Queuing system, its varieties and scientific justification

The queuing system (CMO) under consideration is a mechanism in which a variety of requirements entering the system are satisfied by means of a specially designed set of devices. The key property of this system is the quantitative parameter of the number of working (serving) devices. It can fluctuate from one to infinity.

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

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

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

- a system with a limited capacity drive, where this limitation determines the magnitude of the queue of requirements to be met. Here, those requirements that can not fit into the drive are lost.

In all CMO, the choice of requirements and its maintenance is based on the discipline of service. Examples of such service models are:

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

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

- model random - the system of satisfaction of requirements on the basis of random choice.

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 request for service;

- incoming flow - all requests for meeting the requirements entering the system;

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

- mathematical model - expressed in mathematical form and using the mathematical apparatus of the model of the given SMO.

Being a complex phenomenon by structure, the queuing system is the subject of a scientific study of probability theory. Within this vast field of scientific knowledge, several concepts are singled out, each of which is a fairly autonomous theory of mass service. In these theories, as a rule, the methodology of mathematical statistics is used.

The founder of one of the very first modern SMO is A. Ya. Khinchin, who substantiated the concept of the flow of homogeneous events. Then the Danish telegraph operator, and later the scientist Agner Erlang, developed his concept (on the example of the work of the telephonists waiting for the request to satisfy the connection), in which he already singled out the QMS with expectation and without waiting.

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

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