MODELLINg THE INTERACTION OF TRANSPORT SYSTEM ELEMENTS

. Economy and nonproductive sectors of each country could not function without a transport system (TS). Having analysed research works on the interaction of separate TS elements, it was identified that there is no common model for all types of interaction. TS consists of material (physical) objects: traffic participants and freight to be carried, a transportation process and operations’ control. TS classification scheme devised according to systematically selected criteria, showing that several criteria are often applied at the same time in official documents, is presented. Original TS physical elements’ interaction model with 6 interaction levels is presented as well. The model is suitable for all modes of transport. Six levels of interaction are distinguished: autointeraction of transport elements, the first level; TS elements’ interaction, the second level; TS elements’ interaction with external environment, the third level; interaction of transport modes, the fourth level; TS interaction with the country’s economy and nonproductive sectors, the fifth level; and TS impact on the country’s GAV (Gross Added Value), the sixth level. Properties and factors influenc-ing on the results and parameters of interaction have been systematized. Levels and properties of interaction have been analyzed as well. To evaluate the importance of interaction levels to the parameters of the transportation process, the method of Analytic Hierarchy Process (AHP) has been recommended.


Introduction
Freedom of movement has been one of the greatest values of humanity, which can be used if a developed transport system (TS) of the country is available. The transport sector was and still remains one of the most important economic driving forces in the country, Lithuania not being an exception as well. (Mačiulis et al. 2009). Analysts agree that transport will continue to have a positive impact on the economic growth. The growth of the transport sector, especially road transport, increases congestion and environmental pollution as well as reduces safety. Acts of terror occur in the air and railway transport. Cars are also used for this purpose.
Passenger and freight carriage is a dynamic process since its parameters frequently change in the course of time. The paramers of the carriage process are stochastic; however, their change is usually influenced by concrete conditions, the impact of which may be simulated and forecasted. Dependable forecast requires necessary data. Data are obtained through the simulation of interaction processes, their observation, measuring or reproducing the dynamics of interaction after traffic accidents and catastrophes from devices automatically recording their sequence, i.e. black boxes. It enables to find out the reasons of catastrophes and to reduce their risk.
Separate elements of the system interact in the transportation process. The interaction results (consequences) may be positive and negative as side-effects always occur in the transportation process. The interaction of separate transport modes' elements has been studied by researchers from various countries of the world as well as from Lithuania. Road transport functions in all countries; therefore the interaction of its elements has been studied most thoroughly. Railway transport takes the second place according to the amount of carried freight and passengers. Here we survey some research works where recent findings have been published.
The greatest problems posed by TS are insufficient traffic safety as well as physical and chemical pollution of the environment. To improve traffic safety on the roads, the road or its separate sections' reconstruction or upgrading measures are taken; traffic control, accounting and management measures are improved; vehicles are upgraded; road users are disciplined.
The results of macroeconomic simulation showed that each Litas invested into the Lithuanian transport infrastructure generates approximately a double benefit in 4-5 years.
In most countries, roundabouts have become more and more popular, and it is often considered to be the main type of intersections in urban areas (Antov et al. 2009). Accident rates are very low, and traffic conditions and speed reduction possibilities are excellent on them. A driver's behaviour directly depends on the driver's understanding of the road infrastructure, road environment and the conditions inside the vehicle (Pellegrino 2009).
Steel structures covered with ground are usually used in the construction of culverts on local roads or even motorways as well as railway viaducts, and, currently, in the construction of ecological objects or tunnels (the animal crossing situated under and above a highway) (Beben 2008). Prospects of transport road metal structures' elements and their system design are related with probality calculation elements (Jankovski and Atkočiūnas 2008). Animal passages and net fencing on the roadside enable to avoid collision between animals and vehicles.
Frequently, a vehicle's tire interacts with the road surface through an intermediate element. When a layer of water builds between the road surface and the rubber tires of the vehicle, the risk of aquaplaning occurs (Fwa et al. 2008Ong et al. 2005;Beljatynskij et al. 2010).
