Elements of queuing theory, Basic concepts. Classification...

Elements of the theory of mass service

Basic concepts. Classification of SMO

When researching operations, you often have to deal with systems designed for reusable use when solving similar tasks. The processes that arise in this process are called service processes, and the system - queuing systems (SMO). Examples of such systems are telephone systems, repair shops, computer complexes, ticket offices, shops, hairdressers, etc.

Each SMO consists of a certain number of serving units (devices, devices, stations, stations), which we will call service channels . The channels can be communication lines, work stations, computers, salespeople, etc. The number of channels of SMO is subdivided into single-channel and multi-channel.

Applications are received in SMO usually not regularly, but by accident, forming a so-called random stream of requests (requirements). The maintenance of applications, generally speaking, also continues for some random time. The random nature of the flow of applications and the maintenance time leads to the fact that the CMO is loaded unevenly: a very large number of applications accumulate during certain periods of time (they either queue or leave SMOs unsuccessful), at other times the SMO is working with underload or is idle.

The subject of queuing theory is the construction of mathematical models linking the given working conditions of the QMS (the number of channels, their performance, the nature of the flow of applications, etc.) with the QME performance indicators describing its ability to cope with flow of applications.

As performance indicators SMO are used: the average number of requests serviced per unit time; the average number of applications in the queue; average wait time for maintenance; probability of denial of service without waiting; the probability that the number of requests in the queue will exceed a certain value, etc.

SMOs are divided into two main types (class): QSOs with failures and QMS with waiting (queue). In QMOs with failures, an application arrived at the moment when all the channels are busy, get rejected, leave the SMO and in the future the service process takes part (for example, the call for a telephone conversation at the time all channels are busy, receives a rejection and leaves the SMO unhandled). In SMO, with an expectation, the application, which came at the moment when all channels are busy, does not go away, but becomes in the queue for maintenance.

The QSOs with the expectation are divided into different types, depending on how the queue is organized: with a limited or unlimited queue length, with a limited waiting time, etc.

For the classification of QMS, an important service discipline , which determines the order of selection of applications from among the received and the order of their distribution between free channels. On this basis, the service of the application can be organized according to the principle first came - first served, & quot ;, last came - first served (this order can be used, for example, when retrieving items from the warehouse for servicing, since the latter are often more accessible) or priority service (when the most important applications are primarily serviced). Priority can be either absolute, when a more important claim is extrudes from the service routine application (for example, in the event of an emergency, the scheduled work of the repair teams is interrupted before the accident is eliminated), and relative, when the more important application receives only the best place in the queue.

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