INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 06,2025
Journal:
https://www.academicpublishers.org/journals/index.php/ijai
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MODELING THE INTERDISTRICT CORRESPONDENCE MATRIX
Tukhtapulatova Sh.B.
Master's student
Tashkent University of Architecture and Civil Engineering
Abstract:
This article analyzes theoretical and practical approaches to modeling the
interregional correspondence matrix in the transport sector. The concept of transport demand,
the factors that form it, and ways to use it as a means of managing the demand for the transport
system in modern urban planning are highlighted. The essence, differences, advantages, and
disadvantages of aggregate and disaggregate models used in determining matrix values are
considered. Optimized flows from the user and system perspectives are also analyzed based on
Wardrop's principles. The need for doset models aimed at identifying potential transport needs,
regardless of the network configuration, is substantiated.
Keywords:
transport demand, correspondence matrix, aggregate model, disaggregate model,
Wardrop principles, user optimization, system optimization, transport flows, transport modeling,
doset model.
Introduction.
Management and forecasting of traffic flows in urban planning and transport
planning is one of the most pressing issues today. Especially for the stable functioning of the
transport system in large cities, it is important to analyze data on population movement, to
model this movement through interaction in an interregional context. From this point of view,
the compilation and modeling of the interregional correspondence matrix is one of the main
stages in determining demand in the transport sector and ensuring the effective functioning of
the network. In this chapter, the essence of the interregional correspondence matrix, the factors
of transport demand formation, the significance of aggregate and disaggregate models used in
determining this demand, and the cases of their application are widely covered.
Main Part.
Transport demand is a quantitatively determined need for transportation and
additional transport services. It can be measured in the number of vehicles, passengers, or cargo
per unit of time. The demand for the services of a specific type of transport is determined, in
particular, by the development of various types of transport in the region, the degree of their
integration, the level of transport tariffs, and the quality of service provided to consumers by
various types of transport enterprises and organizations. The demand for freight transportation
is largely determined by two factors: the dynamics and structure of changes in production
volumes, as well as the solvency of enterprises and organizations in all sectors of the economy
[1].
As in the market situation, so-called market equilibrium (balance of supply and demand)
operates in the transport services sector. The flow distribution in the transport network is an
analogue of the market equilibrium situation, in which traffic participants create a demand for
the use of transport system elements, the capabilities of these elements act as a supply, and the
price is the costs (time, cost, comfort level) of traffic participants arising from the use of these
INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 06,2025
Journal:
https://www.academicpublishers.org/journals/index.php/ijai
page 122
elements. In the case when demand exceeds the possibilities of supply, a deterioration in the
conditions of movement occurs, which leads to an increase in such costs. The total increase in
such costs can be used as one of the indicators of the total overload of the transport system. For
individual network sections, such growth can serve as an indicator of their insufficient capacity
(carrying capacity). In addition, it is known that improved traffic conditions provoke increased
traffic - so-called induced demand manifests itself.
It should be noted that in recent years, in the practice of urban planning, transport demand has
often been considered not as a predetermined value determining the flow distribution structure,
but as a tool for managing the city's transport system. In particular, over the past decades,
experience has been accumulated in using a whole range of regulatory measures aimed at
reducing the demand for the use of individual transport ports, especially in areas with dense
urban development [1].
Modeling the inter-district correspondence matrix is the main stage in calculating transport
demand parameters. The problem of distributing movements (correspondences) between pairs
of transport areas with known "departure" and "arrival" values, determined at the trip
generation stage, has an infinite set of solutions. Figure 1 shows a tabular form of the
correspondence matrix, each element of which represents the number of movements between
pairs of transport areas - from area i to area j.
Arrivals
Shipments
1
2
…
n
sum
1
P1
2
?
P2
…
…
m
Pm
sum
Q1
Q2
…
Qn
Fig. 1. Correspondence matrix table form
Correspondence matrix values cannot be directly measured, therefore various indirect
approaches are used to determine them, such as sociological research or the method of restoring
matrix values based on known flow distribution parameters. Within the framework of this
training manual, models based on the study of individual preferences of city residents are
considered; it is precisely such models that have become widespread in the composition of
many well-known software complexes of transport and urban planning modeling.
INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 06,2025
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The models for calculating inter-district correspondence are divided into two large groups:
aggregated and disaggregated. Aggregated models are built on averaged values of variables that
determine the demand for movement. The number of movements determined by such models is
calculated proportionally to the size of the territory generating demand, and the demand is
assessed proportionally to the population residing in the transport area. The number of
movements attracted to a particular transport area is calculated proportionally to the number of
attraction sources located in the considered territory.
However, inter-district correspondence is the aggregate result of individual movements of city
residents. Therefore, it is logical to use disaggregated models as a tool sensitive to the
individual transport behavior of respondents. Disaggregated models describe an individual's
transport behavior, taking into account the impact of socio-economic and urban planning
factors on them. Behavioral principles are associated with two possible situations.
