Mathematics of the market. Service random flow. Alexandr Berlin

Чтение книги онлайн.

СКАЧАТЬ (Σ ^K_i=1 c_i n_i) / Σ^k_in_i

      The average duration of consumption (t’).

      The duration of one consumption it is to the period of time from the date of acquisition until the moment you start searching the same product.

      Time of consumption is always less time of possession of the goods.

      For example, the owner of the car bought it 3 years ago. If he started looking for a new car without selling the old, the time of consumption will be 3 years.

      The duration of consumption of food products is determined by the physical needs of the person also by the allowable time storage.

      The duration of consumption of clothing is determined by its wear resistance, but now mainly accordance to fashion.

      The duration of consumption of control automates, computing machines of cars is limited by their reliability and by their main indicators.

      Therefore, the duration of consumption, is a random value and its the mean value can be determined only on the basis of observations of existing markets and statistical studies. The impact of advertising and managing consumer behavior in this book is not considered. Therefore, the duration of consumption, is a random value and its the mean value can be determined only on the basis of observations of existing markets and statistical studies.

      Sometimes you must take into account the characteristics of the purchase process that affect time of consumption.

      It is possible to allocate

      1. Immediate purchase as the initial moment of consumption.

      2. Purchases when were refunded or replaced

      3. Remote buying (online) with delayed time of consumption.

      4. The purchase requisition, which is not satisfied at the lack of product.

      5. The purchase requisition, which is not satisfied at the lack of goods acceptable to the buyer.

      6. The purchase requisition, which is not satisfied by reason of the expiration of the release of goods etc.

      In determining the parameters of the market should be taken into account that the duration of consumption of most goods (except commodities first needs) and the number of users significantly to effects on the demand the stage when the market is not saturated and it very much to depend on the prices.

      For example, at higher prices on televisions – the number purchases decreases, the time of consumption increases (less likely to alter the old model).

      However, as we will see later, when the market is saturated demand – growth in consumption (purchases) stops regardless of price.

      1.5.4. Characteristics of quality of service of goods

      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 ).

      1.5.5. Traffic-carrying capacity market

      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) СКАЧАТЬ