Rubber deposits change the parameters of the wheel's interaction with the road surface (Chen et al. 2008). In winter, snow falls on the road surface, which worsens driving conditions (Chen et al. 2009;Matsuzawa et al. 2009). At present, to protect the road from climatic factors or to clean the road from the accumulated ice layer in an extremely short time, wet salt technology is applied (Žilionienė, Laurinavičius 2007). In winter technical salt is sprayed, which reduces road pavement slipperisness and directly or indirectly pollutes the environment (Baltrėnas, Kazlauskienė 2009). Studded tires used in winter not only intensively deteriorate road pavement but also pollute the air as well (Vaiškūnaitė et al. 2009;Laurinavičius et al. 2010). Baltrėnas et al. (2008a) presents the technique of mathematical simulation of solid particles dispersion in the air. Traffic is the main air pollution source in most cities (Orru et al. 2008). To investigate dispersion properties caused by transport pollutants on the motorways (Brannvall, Martinėnas 2007), mathematical distribution based on the physical model is used.
Motor transport has the greatest share in the emission of mobile pollutant sources (Baltrėnas et al. 2008b;Lewis et al. 2009). It has been set that of CO, NO x , CH x , SO 2 directly depend on motor transport's intensity.
The noise level generated on urban roads can be excessive and has a negatyve impact on the urban environment (Krezel and McManus 2010). Due to the engine work and air resistance in the interaction between the wheel and the road surface, noise is generated (Pierce et al. 2009;Crocker et al. 2004). Noise level may be meas-ured by a natural experiment or a computer simulation (Shukla et al. 2009). The authors study possibilities of FHWA model application to prognose the noise level caused by transport and to evaluate it in India. Equivalent noise level spread from streets to the residential territory during the day and night time is modelled in work Vaišis and Januševičius (2009). Sources of noise are evaluated Baltrėnas and Puzinas (2009). Reasons of a higher noise level than that presented in the higienic norms and possible causes of its occurance in the teritory of the enterprise and in the neighbouring residential zone. Research (Leipus et al. 2010) of noise level dependence on car speed was performed from 50 km/h to 70 km/h. It was determined during the study that noise level produced by a car moving at a speed of 50 km/h on a road with gravel pavement is higher by 4 dBA than that on a road with asphalt pavement.
Road surface roughness and rutting impact on the dynamics of the running vehicle, which influences on traffic safety. The development of road surface defects and their impact on the vehicles may be simulated (Gallivan et al. 2004;Coleri et al. 2008;Vansauskas, Bogdevičius 2009;Priya et al. 2008;Salama et al. 2007;Xia 2010). Residual deformations leaving ruts is one of the most frequent defects worsening the road pavement exploitation properties (Radziszewski 2007;Suo, Wong 2009;Haryanto, Takahashi 2007). Heavy, frequently recurrent loads of heavy vehicles' axles have the greatest impact on the road pavement layers' deterioration and deformation (Dawson 2008;Tran, Hall 2007;Papagiannakis et al. 2007;Bagamppade, Kiggundu 2007;Wang et al. 2009). Machemehl et al. (2005) measured the truck tire pressure on the road pavement according to the tirepavement contact stress data. Based on the theory of the object's collision with the hole's angle obstacle (Viba et al. 2009), a vehicle's movement when colliding with the hole's angle obstacle has been investigated. The findings of the study can be used in accident experiments when investigating the interaction between the vehicle and one or several obstacles.
Heavy vehicles cause vibrations in bridge structures (Lee et al. 2009). Bridges should be seismically isolated (Han et al. 2009). The residual dependability index of road bridge supportive structures overloaded with contingent variable vehicles (Kudzys 2009) has been proposed.
To improve the parameters of the traffic process on the roads, traffic control and management devices as well as road weather information systems are used (Finley et al. 2006;Nagata et al. 2008). They usually improve drivers' behaviour on the roads (Billot et al. 2009). Five main traffic management groups are pointed out (Lundkvist, Isacsson 2008): road lighting, fencing, guardrailing, vertical and horizontal marking as well as traffic lights. When installed on the road, they shall preserve their exploitation properties.
