Analytical Model for Information Flow Management in Intelligent Transport Systems

Abstract

The performance of this study involves the use of the zoning method based on the principle of the hierarchical relationship between probabilities. This paper proposes an analytical model allowing for the design of information and analysis platforms in intelligent transport systems. The proposed model uses a synthesis of methods for managing complex systems’ structural dynamics and solves the problem of achieving the optimal balance between the information situations existing for the object and the subject under analysis. A series of principles are formulated that govern the mathematical modeling of information and analysis platforms. Specifically, these include the use of an object-oriented approach to forming the information space of possible decisions and the division into levels and subsystems based on the principles of technology homogeneity and information state heterogeneity. Using the proposed approach, an information and analysis platform is developed for sustainable transportation system management, that allows for the objective, multivariate forecasting-based record of changes in the system’s variables over time for a particular process, and where decision-making simulation models can be adjusted in relation to a particular process based on an information situation existing for a particular process within a complex transport system. The study demonstrates a mathematical model that solves the optimal balance problem in organizationally and technically complex management systems and is based on vector optimization techniques for the most optimal decision-making management. The analysis involves classical mathematical functions with an unlimited number of variables including traffic volume, cargo turnover, safety status, environmental performance, and related variables associated with the movement of objects within a transport network. The study has produced a routing protocol prescribing the optimal vehicle trajectories within an organizationally and technically complex system exposed to a substantial number of external factors of uncertain nature.

1. Introduction

Among the features that distinguish intelligent transport systems from the conventional regional and national transport systems is sustainability. System sustainability is defined as the ability to increase (maintain) the required level of performance or provide the most optimal performance conditions in the event of deterioration (change) in external or internal factors. The current cargo transport systems can be characterized as a technically and organizationally complex, unsustainable system with multiple levels. One of the ways to make this system more sustainable is by managing its structural dynamics, which involves a series of control actions to ensure the transition from the currently restructured state to a synthesized multistructural macrostate.

Efforts to achieve the target level of sustainability require the introduction of the management practice of the theory of complex systems into the transport systems—more so because the complexity of interactions between the elements within the systems under study is constantly increasing, requiring new methods for big data processing and analysis [1,2,3,4,5,6,7,8]. In modern conditions, the practice of ITS control and management should be able to take into account a large number of factors, including those of a cognitive nature [9,10,11,12,13]. Solutions to these challenges lie beyond the framework of systems theory, so the modeling of a complex system is always about compromising between model simplicity and system complexity. In practice, compromise decisions are often taken based on a whole range of performance indicators, i.e., in conditions with multiple criteria [14,15,16,17,18,19,20].

In many cases, when a multicriterion problem is reduced to one single criterion within a complex system, this criterion becomes the only (core) one that governs the process of management optimization and identification of the optimal decision, in which case all remaining performance indicators acquire upward or downward limitations, with the deficiency in one criterion being compensated at the expense of another. In this case, the obtained solution can be considered acceptable, yet not objective.

Our comparative analysis of the existing methods shows that they differ in their effectiveness of determining the optimal duration required for maintaining the core quality, or group of qualities, in conditions of dynamically evolving changes in the external environment.

According to Laplace’s principle of insufficient reason, an action can be considered optimal if the subjectivity of its criterion results from the decision maker knowing the possible states of the world but completely lacking the information about the plausibility of each single state. At the same time, the principle of equal distribution builds rather on the knowledge that some outcomes may not have a greater objective possibility of occurrence than others, than on the unawareness of whether they have such an objective possibility or not in comparison with others.

According to Wald’s precautionary principle (maximin criterion), the optimal action is that which has the highest value of the effectiveness indicator for the worst-case state of the external environment.

The precaution is the basic principle also in the Savage minimax risk criterion. According to the Savage criterion, one should opt for an action with the lowest worst-case scenario risk.

The criteria proposed by A. Wald and L. Savage are subjective because they are a priori biased towards worst-case scenarios, which makes them suitable only for idealized decision making. However, the states of external environment exist objectively, regardless of the choices made.

