Читать книгу Mathematics of the market. Service random flow - Alexandr Berlin - Страница 12

Quality of service of suggestion on the market of goods is characterized by the number of unsold within a certain time of the goods or length of expectation of sale.

There are two basic approaches, the two disciplines of servicing coming to market goods: apparent losses and conditional losses.

A discipline services with obvious losses is the discipline in which the marketed product needs to be sold, and if all consumers are busy, then it is removed from sale and no longer has on the market no effect. This discipline is called a discipline with obvious losses. This discipline services implies that if the manufacturer received the refuse due to lack of demand (all groups of consumers are busy), then abandons further attempts to sell the goods (re-attempts of implementation are considered as a special random flow).

To quantify the quality of service with obvious losses are calculated the following quantities:

loss in the number of requests for suggestion of goods —

R _request.;

loss of volume of goods – R _goods. ;

loss of implementation time – P t

The loss of the number of requests received for supply of goods in the time interval [t ₁, t ₂) is the ratio of the number of lost (not serviced) during this period (t ₁, t ₂) to number received in the same time.

P_request (t_1.t₂) =c_lost (t_1.,t₂) /c (t₁.t₂)

Losses in volume of goods in the time interval [ t ₁, t ₂ ) is the ratio of lost quantity (what not sold) in this period of time of the goods – a_lost (t _1, t ₂ ) to the incoming volume goods during the this time, a (t ₁, t ₂ ).

Losing time over a period of time [t₁, t ₂) it is the ratio length of all of time periods to time, when all groups of consumption is available for the group of producers are busy.

If in the expression for the loss of the requests number received for supply of goods, the and in expression, the loss of the amount of goods and loss of time insert the mathematical expectation of the corresponding random variables, and then we can talk about the likelihood of losses these goods.

A discipline of service with the expectation (conditional losses) is a discipline in which incoming goods to the time of the lack of free groups of consumers is not losing and becomes on the storage (discipline of service with waiting).

To quantify the quality of service with the expectation calculated in the following characteristics:

– the probability that the waiting time is greater than zero – that is, the probability of queue – p (γ >0);

– the probability of waiting for any incoming product over time t – p (γ> t); the probability of waiting of the delayed goods over time t – p (γ> t);

– the average waiting time in relation all requests received – (γ )

– the average waiting time of only a delayed requests – γ _delay ;

– the probability that the queue length exceeds the specified value r is p ( R>r );

– average queue length – C _delay.

The main characteristics – p ( γ >0) and p ( γ > t ).