Mathematics of the market. Service random flow - Alexandr Berlin

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the amount of applications received for the goods

      4. The time of greatest demand – THD _________

      a. time of the season with the highest demand

      b. time from sampling successive periods of time with maximum load

      c. time of maximum demand for each month

      d. continuous given period of time, with a maximum value of the intensity of demand

      5.The main parameters of the demand are: __________

      a. the number of consumer groups -n; the average number of bids on the goods unit of time; the average duration of consumption of service the one application t.+

      b. the number of consumer groups -n; the average number of bids on the goods, price per time unit; price per unit;

      c. the quantity of the goods; the average number of bids on the goods, price per unit of time; the average duration of consumption of service the one application t.

      d. the number of consumers is n; the number of served requests for goods; the average duration of consumption of service the one application t.

      6. When overproduction of goods and lowering the prices of the goods the number of consumers ______

      a. increases

      b. reduced

      c.do stabilize

      7. The average number of requests from one consumer per unit time from the k groups of consumers is determined by ______,

      a.. according the group with a large number of requests

      b. according the weighted average number of

      c. according the most frequently used number

      d. randomly

      8. The time consumption of the goods can be _________ time of possession

      a. equally

      b. less

      c. more

      d. dependent on the storage conditions

      9. Under a traffic-carrying capacity market we will understand the value. ________

      a. intensity serviced supplies for a certain period of time when a certain amount of losses

      b. intensity serviced supplies for a certain period of time

      c. the amount of goods sold over a certain period of time

      d. the number of applications for a certain product for a certain period of time

      10. The more allowable are losses, then_________

      a. less a traffic-carrying capacity market and the worse the quality services for producers

      b. more a traffic-carrying capacity market and the worse the quality of service manufacturers

      c. better quality of service manufacturers

      d. stable quality maintenance of producers

      11. A traffic-carrying capacity market is estimated —

      .a number of consumers

      b. value of losses

      c. relation the intensity of services supply to the number of groups of consumers

      d. number of suppliers

      Chapter 2. A mathematical model of the market

      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,…,tn,,

      For

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