The study (Tampère et al. 2009) on evaluating the effect of road charging on social wellness showed that traffic between Brussels and Gent cities has decreased due to the increased travel prices when tolls were introduced on the roads.
Road pavement surface is constantly influenced by environmental factors (temperature, sun radiation, precipitation water, air oxygen, wind), which change its temperature and asphalt properties (Gui et al. 2007). Average daily traffic on the road constantly increases, and on separate sections it varies a lot (Sivilevičius, Šukevičius 2007). Hence, equivalent single-axle load (ESAL) having different deteriorating impact on asphalt pavement varies as well. Erosions caused by transport traffic, the wind and water cause rutting on aggregate road shoulders, break pavement edges, and cross-fall does not meet the needs (Vorobjovas, Žilionienė 2008). After hurricanes Katrina and Rita, the highway contruction cost jumped about 20% statewide and 51% GO Zone (Cheng, Wilmot 2009).
To construct, strengthen and reconstruct a new road pavement, each year more and more hot-mix asphalt (HMA) mixture is produced through the application of more upgraded technologies and equipment (Sivilevičius, Šukevičius 2009). Permitted deviations of components' quantity in HMA mixture are reduced, which enables to pave a maximum duration asphalt concrete layer (Petkevičius, Sivilevičius 2008;Bražiūnas, Sivilevičius 2010).
The homogeneity of the HMA mixture in the road pavement depends on the stochastic technological factors in its production in an asphalt mixing plant, the impact of which is taken into account in HMA mixture grading design model (Sivilevičius, Vislavičius 2008;Sivilevičius et al. 2011). During the asphalt pavement life cycle, the impact of vehicles' axle loads, environmental factors, exploitation and defect repair materials accumulate in reclaimed asphalt pavement -RAP) inhomogeneity (Mučinis et al. 2009).
To simulate and investigate the intercation between vehicles and guardrails and curb, the studies by Macek, Mĕšt'anová (2009);Sokolovskij et al. (2007); Prentkovskis et al. (2007Prentkovskis et al. ( , 2009Prentkovskis et al. ( , 2010b were conducted. According to them, the most important evaluation criteria of guardrails are their safety, economic and ecological aspects. The deformation of road guardrails' metal beam and post when hit by a vehicle has been investigated. To carry out a computer experiment, the mathematical model of the road guardrail has been constructed. Vaidogas (2007) proposed a protective transport structures' design method based on the risk analysis. It is considered that accidents damaging road infrastructure elements is a natural risk analysis object.
Meta-analysis results indicate that the crash rate usually increases during precipitation (Qiu, Nixon 2008). Snow has a greater effect than rain does on crash occurrence: snow can increase the crash rate by 84% and the injury rate by 75%.
It has been identified that (Sathyanarayanan et al. 2008;Gibbons, Hankey 2007;Choubane et al. 2006) the parameters of horizontal marking and pavement reflection have impact on traffic safety on the roads.
Multi-purpose road variant designing optimization methodology was developed and applied (Brauers et al. 2008).
A priority list of the Vilnius city development scenarios, taking the indicators of the city's transport system into account, was identified according to the multi-criteria method (Jakimavičius, Burinskienė 2009). Čygas et al. (2009) state that traffic safety measures implemented in Lithuania influence on all elements of the traffic safety system road user-road-vehicle. The article (Kapski et al. 2007) describes an attempt to apply the theory of catastrophes to the traffic situation development process in a conflict situation, which ends with an accident.
