1) The discipline «the Theory of distribution of the information» provides a reshaping of experts in the field of maintenance service (testing, measurements, replacement, regulation and repairs) as in the conditions of new быстроустаревающей technicians of communication and substantial growth of its reliability the profit on these actions has sharply fallen.

The specified reshaping mentions faculty retraining, overcoming of inertia of thinking and developed traditions in branch of communication and an education sphere, re-equipment of educational laboratories, practically a regeneration of the educational-methodical literature. The matter is that the modern electronic society will claim for creations of own virtual network as paid service in the individual order of the consumer.

The primary goal of discipline includes carrying over of accents from maintenance service principles on principles of technical operation (sale of typical services to subscribers, tariffing of a telecommunication service, construction of chains of tariffing, the device of service of tariffing, the fiscal policy and construction by a network bilingual).

In these new to the post-Soviet territory, conditions it is necessary to build operatively the mixed networks on transportation of the diverse information with various disciplines of service, simultaneously providing demanded structural робастность, a semantic and time transparency of any virtual channel.

Subject of the theory of distribution of the information (teletraffic theory) is the quantitative party of processes of service of streams of messages in systems of distribution of the information. The main objective of the theory of distribution of the information consists in working out of methods on which estimate quality of functioning of systems of distribution of the information. Systems of distribution of the information are one of classes СМО(Система массового обслуживания –Queuing System). Sets of switching devices, a part either all switching knot or a communication network which serve telephone, cable and other messages on separate algorithm can be system of distribution of the information. As well as any other mathematical theory, the theory of distribution of the information (the teletraffic theory) operates not with systems of distribution of the information, and with their mathematical models.

It is necessary to carry problems of the analysis, a problem of synthesis and an optimisation problem to the primary goals of the theory of the teletraffic. Analysis problems in an initial stage of development of telephone technics were more actual, they dared by means of probability theory mathematical apparatus. Therefore the most considerable results for today are received at the decision of problems of the analysis. We will consider two characteristic examples.

The basic methods of the decision of problems in the teletraffic theory are analytical, numerical and a method of imitating modelling. In many cases the reasonable combination of analytical and numerical methods to a method of imitating modelling allows to analyse investigated system in details. At small deviations of parametres of system it is possible to receive the decision exact analytical methods and to analyse limiting cases at асимптотическом behaviour of characteristics of studied system. The received data are supplemented with results of imitating modelling in the field of real values of parametres of system.

The mathematical model of system of distribution of the information includes following three basic elements: * incoming stream of calls (requirements of service); * diagram distribution information of systems; * discipline service of a stream calls.

In the scientific literature for compact record of mathematical models often use the designations offered by D.Kendallom.

Bases of the theory of the teletraffic have been put in A.K.Erlanga's works in 1908 - 1918 years on throughput research fully accessible the bunch of lines serving the Poisson stream of calls with losses and with expectation. A.K.Erlang has entered concept of statistical balance and used it as a theoretical basis for reception of the widely known formulas for probability of losses and expectation. It considered an entering stream of calls from infinite number of sources at an indicative and constant holding time. In 1 918 year T.Engset has generalised A.K.Erlanga's results on a service case fully accessible a bunch of a stream of calls from final number of sources of loading. In 1 933 year A.N.Kolmogorov has performed the classical work on an axiomatic substantiation of probability theory in which A.K.Erlanga's idea about statistical balance has been identified with the stationary measure of Markovsky process. During the same period there were A.J.Hinchina's first works on research of systems with expectation.

2) Property of markovost’

The broadcast signal sender involved (the supplier of the information), the addressee participate in a signal transmission (the client - the information receiver), means of communication and transferring environments which are called as a communication channel.

Senders and addressees of the information can be both people, and technical devices (devices, indicators, cars). The information subject to transfer and expressed in the certain form, is called as the message.

It is necessary to understand with various forms of messages, to learn to choose means for their transfer and switching.

Streams of messages generate streams of requirements of service on communication centres, tell streams of calls or are simply sonorous. We will assume that one of such streams of calls for an establishment of connections on telephone negotiations has arrived on СМО(Система массового обслуживания – Queuing System) and by definition it is specified as Poisson. It is known (the Module 2) see that duration of telephone negotiations submits экспоненциальному to distribution, i.e. function of additional distribution of holding time H (t) decreases in process of increase нормированной duration of negotiations after an exhibitor in co-ordinates (нормированное time of deduction of the established connection - probability of that the call holding time exceeds average holding time СМО).

Let's consider duration of time X as a phenomenon, tell a holding time, and we will note the beginning of this generation (fig. 1 see). Then, if phenomenon Х is distributed экспоненциально with a population mean m-1 probability of that the phenomenon will proceed and after time moment х is defined as P {X> x} = e - m x.

From here the conditional probability of that a phenomenon will last and longer for all period of time t, set upon termination of time x, is calculated as formula

It has been noticed that last probability in expression (1) does not depend on time х. It means that the behaviour of a stochastic phenomenon after (future) time х depends only on a condition at the moment of time х (present) and does not depend on progress to (last) time х. The given characteristic of a phenomenon is called as property марковости or property of loss of memory. It is known that only экспоненциальное distribution possesses this property at continuous distributions.

Actually (see the Module 5) it leads to that if phenomenon Х экспоненциально is distributed, also residual time t, considered in any moment of time x, also exponentially distributed. And distribution functions (both phenomenon Х, and residual time t) throughout all time of life (duration generation) phenomenon Х become identical, i.e. F (x)=F (t). From this it follows that model СМО in which and time intervals between arriving calls, and a holding time of a call both are distributed экспоненциально, is called as Markovsky model; otherwise it is called non-Markov as model.

3) Pasta

Let Pj - probability of that j calls exist during any moment of time in a steady condition, and Пj - corresponding probability just before approach of an epoch of a call (fig. 2 see). And generally speaking, these two probabilities are not equal each other. However for systems with экспоненциальным distribution of time intervals between calls (the Poisson stream of calls) the above-stated probabilities are identical, i.e. Pj = Пj. (2)

The relation (2) is called PASTA (Poisson arrivals see time average,т.е это Пуассоновское поступление вызовов, наблюдаемое за среднее время) - average time of supervision of the Poisson stream. The relation (2) follows from exponential distributions on property марковости. Term PASTA was generated from this the fact that probability Pj is equal to an average (expected) window of time in which it will be observed j calls if supervision was carried out throughout enough long period of time.

Value of the given remark consists that in specified average time of supervision other process, except the Poisson stream can be observed. In this case average time of supervision of process is called ASTA (arrivals see time average,т.е это поступление вызовов, наблюдаемое за среднее время). Such processes can create problems in networks with package switching.

If we unite n independent Poisson streams with rates lj, j=1,2, …, n (fig. 3а see) результирующий the stream becomes again Poisson with rate l=l1+l2+ … +ln. Such occurs because convolution of Poisson distributions gives again Poisson distribution.

If the Poisson stream with rate l goes on a route j with probability pj (fig. 3б see) the stream in a direction j becomes again Poisson. These properties are used at the analysis of systems with Poisson loading.