Therefore, in general, there is no reason for extreme pessimism in decision making. A more balanced approach uses the stability criterion proposed by A. Hurwitz, in which the evaluation function is a middle ground between the extremes posed by the optimist and pessimist criteria. This criterion is a derivative of more traditional criteria. In the Hurwitz rule (pessimist–optimist criterion), it is unreasonable to ignore the highest possible gain and consider only the lower one. A certain coefficient should be introduced into decision making. When this coefficient equals the absolute optimist criterion at 0 and the Wald’s maximin criterion at 1, the action can be considered optimal. When this coefficient is greater than zero and less than one, it represents a mixture of pessimistic and extremely optimistic outcomes of future actions.

Thus, in the case of complex systems, there can be only one decision that can guarantee the highest possible effectiveness that would fully meet all criteria. While all existing methods do enable adequate decision making, they do not ensure their maximum effectiveness. The method proposed herein aims to achieve the most efficient decision making within the boundaries of the system under study.

2. Materials and Methods

When deciding on the appropriateness of a particular method for performance evaluation purposes or for identifying the most optimal action scenario within an intelligent transport system, one should first determine the complexity class of the system under analysis and which methodology best fits its complexity class. One landmark study in the field of complex systems theory (CST) is by Sayama and states that CST incorporates a whole range of methodologies including general systems theory (GST). CST is therefore more general in relation to GST and classical systems analysis. The CST structure according to [20] is shown in Figure 1.

As can be seen from the structure above, CST comprises elements of emergence [21] and self-organization [22], and is closely related to game theory, collective behavior theory, distributed systems (mass service systems) theory, adaptation and evolution, nonlinear dynamics theory, structural modeling, and general systems theory. It is our opinion that this structure lacks one important element—game theory of nature, where “nature” defines the nature of the behavior factors inherent in the external environment under study [23]. The relevance of the games theory of nature in CST is explained by the fact that it allows for analyzing a complex system’s reliability and susceptibility to the impact of external factors, and Hiroki Sayama himself describes his complex system model as susceptive, valid, and reliable, noting that these important characteristics are missing in the classical GST. In this case, “susceptibility” is defined as a cognitive factor [24] and is sometimes replaced by the term “simplification”. But, simplification is more of an arbitrary concept, as it depends on the choice of the effectiveness evaluation criteria. The term “validity” is sometimes used in reference to complex systems to denote the quality of the consistency of the obtained information state with the expected and the actual behavior of a complex system. “Reliability” defines a complex system’s sensitivity to external influences. In other words, a system’s decision regions must display sufficient stability when exposed to certain spectra of external disturbances. If minor external disturbances (influences) have no effect on the decision taken toward actions that are aimed at increasing the complex system’s efficiency, the model of such systems can be considered reliable.

While being a complex system, the ITS is classified as a dynamic system. In CST, dynamic systems theory (DST) occupies a special place, as can be judged from its definition. In the dynamic systems theory, a system’s state is characterized by a set of predetermined laws intended to effect change in the system’s parameters [25]. While this definition cannot be considered comprehensive and sufficiently clear, it reflects the basic principle of the existence and development of complex dynamic systems. It is only natural that dynamic systems evolve not only through intended modifications, but also through their self-organization ability. Being a property of complex systems, self-organization is missing only in rigidly determined technical systems, a class to which ITSs can clearly not be attributed. Figure 2 shows the structure of a complex system with features inherent in intelligent transport systems [21,22,23,24,25,26,27,28,29].