To investigate the interaction of railway transport elements, several models have been constructed as well. The main assets of a railway system are its infrastructural objects and rolling stock (Povilaitienė et al. 2006). Rail wear reduction possibilities in curves have been investigated. The mathematical model which takes into account the impact of track width on the rail wear in curves is presented. Turkish researchers Sonmez, Ontepeli (2009) presented the calculation method of the city's railway system pre-design expenses based on the parametric simulation. The proposed method enables to construct parametric design expenses model in the early pre-design stage. The importance of quality criteria has been evaluated through the use of AHP (Analitic Hierarchy Process) method in the paper (Sivilevičius, Maskeliūnaitė 2010) dealing with the improvement of the quality of carrying passengers by railway.
The aim of the work is to construct the model of transport system's elements, to present the levels of their interaction, to work out the method of determining the interaction priority and to reveal its impact on the transportation process properties as well as the country's economy and nonproductive activity sectors.

Transport System Elements and their Classification
Transport is a constituent part of the country's infrastructure, which has to satisfy the needs of the people and economy in terms of freight transportation and passenger carriage. The transport sector is an integral service provision economy branch. Transport services are used by all economy and nonproductive activity sectors without any exception.
Transport may be analyzed in a broad or a narrow sense. In a broad sense, the transport system (TS) includes all transport modes (TM) in the country. Each TM consists of three integral parts: transport material (tangible) elements, transportation process (TP) and activity regulation (Fig. 1). Their complex and required properties guarantee proper functioning of TS. In a narrow sense, according to some researchers, only transportation facilities or/ and transport management, economy and logistics are considered to be transport. In their opinion, transport ways are not TE.
The classification of transport, like other objects, economy and service sectors is a conventional matter as it depends on the selected principles, features and criteria. So far there has been no common strict transport classification system. In different laws, codes and directives it is presented incomplete, varying and is constantly changed. Overall classification is rather complicated and depends on the classification criteria or combinations of properties (Table 1).
Experience shows that transport is usually classified into modes according to the first property, i.e. the type of the way used by vehicles, which carry freight or passengers. Such classification is clear and complies with the administrative dependence and division.
The system of any major TM (road transport, railway transport, air transport, maritime transport, inland water transport) consists of the following (Fig. 1): -transport material (tangible) elements (traffic users and freight, vehicles and transport technological equipment (TTE), transport ways and terminals, which are called infrastructure); -TP (planning and organization of carriage, preparation of transportation, passenger embarkation or freight loading, carriage of passengers and freight, passenger or freight transshipment in a terminal, passenger or freight disembarkation at their destination point);  Preserving stable freight properties, slightly changing freight properties, changing freight properties -activity regulation (political, strategic, directive, economic, scientific, legislative, social guaranties, regulatory injury insurance). Pipeline transport, technological road transport, and cable road transport may be considered additional modes of transport. The interaction of TS structure model material constituents (elements) is shown in a model (Fig. 2). In case one of the elements is missing, the TP is usually impossible or irrational. In case of exception (sometimes), a vehicle may run idle, i.e. without any freight or passengers. However, such activity is ineffective as it does not create any gross added value (GAV).
Other reseachers (Benson, Whitehead 1994) claim that every mode of transport uses four major components, or essential elements of transport. These are the way, the terminal, the unit of carriage and unit of propulsion. When classifying transport into modes, researchers do not distinguish inland water transport.
To analyze the structure of TS, the terms and their definitions presented below are important. A TM is the field of activity organizing, implementing, developing and maintaining carriage of freight and/ or passengers on one (the same) structure and purpose natural (water, air) roads or artificial ways (car, railway, pipeline). A transport object (TO) is a material part of a special purpose TS for performing and/ or servicing passenger and freight TP. A transport element (TE) is a transport object of any TM or its TO material constituent.
Traffic participants are people who take part in traffic: drivers, passengers and pedestrians. A driver is a person who drives or teaches how to drive a vehicle, herds animals or birds as well as a horseman. Different minimum age is set for drivers of different categories of road vehicles. A pedestrian is a person who is on the road but not in the vehicle as well as the one who goes in a wheelchair, roller-skate, skateboard, scooter, pushes a bicycle, a moped, pulls (pushes) a sledge, a perambulator or any other type of a trolley. This first (1) group of physical components partly includes people working on the road, i.e. traffic controllers, wardens, supervising officials, people who repair or supervise a road, technical traffic control facilities, those who eliminate the consequences of accidents, customs and border crossing points' officers or people working near running vehicles or inside TTE. According to traffic regulations, people working on the road are not considered pedestrians as the road is a working place for them. However, they take part in the traffic process.
