Introduction group includes Transyt [6], MATsim [7], SUMO [8],


It has commonly
been assumed that ???1 transport
modelling is a part of urban research, which is important for a wide range of
scientific and industrial processes ???2 such as population
mobility, financial and commodity flows, or street congestion. Nowadays, there
are many approaches to transport modelling such as generalized fluid-dynamical
macro-models or car-following models trying to explain driver behavior. However, the main disadvantage of ???3 ???4 most of these
models is that they could be ???5 inappropriate for
the task of realistic visualization of traffic dynamics.

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An objective of this study was to review recent research into the ???6 transport
modelling, summarize common use cases for transport models and traffic
visualization and detect common drawbacks or bottlenecks of existing solutions.
a full discussion of transport modelling lies beyond the scope of this study,
and its main purpose is to analyze these models from the point of visualization


There is some
evidence to suggest that ???8 transport models are
used in variety of tasks not limited by scientific purposes. Based on their
purpose, transport
modelling solutions may be divided into four main sub-groups???9 , listed below.

Complex solutions are the software packages able to model many process of
city transport life on different levels, including both macro- and micro-models
working together. Several
packages can be listed as example for this group.  These are ???10 Quadstone Paramics
1, developing from early 1990’s; PTV Vision 2, contains separated applications for global traffic
flow dynamics(VISUM), behavioral  traffic
models (VISSIM 3, the most popular part of the package), pedestrian
models (VISWALK) and cross-junctions model (VISTRO); Aimsun Next 4, combining all levels in the same model; or Synchro
and SimTraffic from Trafficware 5.

At other hand???11 , there are some
solutions which model traffic only on micro-level, but not limited to single
junction or street. This group includes Transyt 6, MATsim 7, SUMO 8, TransModeller 9, or Movsim, presented by Trieber and Kesting 10.

In contrast, some solutions allow only narrow area of application, like only
junctions in LINSIG 11, Highway Capacity Software (HCS7) 12 or Sidra Intersection 13, or otherwise, estimating of traffic flow parameters
without behavioral models in Saturn 14. Also, the solution available systems list may be
limited to particular task, like airport modelling in CAST 15.

Fourth group is a transport models as parts of not
transport-focused software such as Autodesk Infraworks 16 – multy-purpose civil engineering  software or UNIGINE 17 – game engine. Transport models in computer games require
special attention. The  transport models
are widely used in management and simulation games, as well as in “sandbox”
games with realistic world interaction, including also drive-training sims or
racing games. Developing transport models for game was already studied in research
of Lauinger 18, and, at other hand,  Johnson-Roberson et al. 19 presents example of self-driving cars teaching using in-game

Let us now
consider ???12 different types of
transport models. Chowdhury
et al., in “Statistical physics of vehicular traffic and some related systems” (2000)
20 (chapter. 6.2), listed ???13 following
theories of vehicular traffic: fluid-dynamical theories, threatening traffic
flux as a continuous fluid with density and flux values; kinetic theories,
threatening the traffic as a gas of interacting particles; and car-following
theories, considering the driver behavior in the line based on surrounding
conditions. Moreover, they also considering coupled-map lattice models,
discretizing car-following process with discrete grid, and cellular-automata
models, updating grid values by cellular automata rules.

to Treiber and Kesting (“Traffic Flow Dynamics” 2013) 10, traffic models may be classified according
to their aggregation level into macro, micros and mesoscopic models.???14  Macroscopic
models, as
defined by these authors???15 , are
models, that describes traffic flow similarly to motion of liquids or gases. Based
on these definition, macro-models are the same as fluid-dynamical theories from
Chowdhury’s paper. Microscopic models, according to the authors, including
car-following and most cellular automata models, where each vehicle is
presented as a set of individual parameters and interact with surrounding
traffic. Mesoscopic models, for Treiber and Kesting, ???16 are models
that combining both micro- and macroscopic approaches. These include
gas-kinetic models; local-field models, parametrizing microscopic process with
macroscopic quantities; “master equations”, describing macroscopical dynamics
based on microscopic data such as number of vehicles passed; and
parallel-hybrid models describing critical parts microscopically while handling
other traffic flow on macro-level. Similar classifications were introduced in
other researches, such as “Genealogy of traffic flow models” by Femke van
Wageningen-Kessels 21 or “Traffic and related self-driven
many-particle systems” by Helbing 22. However, Helbing do not lists mesoscopic models
as separated category???17 , but
introduces some of them as separate unclassified approaches.

While microscopic models are likely more applicable ???18 to
realistic traffic visualization, macro- and mesoscopic approaches also require
an attention. According
to many in the field 10202221,???19  history
of ?acroscopic traffic modelling begins with the
Lighthill-Whitham model (1955)23 (also called Lighthill-Whitham-Richards
because of same model independently present by Richards in 1956 24)  based on the idea that traffic flow per line
can be described by the continuity equation, followed by many researches,
forming shock-wave theory. However, it had some disadvantages, for example, ???20 difficulties
with numerical solution, so it was followed by Burgers equation model,
introduced by Whitham in 1974 25, and by Payne’s model (1971) 26. Then, variety of models was developed up
to present days, improving classical approach. Femke 21 provides some examples of these improvements,
such as bounded-acceleration models of Lebacque 27 and Leclercq 28, where boundary conditions are applied to
acceleration and speed; or introducing lane-changes (Daganzo 29, Daganzo and Laval 30, Jin 31)


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J.M. A simple physical principle for the simulation of freeways with special
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30.         Laval J.A., Daganzo C.F. Lane-changing
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31.         Jin W.-L. A kinematic wave theory of
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purpose of research

 ???7Introducing Work -> Indicating

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 ???9Classifying and listing

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 ???12Signaling transition

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cautious,  ???14Classification and listing

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