As can be seen from Figure 2, the ITS has all the features essential for a complex system, one being the high number of elements and interconnections. Like sociotechnical systems [26], organizational and technological systems [27], technological systems, and complex social systems [28], ITS is classified as a complex system in the definition given to it by GST and CST. And like any complex system, the ITS must have the ability to handle big data [29,30]. Therefore, when modeling an ITS and its optimization principles, it is necessary to

• Ensure that the ITS is presented simply, with all its dominant features, i.e., there should be a balance between the description of complexity and the simplicity of modeling.
• Give theoretical form to the complexity of ITS, using as a basis the system’s information states, which, in turn, depend on possible internal and external disturbances.
• Identify divisibility criteria with due account of the heterogeneity of elements within the ITS [31].
• Design the tools for managing and optimizing ITS performance using the existing decision-making methodologies. This is particularly important from the perspective of the system management processes, as their level of complexity is growing steadily, requiring new, CST-based models.

3. Theoretical Studies

The ambiguity with regard to quantifying the effectiveness of various decision-making management models has been addressed in quite a number of studies, evidencing the need for the further search for more objective decision-making models what would meet the modern requirements to complex systems and their interconnections within road transport systems [32,33,34,35]. The need for more in-depth, system-based theoretical research into the processes of complex transportation systems management is stated in all studies that we mentioned earlier. That said, these studies appear to pay little attention to the mathematical modeling of the processes under study and to present their outcomes as objectively verified mathematical algorithms [36,37]. The algorithmization of processes is key to the transition to digital management models and further evolution of software products [38]. This prompts a conclusion that streamlined data (databases) is a prerequisite for implementing multi-level, hierarchical systems for evaluating the efficiency of road container transport, reinforcing the relevance of the systems approach and its underlying principles. It is through the systems approach that the need for the improved coherence of data on the system’s heterogeneous properties can be validated, with the process of streamlining representing the “methodology” itself and determining the form and degree of the formalization of the outcomes.

By revealing the essence of the systems approach and its use in various fields of knowledge, we help ourselves to answer questions as to what this given process is about, what algorithm it uses, and, most importantly, what element serves as the object of management. In our case, the object of management is the multitude of road container transport systems, as well as the processes responsible for their efficient management.

The problem of systematizing the numerous indicators of road transportation performance is not new, and the need for specific solutions is only growing. Concluding what has been said above, there is a need for applied mathematical methods, especially those that use discrete mathematics and the theory of information interaction. These two fields of mathematics offer tools for formulating answers to the questions set above, guaranteeing the objectivity and the effectiveness of research. Let us use the theory of sets to show the essence and the algorithm of one of the main types of systematization—ordering, which is represented as a classification process within a particular field of knowledge.

Having noted the importance of classification in creating and improving the thesaurus, let us formulate a mathematically precise and, consequently, exact statement of the problem of the performance of classification. The need for this is due to the presence of multiple objects, their characteristics, interaction processes, and, hence, the frequent use of ordering, on the one hand, and the requirements posed to the object of research, on the other. As this task will arise more often in the future, in each specific case, it will have its own specific content, which poses the need for an evaluation methodology that would be suitable for use in any information situation existing for a particular road container transport system.

For the purposes of description, let us take a set X = {X}, the elements of which can be of diverse nature within the limits of the problem being analyzed. These elements can be objects or properties, processes, or situations pertaining to system performance.

We will call a finite set {$x_1, \dots , x_i, \dots , x_l$} of nonvacuous pairwise disjoint subsets as a classification of set (X), i.e.,

$$x_i=0, x_i\in X, i=\overline{1,L}$$

(1)

The sets (x) that give the cumulation of all (X):

$${{\displaystyle \cup }}_{i=1}^l{x}_i=X$$

(2)

$$x_i\cap x_i+1=0, \vee i, i\in \left\{i=\overline{1,L}\right\}$$

(3)

The classification procedure is performed based on a property or attribute:

$$P= \left\{P_1, \dots , P_i, \dots , P_l\right\}$$

(4)

when the elements of each distinguished subset {$x_1, \dots , x_i, \dots , x_l$} possess one of the varieties (L).

The characteristic of classification P can take the form of a set of characteristic properties

$$m=\left\{m_1, \dots , m_i, \dots , m_l\right\}$$

(5)

or of one particular property with (L) of non-spannable intervals.