A passenger is a person who is waiting for a vehicle or is inside a vehicle, but does not drive it. Freight is an article or an animal suitable (prepared) for transportation or is transported. Properties of freight, especially those of hazardous freight, impact on their transportation technology.
The second (2) group of transport physical components includes vehicles and TTE. A vehicle is a device for carrying people and (or) freight. This term in road transport also includes tractors and self-propelled machinery, trailers and semi-trailers. In road transport, the most important vehicle is a car. A car is any motor vehicle using the road and carrying freight and (or) passengers or towing other vehicles. Trolleybuses belong to the category of cars as well. Motorcycles, tractors and self-propelled machinery (TTE) do not belong to the category of cars.
Mobile and stationary equipment used in the loading process in terminals, road, railway, airport maintenance and construction as well as traffic accounting, management and information equipment shall be considered TTE.
Transport ways (TW) are natural and artificial roads with their structures (bridges, jetties, intersections, viaducts, overhead roads, tunnels) and facilities (road signs, guardrails, traffic handling and accounting, lighting, information technologies) as well as terminals to be used by running, sailing, flying, flowing vehicles. Transport ways comprising the third (3) group of physical components are also called transport infrastructure. The road is a lane of land or structure's surface used by transport at its full width, including carriageways, intersections, sidewalks, road shoulders, walkways and cycle tracks. Highways and motorways, canals, railways, tramways, tunnels and monorails are similarly constructed (Benson, Whitehead 1994).
A TP is a process of movement of a vehicle with freight, passengers or only with a driver for changing their place. Traffic is the movement of vehicles and/ or pedestrians, horsemen along a set route intended for all or only some types of vehicles.

Interaction Model of TS Elements
The TS is investigated as a whole of interrelated integral elements in the external environment, the activities of which are intended for carrying freight and passengers. TS mission is to guarantee sustainable mobility of society members and carriage of goods, maintaining the dynamic development of the country's economy and increasing competitive capability of the country in international markets. The necessity of transport is based on the existence of its three physical components (traffic participants and freight, vehicles and TTE, TW and terminals, i.e. its infrastructure (Fig. 3). The system of three 'supports' survives if all three supports showing transport's material (physical) objects are available.
The following six levels of TS elements, external environment factors as well as economy and nonproductive activity sectors' interaction may be pointed out in the model (Fig. 3): I, II, III, IV, V, VI. The first (I) level consists of autointeraction, written on the top of the model with arrows at the ends of U-shaped bands drawn on a horizontal plane. Freight, traffic participants, vehicles, TTE as well as TW and terminals (infrastructure) interact .
The second level of interaction (II) consists of the physical interaction of transport material elements. Traffic participants and freight interact with vehicles and TTE. Vehicles and TTE interact with transport infrastructure. TW and terminals (infrastructure) interact with traffic participants and freight. The interaction of the second level is shown by arch-shaped (bent) bands with arrows at the ends drawn on the horizontal plane on the bottom of the model. Transport functions in the external environment, which is made up of people, energy objects (power plants, its transfer by air and underground lines), plants (flora), buildings, air and its constituent gases (hurricane, tornado, wind), water (rain, shower, steam, mist, ice, snow, cunami), ground (volcano ash formed from the depth of earth, lava, mountains, earthquake formed due to tector plane movement, dirt slumps), animals (fauna). Eight elements comprising physical environment interact with the following TE: traffic participants and freight, vehicles and TTE, TW and terminals (infrastructure). This physical interaction is attributed to the third (III) level. It is illustrated by vertical bands drawn on the sides of the model with bent ends and arrows. Transport should be eco-friendly. Environment may also be internal (inside vehicles) and macroeconomic. The fourth (IV) level of interaction is comprised of the interaction of TM. TS transport of different modes usually interacts not physically but in organizational, competitive, economic, carriage market division areas. In spring 2010, when the volcano errupted in Iceland, air space was polluted. Due to the cancellation of flights, passengers had to use other modes of transport. The physical interaction of TM is made up of the interaction of different modes' material elements. The fourth level of interaction in the model is illustrated by horizontal circles, corresponding with various TM, on the left side 6 arrows reminding vertical comb teeth.