1) network users independently choose the route route corresponding to their minimum
transportation costs (time, money);
2) Network users choose travel routes based on minimizing total transport costs in the network.
These behavioral principles were called Wardrop's first and second principles, respectively. In
the first case, everyone strives to reach the final destination of their journey as efficiently as
possible for themselves and chooses the route that will incur minimal travel expenses (time,
financial, moral, etc.). Therefore, this principle is also called custom optimization.
Wardrop's second principle assumes centralized control of movement in the network. The
corresponding distribution of transport flows is called the system optimum, and the principle
itself is called system optimization. An example of users moving according to the second
principle is the drivers of route transport [2].
In the classical (network) demand calculation scheme, it is assumed that correspondents choose
arrival districts based on the capabilities of the transport network, i.e., the time spent traveling
between districts is calculated taking into account the possible travel speeds. When developing
projects for the future, even when it comes to established cities, such an approach is not always
acceptable. For example, nearby districts, separated by a water barrier and therefore practically
inaccessible to each other through the network, can be mutually attractive for residents during
the construction of a bridge crossing.
When calculating the correspondence matrix in the network model, it turns out that the costs for
such movement are high, and, as a result, the number of correspondents between these districts
will be small, from which it can be concluded that it is not advisable to build crossings for the
connections of these districts. Speaking about the 20-30-year perspective, for which many
projects are being developed, one cannot focus on network configuration, as its construction is
one of the main goals of developing such projects. Thus, there is a need to develop pre-network
models for forming inter-district correspondence that would take into account the overall level
of transport services, network speed parameters, but would be less susceptible to the influence
of geometric features and network limitations. Such models will allow for more adequate
identification of potential demand for inter-district movements.
INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
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The determining factor in modeling the distribution of correspondences at the pre-network level
is the relative location of settlement areas and labor application areas, i.e., such factors as the
parameters of the city territory configuration, the density of population and labor application
areas, as well as the relative location of functional zones come to the forefront (Table. 1). Pre-
network models provide the designer with information about the directions of transport network
development under the given location of functional zones. Modeling the distribution of
correspondence at the pre-network level allows for calculating the situation of the most
complete disclosure of the territory's potential by proposing a rational structure of attraction,
which can be supported by network solutions.
Table 1
Comparison of matrix calculation approaches
Method for calculating inter-
district movement matrices
Network method (network
level model)
Pre-network method (pre-
network level model)
Approach to determining
time expenditures between
departure and arrival points
Taking into account the speed
parameters of the transport
network elements
Based on the average level of
transport services
Method for calculating inter-
district movement matrices
Network method (network
level model)
Pre-network method (pre-
network level model)
Factors
influencing
the
distribution
of
correspondence
Mutual arrangement of flow-
forming and flow-absorbing
centers
Transport
network
configuration and parameters
Behavioral factors (attractive
function)
Mutual arrangement of flow-
forming and flow-absorbing
centers
Behavioral factors (attractive
function)
The gravitational model is based on the following statement: the correspondence from area i to
area j is proportional to the total volume of departure from center i, the total volume of arrival
at center j, and some function dependent on the transportation distance between centers i and j.
Transport distance reflects the degree of proximity of districts, taking into account the speed
and convenience of movement provided by the transport network. The method of determining
this quantity may differ in different model variants. In essence, the gravitational model is based
on the analogy between the mutual attraction of two masses and the attraction of those leaving
the i region to the arrival points in the j region [3], i.e., it is assumed that
x
ij
=
kP
i
Q
i
c
ij
2
where
x
ij
- the volume of correspondence between districts i and j, thousand people;
INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 06,2025
Journal:
https://www.academicpublishers.org/journals/index.php/ijai
page 125
P
i
- volume of shipments from the i-th district, thousand people;
Q
j
- volume of arrivals to the j-th district, thousand people;
с
ij
- generalized cost of travel between districts i and j (distance analogy);
k
- is some constant.
Conclusion.
Modeling the matrix of interregional correspondences plays a key role in the
planning of transport systems, and in this process, the correct assessment and forecasting of
transport demand occupies a central place. Due to the difficulty of directly determining matrix
values, various fuzzy but practically useful models are used. Aggregate and disaggregate
models have their own peculiarities, and disaggregate approaches are relevant because they
reflect the individual characteristics of transport users' movement. Optimization approaches
based on the Vardrop principle are an important tool for regulating traffic flows. The use of
existing non-network-based doset models allows for a more accurate assessment of potential
needs in the formation of long-term transport strategies.
REFERENCES:
1. D. V. Kapsky L. A. Losin "Transport in Urban Planning."
2. Introduction to the mathematical modeling of transport flows / ed. A. V. Gasnikov. - M.:
MSNMO, 2012. - 377 p.
Popkov, Yu. S. System Analysis and Problems of Urban Development / Yu. S. Popkov, M. V.
Posohin, A. E. Gutnov, B. L. Shmulyan. - M.: Nauka, 1983. − 512 p.