The distinguished subsets, called classes, are ordered based on a set of characteristics (P) and form a “cluster”. The numbering of characteristics is possible through exhaustion and formal search for each individual representative of the “cluster” of classes.

The above description of a single-level classification does not embrace the whole variety of cases of ordering. More often than not, the number of characteristics and their varieties predetermines the need for multilevel structure of classification.

Let us consider a simply ordered set of characteristics:

$$P= \left\{P_1, \dots , P_v, \dots , P_L\right\}$$

(6)

where each $P_y$ has varieties $P_y\left(1\right), \dots , P_v\left(n\right)$.

Once the set of characteristics and their varieties have been brought into order, we can “distract” from their semantic content and replace them, for classification purposes, by ordered numerical sets of indexes, or identifiers:

$$i= \left\{1, \dots ,v, \dots , L\right\}$$

(7)

or of their varieties, if the classification of characteristics is multilevel:

$$\left\{{(1)}_v, \dots ,{(n)}_v \right\}$$

(8)

Fixing values $\left(i_1^{\ast }, \dots , i_v^{\ast }\right)$ as v-initial characteristics and the values of the remaining $\left(i_{v+1}, \dots , i_L\right)$ as variables, we obtain a formalized, multilevel structure of classes that are connected into a hierarchy and can be presented as the “tree of classes”.

$${{\displaystyle \sum }}_{v=1}^L{{\displaystyle \prod }}_{x=1}^v{n}_x=S_r$$

(9)

Given the total number of characteristics, this tree will have (L) levels in the hierarchy of the system under study:

$${{\displaystyle \prod }}_{x=1}^v{n}_x=s_r$$

(10)

with (n) classes at the (v) level and with $n_{v-1}$ classes subordinate to each particular level.

One important property of the proposed method is the possibility of determining the set of effective plans (Pareto sets) and thus allowing the decision-making process to remain focused solely on the most expedient scenarios and ignore less competitive ones. [39,40]. In other words, using these methods provides an objective opportunity for subjective decision making [21,40]. Generally, the method for determining the Pareto set in multicriterion problems does not claim to prescribe one certain action, but rather aims to eliminate uncertainty, identify critical parameters, and provide requirements to improved information on such critical parameters (performance criteria) [21,41]. This reveals a strong correlation between the determination of the Pareto set and decision making with insufficient information, both aiming to achieve the maximum possible elimination of uncertainty and to improve the information on the probability of states occurring within the environment to which the method is applied [21,40,42]. Therefore, in order to enhance the reliability of the decision making in multicriterion problems, it is expedient to create an analytical tool based on vector optimization methods for obtaining the Pareto set, which would allow for the most optimal decision making under multicriterion conditions where the information on the state of the external environment is minimal.

The drawback of the proposed method consists in the fact that the capacity of a system’s object can be determined based solely on empirical data. This drawback can be eliminated with the use of analytical methods for obtaining the values forming the Pareto set, i.e., the multicriterion problem methods where sets of possible environment states are classified according to the principle of the hierarchical relationship between the probabilities of their occurrence (zoning methods).

The main principles of the zoning method rely on hierarchical relationships between the probabilities of possible environmental states (ESs) and are as follows:

• Since zoning represents an inverse parametric problem of linear programming, it is expedient that zoning is performed based on the principle of maintaining a preset hierarchical relationship between all possible environmental states, not according to the dominant effect principle.
• When dealing with “game with nature”-related problems, it is expedient to use vector optimization techniques, and many multicriterion problems can generally be solved using the tools of game theory of nature. When passing from a multicriterion problem to a “game with nature”, the probabilities of nature states $p_j$ are coincident with relative significance coefficients for criteria ${\mathrm{c}}_j$, i.e., $p_j\equiv {\mathrm{c}}_j$.
• The procedure for zoning that uses hierarchical relationships between the probabilities of possible environment states is determined by manifestations of the ESs under analysis.

