Читать книгу Mathematics of the market. Service random flow - Alexandr Berlin - Страница 13

One of the most important properties of the market is its efficiency.

As indicators of the effectiveness of the market as well as economic (price, cost of goods, etc.) can be used such characteristics as the traffic-carrying capacity market.

Under a traffic-carrying capacity market we will understand the value of the intensity of served supplies of goods (sold goods for a certain period of time) when a certain value of loss (what not sold).

The traffic carrying capacity of market depends on the value of losses that satisfy market participants, the number of consumer groups, distribution of duration of consumption and services discipline ( obvious losses or conditional loss), the type of the input flow.

The quantity of loss which characterizes the condition of the market, different for different categories of goods.

Obviously, the more norm of allowable losses, the more a traffic-carrying capacity market and the worse the quality of producers service, i.e. market can accept from manufacturers a greater of goods and most to lose or will keep on storage more a specified time.

Flow of goods (offer) in mathematical models, often adopted as the simplest flow, flow of Palm or primitive. In these cases it is relatively easy to obtain the solution of the problem using analytical methods.

Real flows of goods have a more complex structure, and the decision of task is usually carried out according results received for the simplest stream in the form of the boundary estimates of indicators (results for simplest stream better or worse).

The most convenient distribution function of service time from the point of view of the analytical description and analysis of the throughput of the market is the exponential distribution, since it has no aftereffect.

Practical widely application founds probability distributions – density distribution, Erlang distribution etc.

Discipline of service has a significant impact on the mathematical model of the market, therefore it is necessary to describe in great detail. For example, in the system with the expectation of the accumulated goods may be return from storage back on market:

– in order of receipt;

– in the reverse order of the order of arrival;

– random order;

– with different kinds of priorities.

Traffic-carrying capacity market of consumer groups may be estimated the ratio of intensity a_serv of supplies of goods υ what was serviced.

η =a ₀ / υ,

The value η is called the average traffic-carrying capacity market, or average utilization of one group of consumers.

For example, in one people can buy 400 kg of milk per year. By delivery to the dairy market in 1991, was sold to 347 kg of milk per person per year, η = (347/400=0.8675), and in 2014 sold 240 kg of milk per person per year (η =240/400=0.6) [4.5]. Therefore, the capacity of the dairy market fell by 26%/

The capacity market can be analyzed from the point of view of arriving of the supply η =f (y) or in terms of a number of consumer groups η = f ( υ ) ) at fixed values of losses.

The value of η by increasing the intensity of the incoming of supply asymptotically approaches unity. This is due to the decrease in the influence of temporary fluctuations of demand. This property shows the usefulness of combining groups of consumers (larger market), which reduces these oscillations.