/supply interaction simulation (treated in chapters 7, 8, and 9).
In the following paragraphs the above listed steps are described in more detail. The first three
steps are referred to the supply subsystem, whereas the last point refers to the demand one.
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2.2 Study area boundary identification
The study area is defined as the geographic area within which the transport system is or in the
intervention effects run out.
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The area boundary is called bar and usually it dovetails with
administrative borders. Everything not belonging to the study area is called external
environment; it interacts with the study area and vice versa. However, initially we will consider
the external environment influence on the transport system only.
The choice of the study area boundary is a tricky step: there are not fixed rules to indentify it,
and generally a wrong identification can lead to rough errors in the simulations.
2.3 Zoning
This phase is one of the most ticklish tasks since it will relentlessly influence both the model and
the supply subsystems. It consists into transform the initial continuous problem into a discrete
one in order to treat it with mathematical tools. A movement within the study area can be any
departure/ destination point. So, the possible origin/destination points can be, theoretically,
infinite. During the zoning process, all the movements origin/destination points related to a sub-
area of the study area are round down with a unique point, the so-called centroid. So, the
centroid can be defined as the network node in which all the departure/arrival points of the sub-
area are concentrated. In this way, we will take into account the movements between two zones
only, neglecting the movements within a zone. Consequently, the O-D matrix of the movements
will be characterized by the elements on the main diagonal, which represents the movements
within a zone, equal to zero. The error magnitude increases with the width of the zones related to
each centroid. However, create a very detailed representation is not a good idea because:
a) If we have a great number of both nodes and links, the problem can’t be treated from a
mathematical point of view;
b) It leads to an error (in terms of difference between the measured and simulated flows) higher
than the one produced by a lower detailed representation. Indeed, it can be proved that assuming
a constant sampling rate (which represents the ratio between the number of interview and the
number of the candidates to motion) and, consequently, assuming a constant cost of the research,
the estimation of the transport demand obtained by the sample is closer to the real value as wider
and populated the zones are. Thus, it is better it is better to have a lower value of links and nodes.
c) Moreover, a more important reason why it is better to avoid a too detailed representation of
the network is related to the cost functions definitions. Using very detailed representations of the
6
Cascetta, Ennio. "L'ingegneria dei sistemi di trasporto per la progettazione e la valutazione degli interventi." Teoria
e Metodi dell'Ingegneria dei Sistemi di Trasporto. UTET, 1998.
Transportation Theory and Planning
11
real network require defining the cost function for local streets also: generally, for these streets it
is very difficult to define standard cost functions.
Therefore, the zoning of the study area affects both the demand and the supply models because,
respectively, it doesn’t take into account for movements within a zone, and because it lead to
overestimate the flows since the real network is represented through a lower number of
infrastructures (links).
To perform the zoning of the study area, the below listed criteria
7
can be followed:
a) for the internal zones, we can assume the centroid positions coincide with center of gravity of
the sub-area with respect to the activities locations;
b) for the external zones, the centroids should be placed in correspondence of both the bar and
the streets which link a zone of the external environment with the study area;
c) assuming, if possible, the zone edge of the zones with physical edge of the territory;
d) choosing the boundary in relation with the transport mode we are going to consider. For
example, in case of private transport, the main streets coincide with the zone edges;
e) accounting for the homogeneity of the zones with respect both the use of the soil and the
accessibility;
f) create an adequate zoning which allows to investigate in a simple and detailed way the study
objectives (which mainly influence the zoning process, obviously);
g) enumerate the centroids in a growing way, starting from the ones of the internal zones. In this
way it is possible to divide the O-D matrix in blocks and to study in a faster and immediate way
the consequences produced by the interventions we will suggest.
7
Angelini, Stefano. “Traffic Analysis”. A sustainable mobility concept and infrastructure plan for the Engineering
Faculty. DISTART-Trasporti, Bologna, 2010.
Transportation Theory and Planning
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Figure 2.3 (a): centroids enumeration example
It is worth to discuss the O-D matrix concept now in order to clarify the last criteria (criteria e).
An O-D matrix represents the movements related to the study area, in a defined time interval,
splitting them on the base of the origin and destination nodes.
8
Thus it is a square matrix with a
number of rows and columns equal to the sum of the internal and external centroids. Its generic
element, null null null , represents the number of movements that, in the considered time unit, has origin in
zone null and destination in zone null . The sum of the elements of the generic i-rows, represent the
total flows generated from the i
th
-zone in the considered time unit:
null null .
= null null null null null
In the same way, we can define the total entering flow in the d-zone as:
null . null = null null null null null
In relation to the e-criteria discussed above, the O-D matrix can be subdivided in four blocks.
With reference to Fig. 2.3 (b), we can distinguish:
- the within study area movements, characterized by the fact that both origin and
destination belong to the study area, and the intra-zone movements (the origin node is
also the destination one), in the upper-left part of the figure;
8
Gallo, Mariano. Appunti di Tecnica ed Economia dei Trasporti. Università degli studi del Sannio, 2002.
Transportation Theory and Planning
13
- the blocks related to the exchange movements between the study area and the external
environment, represented by the upper-right and lower-left blocks of the O-D matrix;
- the crossing movements, characterized by the fact that both the origin and the
destination node do not belong to the study area, represented in the lower-right block
in the figure.
Figure 2.3 (b): movements types and identification in the O-D matrix
Lastly, it is worth to notice that the O-D matrices can be specified as a function of the relevant
movements features for a particular analysis. These features are;
- referent time unit (hour, day, year, ecc…);
- reference time period (peak hour, average weekday, ecc…);
- transport mode (pedestrian, car, truck, bus, bicycle, etc…);
- movements purpose (home-work, home-shop, etc…).
2.4 Graph extraction
Once we have performed the zoning phase and indentified the centroids, we have to represent the
infrastructures which link the zones and we have to represent the spatial-temporary significant
positions through the nodes. Two nodes can represent two different position in space or the
same position in different time instants. In the first case, the link which connects the nodes
represents the real infrastructure, whereas in the second one it represents the time spent at the
node (i.e. the delay due to the presence of a signalized intersection). The links must refers to
connections for which it is possible to assume with a reasonable approximation that both
physical and operational characteristics of the represented infrastructure are homogeneous: this is
very important because subsequently we will have to associate at each link a cost function, which
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mainly depends on the geometrical and operational characteristics of the link itself. To complete
the graph we have to define also two fictitious entities: the fictitious nodes and the fictitious
links. The fictitious links do not represent real infrastructures necessarily: they are of use to
connect the centroid of a zone with the real network. The intersection between the fictitious link
and the real network identifies the fictitious node.
So now it appears to be clear why the transport system has to be modeled through a graph. Given
a set null of elements null , which are the nodes, and a set null of couple elements ( null , null ) with null , null ∈ null ,
which are the links, the set null = ( null , null ), formed by the union of null and null is a graph.
9
The graphical representation is commonly used since it is the most intuitive and easy to
implement in a calculator because it can be described by just two vectors. Indeed, the graph can
be easily represented by two matrices: the A-matrix and the B-matrix.
The A-matrix is the so-called link-route matrix. The number of its rows equals the number of the
network links, and the number of its columns equals the number of possible routes. Thus, its
generic element null null is equal to 1 if link null belong to route null , and 0 otherwise.
The B-matrix is the so-called O/D couple-route matrix. The number of its rows equals the
number of the O/D couple, and the number of its columns equals the number of possible routes.
Its generic element null null is equal to 1 if the couple null belong is linked by route null , and 0 otherwise.
These two matrices are strictly related to other mathematical tools used to represent transport
system features, such as the demand vector, null , obtained from the O-D matrix putting all the
element of its rows in column, the route flow vector null and the link flow vector null .
In particular:
null = null ∙ null
null = null ∙ null
The first equation tells us that the link flow is equal to the sum of the flows of the routes
containing the considered link. The second equation states that the demand between a certain O-
D pair is equal to the sum of the flows of the routs containing the considered O-D pair.
From this last equality we can derive null as:
null = null ∗ null ∙ null
9
Cascetta, Ennio. "L'ingegneria dei sistemi di trasporto per la progettazione e la valutazione degli interventi." Teoria
e Metodi dell'Ingegneria dei Sistemi di Trasporto. UTET, 1998.
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