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2. 1.Definition

For the mathematical estimate of processes in the economy it is necessary to create a model that would reflect them in mathematical form. In conjunction with the definition of units of measure of supply, demand and also definition of relative consumption, this model allows to obtain and to provide a quantitative calculation, analysis and give assessment of possible market behavior. The proposed model is shown in Fig.2.1.

Figure 2.1.A mathematical model of the market

The market contains a subsystems they performs the following tasks.

Production system – generates a random flow of goods (in general case different from each other). Under the product refers to any product or a service offered for sale, in which there is a need (in the following we will show how to define the demand in numerical form). These can be food items such as milk and other food products, cars, homes, cleaning home, stocks, services in construction of houses, etc.

The flow enters the distribution system.

The distribution system can the request handle immediately or with some delay. The refusal can be of two types:

– the refusal to accept the goods because of lack of demand;

– or installation on waiting of implementation (accumulation of goods);

There are two types of distribution systems.

The first of these it is the task as quickly as possible to sell the goods without any additional conditions. In queuing theory, such a system service is called“full accessibility system” because it provides equal access to the system of consumption, and this system can be not take into account for calculation of behavior of the market.

.Systems of the second type – they sell goods given the specified priorities and limitations for individual consumers or consumption. For example, the sale of tobacco, alcohol, weapons … systems of this type is called “not full accessibility system”.

If the order is accepted, the distribution system seeks deliver its in the system consumption.

Consumption system serves the flow of goods. This is reflected in the fact that individual consumer or group of consumers can buy the offered goods or to refuse from the purchase.

If all consumer groups are busy, then the system of consumption is refuses from the purchase of goods, i.e. occur losses.

And not purchased goods more is not offered for example can be removed or in distribution system can be supplied to the queue for waiting the implementation (the accumulation and storage of goods). In this case it is important to know the waiting time t

2.2. Types of SERVICE systems and input flows goods

Flow of events (in our case products) is a sequence of goods coming through any interval or any moment of time.

Deterministic flow of events – the sequence in which events arrive in a certain, strictly fixed non-random moments or in certain, strictly fixed, non-random intervals. For example, sale of products from the conveyor.

The random flow of events is differs from the deterministic, only one property that the moment of the arrive of goods and intervals arriving time between deliveries are not strictly fixed and random variables. Deterministic flow is a special case of random flows and is rare in practice. Strictly speaking, even such flows often contain moment’s fortuity. In this regard, in the theory of mass service flows basic attention is devote the consideration of random call flows.

The flow of events can be determined by one or more of the three equivalent ways:

1. A sequence of moments of occurrence of the event t₁, t₂,…,t_n,,

For example, the probability of admission of a particular product, and at the time t₁.

This may be a possibility that mobile phones will be shipped to the store every Friday.

In the lottery is, for example, the probability of occurrence in the draw of lottery with numbers 5, 7, 15 will be the number 6. These events i can be described as moments of time.

2 The sequence of intervals between the events – the moments of z₁, z₂,…,z_n

Example, the probability that mobile phones will be shipped to the store every 7 days.

In the lottery is, for example, the probability of occurrence number 6 every 5 lottery draws.

3. A sequence of numbers k₁, k₂,…,k_n, determining the quantity of events arriving within the time intervals [t₀, t₁), [t₀, t₂),…, [t₀, t_n).

Example, the probability that during 5 months (counted from the initial moment t₀ – t₁₅) fresh fish will goes on sale 5,6, … 10 times.

2.2.1. Types of systems service goods

Below show a classify service goods, it is widely used in queuing theory [2.1], but in the economy has not yet is applied.

Types of systems service the goods is shown on Fig.2.2

Figure 2. 2. Types of systems service the goods

We will explain the figure

System with obvious losses

System, in which if the goods is not sold, then it is removed from the market, is called system with obvious losses

System of service with the expectation

System, in which if the goods is not sold, then it will stand is queued for implementation is called system of service with the expectasion

2.2.2. The types of input flows

The flow of goods is a sequence of goods incoming through any interval or at through any moments of time.

Deterministic flow of events – the order in which events arrive in a certain, strictly fixed non-random moments or in certain, strictly fixed, non-random intervals. For example, sale of products from the conveyor.

The random flow of events differs from the deterministic, those and only, that moments of supply of goods and intervals between deliveries are random variables, but not strictly fixed values. Deterministic flow is a special case of random flows and is rare in practice. Strictly speaking, even in such streams often occurs a random event.

The flow of events can be determined by one or more of the three equivalent ways: