# Queuing system, its varieties and scientific justification

The queuing system under consideration (QS) is a mechanism in which, with the help of a specially developed set of devices, this satisfies a variety of requirements coming into this system. The key property of this system is the quantitative parameter of the number of working (maintenance) devices. It can range from one to infinity.

In accordance with whether there is a possibility of waiting for service or not, the systems are distinguished:

- QS, where there was not a single tool (device) to meet the requirements received at a given time. In this case, such a requirement is lost;

- a queuing system with expectation, which contains such a store of requirements that is able to accept them all, forming a queue;

- a system with a limited capacity drive, where this limitedness determines the size of the queue of requirements to be satisfied. Here, those requirements that cannot fit in the drive are lost.

In all QS, the choice of requirement and its maintenance is based on the discipline of service. Examples of such service models include:

- FCFS / FIFO - a system in which the first in line request is satisfied first;

- LCFS / LIFO - QS, where the last request in the queue is served first;

- random model - a system for satisfying requirements based on random selection.

As a rule, such a system has a very complex structure.

Any queuing system is described using the following concepts and categories:

- requirement - the formation and presentation of a service request;

- incoming stream - all requests for satisfaction of requirements received in the system;

- service time - the time interval required for full service of the received application;

- mathematical model - expressed in mathematical form and using the mathematical apparatus model of this QS.

Being a complex phenomenon, the queuing system is the subject of a scientific study of probability theory. Within this vast area of scientific knowledge, several concepts stand out, each of which is a fairly autonomous theory of mass service. These theories typically use the methodology of mathematical statistics.

The founder of one of the very first modern QS is A. Ya. Khinchin, who substantiated the concept of a stream of homogeneous events. Then the Danish telegraph operator, and later the scientist Agner Erlang, developed his own concept (for example, the work of telephone operators waiting for a request to satisfy the connection), in which he already identified QS with and without expectation.

The construction of modern queuing technologies is carried out mainly by modeling methods. There are also systems whose research is conducted by analytical methods, but this approach is rather complicated. QS also includes those systems that can be investigated using the methods of statistics - statistical modeling and statistical analysis.

Each such queuing system a priori assumes that there are some standard ways in which entities' requests for satisfaction go. These applications go through the so-called service channels, which are diverse in their purpose and characteristics. Applications come predominantly randomly in time, there are many of them, so it is extremely difficult to establish logical and causal relationships between them. The scientific conclusion, on this basis, is that QS, in its overwhelming majority, operate on the principles of chance.

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