Let us form an effectiveness matrix of possible actions under various environmental states. Any task relating to decision-making optimization is characterized by three basic concepts—a set of candidate decisions; a set of environmental state types; and the efficiency of a proposed decision under each environment state. Here and elsewhere, we shall use the following designations:

• $m$—number of possible action scenarios;
• $n$—number of possible environmental states or criteria that correspond to them;
• $a_{ij}$—effectiveness of i-th action for j-th criterion,$i$ = $\overline{1,m}$, $j$= $\overline{1,n}$.

Then, the effectiveness matrix of action scenarios under various ESs shall have the form:

$$║a_{ij}║=\left(\begin{array}{cccc}{a}_{11}& a_{12}& \dots & a_{1n}\\ a_{21}& a_{22}& \dots & a_{2n}\\ \dots & \dots & \dots & \dots \\ a_{m1}& a_{m2}& \dots & a_{mn}\end{array}\right)$$

(11)

It has been found in studies [21,41,42,43,44] that there is a relationship between the Pareto set in multicriterion tasks and the zoning method for solving “games with nature”-related problems under uncertainty [45,46,47,48]. Provided that the effectiveness function of the differential state vector is continuous, the matrix game with nature can be reduced to a linear vector optimization problem [49,50,51,52]. The distribution of the effectiveness relative significance coefficients is constrained by

$$0\le {\mathrm{c}}_j\le 1, j=\overline{1,n}, {{\displaystyle \sum }}_{j=1}^n{\mathrm{c}}_j=1,$$

(12)

i.e., it is determined by a set ($n-1$) of independent values.

Every possible complete set of ES distributions corresponds to a distribution field presented as a rectangular hypertetrahedron in dimensional space ($m-1$) [21,53,54,55]. In the Cartesian coordinate system $\left({\mathrm{c}}_1,{\mathrm{c}}_2\dots ,{\mathrm{c}}_{n-1}\right)$, this hypertetrahedron is a product of the intersection of a positive hyperoctant by a hyperplane that cuts on each coordinate axis a segment equal to unity [56,57,58,59,60].

$${{\displaystyle \sum }}_{j=1}^{n-1}{\mathrm{c}}_j=1$$

(13)

Let us arrange the values of the coefficients $c_j$ into a sequence [21,46,61,62,63,64,65,66,67]:

$${\mathrm{c}}_1\ge {\mathrm{c}}_2\ge \dots \ge {\mathrm{c}}_{\mathrm{j}}\ge \dots \ge {\mathrm{c}}_{n-1}\ge {\mathrm{c}}_n$$

(14)

The total of the sequences of this type for system allocations is determined by the number of permutations $P_n=n!$:

• With $n=3,$ the distribution of the field of relative significance coefficients degenerates into a right triangle with ordinary sides (Figure 3). The number of subsets, each having its own relative significance ratio, equals $P_3=3!=6$;
• With $n=4$ (Figure 4), the number of subsets, each having its own relative significance ratio, equals $P_4=4!=24$.

Let us analyze Figure 3.

Table 1. Side and median equations for triangle ABC.

Triangle Segments	Segment Equations
AB side	${\mathrm{c}}_2+{\mathrm{c}}_3=1;{ \mathrm{c}}_1=0$
AC side	${\mathrm{c}}_1+{\mathrm{c}}_3=1;{ \mathrm{c}}_2=0$
BC side	${\mathrm{c}}_1+{\mathrm{c}}_2=1;{ \mathrm{c}}_3=0$
AE median	${\mathrm{c}}_1={\mathrm{c}}_2;{ \mathrm{c}}_1+{\mathrm{c}}_2+{\mathrm{c}}_3=1$
BF median	${\mathrm{c}}_1={\mathrm{c}}_3;{ \mathrm{c}}_1+{\mathrm{c}}_2+{\mathrm{c}}_3=1$
CD median	${\mathrm{c}}_2={\mathrm{c}}_3;{ \mathrm{c}}_1+{\mathrm{c}}_2+{\mathrm{c}}_3=1$

presents the side and median equations for triangle ABC, each of the six subsets has been assigned with its own distribution of relative significance coefficients, as shown in

Table 2. The geometric field of distribution of relative significance coefficients.

