Mathematics of the market. Service random flow

).

The following theorem facilitates the determination of intensity of the supply goods

It shows that this value has the property of ergodicity, which is that

Average at the time is equal to the average of the ensemble.

In this case, monitoring the arrival of shipments on time can be replaced by monitoring the number of simultaneously incoming groups of consumers.

The theorem on the quantification of the intensity incoming supply of goods:

The intensity of incoming supply of goods, which is expressed in units o relative consumption, quantitatively equal to the average number of simultaneously busy consumer groups serving this load.

Suppose that during the T hours continuously recorded the number of simultaneously busy groups of consumers market, which receives steady flow of supplies for consumer groups. Let the result of the observations was that during the time t

was busy υ

consumer groups, during the time t

. was busy v

consumer groups, etc. (Fig.1.1). In General can imagine that during the time t

was busy υ

consumer groups,

Σ

 t

= T

and where n is the number, the value of v which is taken, within T hours.

Total time, when busy all consumers of the market at time ti expressed by the product of υ

t. In the time interval T total time when all users busy of the market will be expressed by amount. This amount, it is supplies of goods all consumers of the market at the time T.

The supplies of goods what, all consumers acquired of the market per unit time are equal to:

A

 = (1/T) Σ

v

 ⋅ t

On the other hand, the average number of simultaneously consumer groups occupied during the time T can be defined as a weighted average of t

:

v‘= (v

t

 + v

t

 +•••+ v

t

) / (t

 + t

 + ⋯ t

) =

= (1/T) Σ

 (v

 ⋅t

)

therefore A

= v’

A theorem about the quantitative assessment of the intensity of the incoming floe supplies of goods.

To quantify the intensity of the incoming flow supply of goods you can use the following theorem:

The intensity of the incoming flow supplies of goods, which expressed in terms of relative consumption, creates a simplest flow of goods, which quantitatively equal to the mathematical expectation of the number of goods (c’), received for a time equal to the average duration of one consumption of one batch products (t’

)

Figure 1.1. The moments of arrives of goods

Let the inputs of the market comes a simple flow of goods with the intensity μ. We assume that the duration of consumption – T is a finite random variable

0≤T≤ T