The following physical parameters impact on the physical interaction of transport and their interaction with the external environment: the state and properties of a material, temperature, noise and vibrations, friction, adhesion, cohesion, time, speed and acceleration, weight, dimensions and shape, lighting, gravitation. The interaction process and its result are influenced by standardi-zation, normative and legal regulation, marketing. Their impact on the interaction is illustrated in the model by a dotted line surrounding 'Transport modes and elements' and 'External environment' .
Transport is an integral part of the country's economy and nonproductive activity sectors. The following economy sectors use transport services: mining, energetics, agriculture, fishery and hunting, foresting, construction, industry, trading, municipal economy, tourism and sports, communications and consignment. The following nonproductive sectors could not exist without it: education and culture, public health, social security, environmental protection, national defence. Its services are used by special and diplomatic services, banking and cash services. Transport interaction with separate economy and nonproductive activity sectors belong to the fifth (V) level. It is illustrated by arrows pointed to the exterior of the model (Fig. 3). The most important result of this level of interaction is its impact on the country's economy, expressed by gross added value (GAV).
The role of transport in generating GAV is of paramount importance. (Fig. 4, VI interaction level). In the Lithuanian transport sector, approximately 5% of the country's employed work; however, during the last seven years they have generated 9.4-11.0% of GAV. Income generated from transport and stocking activities was constantly increasing: from 4.81 billion LTL in 2003 to 9.1 billion LTL in 2009.
Physical interaction of TS material elements may be classified and analyzed in various aspects. From my personal experience and analysis of research works, we recommend to point out the following features and forms of expression: 1) According to the distance between elements (immediacy), the interaction may be as follows: -contact (direct) when TS elements directly, without any medium (TS element or environmental element), physically touch each other and interact; -noncontact (indirect) when one element (body) does not touch another but impacts another remote element through an intermediate TS or an environmental factor element. 2) According to the utility of the interaction result to theTP, the interaction may be: -positive, when it enables to obtain the expected result or approximates to this result; -negative, when the result is undesirable and dangerous. 3) According to the change of interaction parameters in the course of time, the interaction may be: -static, when the impact of TS's one element on another element does not change in the course of time; -dynamic, when TS elements' interaction parameters (size of forces, directions of movement, speed and acceleration, tem- Fig. 3. Model of transport system elements' interaction and its impact on the country's economy and nonproductive activity sectors perature and others) change in the course of time. 4) According to the purposefulness of interaction (the number and origin of purposes), it may be: -single-sided (one-direction), when any TS element impacts on another element, not impacting on the first element; -double-sided, when interacting TS elements have the same or different impact on each other. 5) According to the duration, the interaction may be: -permanent (continuous, constant), when elements' interaction lasts for a long time without any interruptions during the whole transportation cycle; -episodic (random, discontinuous), when TS elements interact for a short time during a certain preset or unforecasted time and under certain circumstances. 6) According to the impact on the TP, the interaction may be: -passive, when interacting TE do not change the parameters of the TP (and interacting elements); -active, when interacting TE change each other's and/ or TP parameters. 7) According to manageability, the interaction may be: -uncontrolled, when TS elements' interaction commencement, its duration and completion time as well as parameters cannot be changed with all possible means available; -controlled, when a traffic participant (driver, pedestrian, passenger) or a worker may with the help of certain actions or equipment automatically or programmably change the parameters of elements interacting in the TP. 8) According to its eco-friendliness, the interaction may be: -ecological, when the consequences of TE' interaction on the environment and traffic participants do not inflict any harm or harm is not significant and does not exceed the permitted one; -not ecological, when TE' interaction inflicts significant harm on the environment and traffic users. Improving the interaction between the TS elements by using research-based decisions.
These eight features may be used to describe any interaction of TE. It is not always expressed numerically. It is difficult to compare interactions if qualitative parameters are not expressed quantatively.

Evaluation of TS elements' interaction by AHP method
'Not everything that counts can be counted, and not everything that can be counted counts' (Albert Einstein). It has become common to simulate TS elements' interaction and to calculate its parameters. It is quite complicated to compare different types of interactions; however, it has become possible with the help of modern research achievements. A previous provision that apples cannot be compared to oranges is not correct any more (T. L. Saaty). From the model (Fig. 3) and its analysis we can see a lot of possible TS elements' interaction levels and their combinations. Ranking methods enable to determine which interaction is more important to the parameters of the TP and its final result. Complex evaluation and rating of objects (interactions) according to the aim under investigation depend on factual values of indicators and their importance.
Indicators' importance determination methods are classified as subjective if evaluated according to the opinion of specialists (experts). High qualification skills of experts are necessary for subjective evaluation.
As a rule, the more a person knows the situation, the more consistent he is in his solutions. Although an opposite correlation is not necessarily correct, excellent compatibility of solutions does not necessarily mean that a person understands the situation well.
Recently, a popular twin comparison method called Analitic Hierarchy Process (AHP), which was offered by Saaty (2000) and Saaty et al. (2003), has been widely used. Twin comparisons enable to increase the compatibility of evaluations. AHP method enables to identify one level hierarchy indicators' significance (importance) in terms of a higher level or hierarchically non-structured significance of indicators. The essence of the method lies in the matrix of twin comparison. An expert compares all evaluated indicators (TS elements' interactions) i R and ( ) , 1,2,...
, here n -a number of comparative indicators (TS elements' interactions).
The method is convenient as it is easier to compare TS elements' interactions in pairs, but not all at a time. The importance of one TS elements' interaction than that of another is shown as well. The method enables to replace qualitative indicators given to TS elements' interaction by experts by quantative ones.
Suppose that the importance or impact of TS elements' interactions 1 ,..., n S S on the parameters of the transportation process shall be compared.
We will study an ideal situation assuming that the importance of our compared interactions is absolutely identical. We will mark this significance by values 1 2 , ,..., n ω ω ω . Ratio shows how many times i TS elements' interaction i S is more important than j interaction j S .
We will write ratios (1) by a square matrix: where: / i j ω ω -relative importance of factor i compared to factor j ; n -the number of factors in a set.
The relative importance of n factors can be obtained by resolving the following equation: ( 3) where: -a vector of relative weights; and max l -largest eigenvalue of matrix A . If there is no judgement inconsistency, max l should be equal to n (matrix size).
The AHP method assesses the consistency of each expert's estimates. Consistency index C.I. is defined (Saaty et al. 2003;Sivilevičius, Maskeliūnaitė 2010;Podvezko 2009) as a relationship: The smaller the consistency index C.I., the higher the consistency of the matrix is. In the ideal case, . . 0 C I = .
Inverse second-order simetrical matrices are always consistent. The relationship between the calculated consistency index C.I. of a particular matrix and the average random index R.I. is referred to as consistency ratio C.R. It determines the degree of the matrix consistency: . . . .

C I C R
R I = . (5) The value of consistency ratio C.R. which is smaller than or equal to 0.1 is acceptable, implying that the matrix is consistent.