Subset	Triangle	Coefficients Ratio
I	AOD	${\mathrm{c}}_1<{\mathrm{c}}_2<{\mathrm{c}}_3$
II	DOB	${\mathrm{c}}_1<{\mathrm{c}}_3<{\mathrm{c}}_2$
III	BOE	${\mathrm{c}}_3<{\mathrm{c}}_1<{\mathrm{c}}_2$
IV	EOC	${\mathrm{c}}_3<{\mathrm{c}}_2<{\mathrm{c}}_1$
V	COF	${\mathrm{c}}_2<{\mathrm{c}}_3<{\mathrm{c}}_1$
VI	FOA	${\mathrm{c}}_2<{\mathrm{c}}_1<{\mathrm{c}}_3$

[40,41,42].

Triangle ABC reflects the system-described distribution of coefficients. As can be seen from Table 2, each of the six subsets has been assigned with its own distribution of relative significance coefficients [68,69,70,71,72,73]. For example, all possible solutions of the system of equations and inequations

$$0\le {\mathrm{c}}_j\le 1;j=1, 2, 3; {\mathrm{c}}_1+{\mathrm{c}}_2+{\mathrm{c}}_3=1;{ \mathrm{c}}_3\le {\mathrm{c}}_2\le {\mathrm{c}}_1$$

(15)

are in subset IV, i.e., within triangle EOC, and point (O) has coordinates

$${\mathrm{c}}_1={\mathrm{c}}_2={\mathrm{c}}_3=1/3.$$

(16)

4. Results

The proposed approach to zoning modeling has enabled the following algorithm for finding the maximum possible variant of the desired solution or of system boundaries:

• The relative significance of indicators ${\mathrm{C}}_j$, or their corresponding criteria, will be arranged as a sequence (14);
• For each comparable variant i, there is a linear programming problem:

  $$\left\{\begin{array}{c}{D}_i={{\displaystyle \sum }}_{j=1}^n{a}_{ij}{c}_j\to max, \\ {{\displaystyle \sum }}_{j=1}^n{\mathrm{c}}_j=1, 0\le {\mathrm{c}}_{\mathrm{j}}\le 1, {\mathrm{c}}_j\ge {\mathrm{c}}_{j+1}, j=\overline{1,n-1}\end{array}\right.$$

  (17)
• The values of the relative significance coefficients will be determined analytically:

  $${\mathrm{c}}_j=\left\{\begin{array}{c}\frac{1}{k}, \mathrm{if} j\le k,\\ 0, \mathrm{if} j>k,\end{array}\right.$$

  (18)

or to increase solution’s sensitivity to optimization parameters:

$${\mathrm{c}}_j=\left\{\begin{array}{c}\frac{1}{k}, \mathrm{if} j=k\\ \frac{\lambda }{k}, \mathrm{if} j<k, \mathrm{where} \lambda =\frac{n-1}{n}.\\ \frac{1-\lambda }{n-k}, \mathrm{if} j>k\end{array}\right.$$

(19)

where $k$is defined by $a_{kj}=\underset{j}{\max }{a}_{ij}$.

The proposed mathematical model can serve as a tool for transferring a transport system to a sustainable state, as well as a mechanism for managing the structural dynamics responsible for a system’s transition from a currently restructured state to a synthesized multistructured macrostate [40,42]. Thus, a method is in place for developing the transport efficiency management algorithms in intelligent transport systems [21,40,41,42].

In the present-day ITS, the management processes are characterized by highly dynamic changes within its operating environment; the dynamic evolution of the system’s process parameters; the high degree of uncertainty of information state; and the existence of a large number of logic criteria and possible solutions [40,41,42]. Therefore, to enhance the management efficiency in ITS, it is logical to switch from the traditional subject-oriented (scenario development) methods to object-oriented analytical models, the latter allowing for management automation through the use of the decision-making theory and its analytical techniques [40]. The proposed analytical solution for achieving a sustainable state through the transport system is facilitated through the use of vector optimization techniques, which allow an extremum problem to embrace multiple criteria and an unlimited number of indicators [42]. The proposed zoning-based mechanism for managing the structural dynamics of the objects within ITS allows for the decision making to take place under uncertainty, specifically, when

• The study has no clearly defined quantitative or qualitative characteristics of its target;
• The object of the study has not received thorough analysis at the stage of investigating the phenomena accompanying the system’s performance; or
• The external environment causes no counteraction to system parameters or the process under analysis.

In such problems, the choice of a decision often depends on the state of the “nature” of factors, and their mathematical models are called “games with nature”. Given this, the desired effective decisions can be obtained using the proposed method.

The quantified effectiveness of the proposed method, as compared to those of other methods, is presented in

Table 3. Method effectiveness comparison table.

Decision-Making Method	Solution Variant	Quantified Effectiveness
Wald criterion	1	0.200
Savage criterion	2	0.660
Hurwitz criterion	3 (4)	0.366 (0.676)
Laplace criterion	4	0.4975
Fishburne sequences	4	0.5034
Proposed method	4	0.8400

.

The proposed solutions have a high potential for facilitating the further introduction of information commutation and digital technologies into the modern reality of transport systems operation, as they allow for the parallel processing of multiple “inputs” and “outputs” within intelligent transport systems and ensure adequate amounts, or a “database”, of optimization parameters.

The digital mechanisms that are currently used in the transport sector have a high potential for employing the proposed method for more effective decision making and process optimization. Possible applications include intersection traffic safety analysis and signaled crossing safety assurance [74,75]; hardware and software packages for measuring driver reaction time in road accidents investigation [76]; and transport safety assurance with the use of intelligent driver assistance systems [77]. The proposed method will prove useful also in modeling the transport infrastructures for modern cities with growing efficiency; measuring the effectiveness of automated road accident scene sketching based on data from a mobile device camera; analysis of road safety, the reliability of the sustainability criteria for urban passenger transport, and route-optimization-based mechanisms for improving the safety of cargo transportation in urban agglomerations; forecasting the levels of energy consumption and greenhouse gas emissions from vehicles; introducing pedestrian early warning systems into intelligent transport system infrastructures; traffic accident risk analysis in conditions of urban traffic demand change; and designing a man–machine interface for self-driving vehicles with account of the time needed to take back control [78,79,80,81,82,83,84,85,86,87,88,89].

Since the proposed model is suitable for use in problems with an unlimited number of system inputs (indicators), it is possible, and advisable, to include in databases not only vehicle performance (mileage, volume of transportation, cargo turnover, etc.), but also the performance of cargo-handling facilities (terminals).

5. Discussion

The introduction of the information commutation, or digital, technologies into the modern reality of transport systems operation allows for the parallel processing of multiple “inputs” and “outputs” within intelligent transport systems [74,75,76,77,78,79] and ensures adequate amounts, or a “database”, of optimization parameters [80,81,82,83,84,85,86,87,88,89]. Using the proposed analytical model, it is possible to equip the ITS management system with an information analysis platform that builds on a synthesis of methods for managing the complex systems’ structural dynamics and allows for optimal correspondence of the information situation to the decision making. In this model, the formation of the candidate decisions space and the division of the information situation into levels and subsystems based on the principles of technology homogeneity and information state heterogeneity, are achieved through an object-oriented approach. In this way, the essence is revealed of the process of assigning to the general ITS model the specific contents that meet all pre-set conditions, economic feasibility requirements, and efficiency standards. It should be noted here that the proposed ITS modeling principles have a dual nature:

• On the one hand, when the task is to provide the state forecast, any object or process should be considered as an organized, dialectically developing system.
• On the other hand, when the task is to analyze this system for structural arrangement, properties, and internal and external interactions with the environment, a multidimensional study is required – the one that will provide an in-depth knowledge and description of the system’s current state as a prerequisite of problem solving.