Numerical simulation influence of TS elements interactions in roadway transport safety
In the road transport (model Fig. 3) as in any other transport mode the following three first TS elements' interaction levels are pointed out: 1. Traffic participants-traffic participants interaction (interaction code I-1-1); 2. Vehicle-vehicle interaction (I-2-2); 3. Transport road-transport road interaction (I-3-3); 4. Traffic participants-vehicle interaction (II-1-2); 5. Traffic participants-transport road interaction (II-1-3); 6. Vehicle-transport road interaction (II-2-3); 7. Traffic participants-environment interaction (III-1-E; E-environment); 8. Vehicle-environment interaction (III-2-E); 9. Transport road-environment interaction (III-3-E). Interactions of all these levels have impact on traffic safety. TS elements' interaction parameters change in the course of time and frequently have stochastic origin. To identify their impact on traffic safety on the roads, statistical data or expert investigation methods, including AHP method, may be applied.
AHP method is special so that it requires high level thinking of experts. The opinion of a competent expert is much more important than that of several inexperienced (unable to think logically) specialists. Therefore, researchers often interview several experienced experts, e.g. 5 experts (Farhan, Fwa 2009).
The significance of the impact of TS elements' interaction on the number of accidents on the road has been identified according to the opinion of one expert, which enabled to calculate the consistency of a comparative matrix. Using his experience, competence, knowledge and intuition, the expert compared TS elements' interactions with each other (double comparison). He has also taken into consideration the significance of the intensity of criteria (interactions) in terms of each other on a five-point scale (1-3-5-7-9), pointing out how one interaction of TS elements is more important than the other (Table 2).
Double comparison matrix of all TS elements' interactions (Table 2) enables to calculate eigenvector ω according to the formulas suggested by Podvezko (2009). Its calculation sequence is presented in Table 3.
The consistency of compared matrix is verified ( Table 2). Thus, the sum of multiplications 9 1 ij j j a = ω ∑ is divided by the corresponding criterion calculated value i ω , presented in Table 3. Calculation results are presented in Table 4.
We find the arithmetic mean of these values, which is equal to the largest eigenvalue of matrix max l : We obtain max 10.02 l = . It is known that inverse symmetric n row matrix maximum eigenvalue max n l ≥ . The closer max l criteria number n (compared TS elements' interaction number) is, the more consistent result is obtained. In our case, the comparison matrix row or the number of compared TS elements' interactions (criteria) (matrix size) 9 n = . Hence, 10.02>9. The condition is met. Now we can calculate consistency index C.I. according to the following formula (4) The ratio of matrix consistency index C.I. and random index R.I. found in the publication (Saaty 2000), is obtained according to the following formula (5): A matrix is considered consistent if the value of ratio C.R. is smaller than 0.1. In our case 0.088<0.1; therefore, the matrix of the presented digital sample is consistent.

Conclusions
1. The functioning of the transport system (TS) is related to various interactions of its elements. A number of research works are dedicated to investigate the interaction of separate material elements of various transport modes (TM), the analysis of which showed that a model common for all interactions does not exist. Table 2. Significance of TS elements' interaction to the accident rate in road transport criteria double comparison matrix 2. Transport system objects (elements) classified according to the set new criteria enable to reveal its structure more accurately and simplifies the process of analysis.

An original model showing six levels of TS elements'
interaction is presented. It reveals the relationship of its material elements' interaction, the interaction with the external environment and the interaction among TM and the interaction with the country's economy and nonproductive activity sectors. Interaction expression properties, which reveal its qualitative aspects and differences, are systematized. 4. Separate levels of TS elements' interaction differently influence on the parameters of the transportation process (TP). We recommend to use the Analytic Hierarchy Process (AHP) method to evaluate the Table 3. Calculation sequence and results of eigenvector ω

Calculation step TS elements' intersection (criterion) mark (code)
I-1-1 I-2-2 I-3-3 II-1-2 II-1-3 II-2-3 III-1-E III-2-E III-3-E Step one Calculated elements a ij from each row of Table 2 E.g., first row ij a elements multiplication Table 2   importance of different interactions to the parameters of the TP. The effect of the interaction of the TS elements of various levels on traffic safety on the road demonstrated by a numerical model proved the effectiveness of using AHP method for establishing the priority of various interaction forms.