This duality is not a drawback and reinforces the relevance of the systems approach in dealing with innovative developments. The proposed approach has been used by the authors to create an analytical model of ITS management that allows the tracing of the variables over time for a particular process from the perspective of multivariate forecasting. The decision-making simulation tools used in this model can be modified in relation to a particular process depending on the information situation existing for the given conditions of transportation.

When developing a management routing method, the task is to provide not only the descriptions of the objects and criteria of multicriterion systems, but also methods for transforming attributes that are essential for deriving structures for more complex system states and making the management process more flexible and versatile.

The proposed method offers the analytical tools allowing the decision-making process to be effective under stochastic uncertainty, i.e., in conditions where the information needed for the choice of the (normal, lognormal, etc.) random variable distribution law is limited.

6. Conclusions

This study has as its main outcome the method that enables the identification of the most optimal traffic routes in the dynamically changing, multi-criterion context of commercial operations planning. Specifically, the method allows for the following:

• Formalizing a transport system with due account of its information states, which, in turn, are determined by exposure to internal and external disturbances;
• Identifying a transport system’s criteria that take into account the heterogeneity of its elements;
• Achieving the tools for managing and optimizing transport systems’ performance, that build on the existing decision-making methods and allow the disadvantages of the heuristic methods used in determining the weighted coefficients of factors to be avoided.

The proposed analytical method employs a zoning technique that builds on the hierarchical relationship between probabilities and allows

• Big data in transportation systems to be processed;
• AI-based analysis of transport systems’ operating environments that involves an unlimited number of criteria or performance attributes.

Further, the proposed method allows the avoidance of the limitations of the subjective methods used in the decision-making theory, namely, the methods for

• The a priori ranking of factors (methods based on expert assessments);
• The a priori distribution of probabilities;
• Ensuring guaranteed decision levels.

With complex systems, the number of decisions that can fully meet all the criteria is always one. While the existing methods do yield competent decision making, they do not ensure its maximum efficiency. The method proposed herein allows for the most effective decision making within the boundaries of the system under study.

The proposed method is 23.81% more effective than Wald’s method, 78.57% than Savage’s, 43.57% than Hurwicz’s, 59.23% than Laplace’s, and 59.93% than Fishburne’s.

The outcomes of this study have been implemented in the research and development project entitled “Developing the Object-Oriented Management Models and Their Software Prototypes for Transport and Logistics Systems”. The project has produced an intelligent transport management system for a domestic logistics provider, that has been tested on a busy interchange road in one of the districts of St. Petersburg. According to the test results, the proposed method leads to a 15% increase in cost reduction.

The method’s high degree of reliability is assured by the use of systems analysis and systems engineering methods in creating the digital technologies implementation concept for road freight traffic, as well as by the use of vector optimization and linear programming methods in creating the analytical models for the more optimized design of road freight traffic management plans. Further, its high reliability is attested by the proprietary software product intended for automating the newly developed, centralized transportation management methods: “The Software for Identifying Optimal Transportation Routes in Dynamically Changing Road Environments”, authored by Andreev A.Yu., Egorov V.D., Terentyev A.V., Evtyukov S.A. Software Registration Certificate 2021667592, country: Russia, 2021, registration date: 1 November 2021.

The principal advantages of the proposed model for assuring effective decision making in complex, big-data-based information and analysis systems and software products, consist of:

• The absence of a formalized relationship between the weighted coefficients obtained for individual criteria and action options in transport systems;
• The resultant decision being the maximum possible under the initial values of performance indicators for the criteria under consideration;
• The resultant decision allowing not only the desired Pareto-optimal decisions to be obtained, but also the number of required computations to be substantially reduced.

The proposed method is unique in the sense that it offers analytical tools, allowing the decision-making process to be effective under stochastic uncertainty, i.e., in conditions where the information needed for the choice of random variable distribution laws is limited.