Classification of Queueing Systems

In various fields of human activity (in industry, science, trade, everyday life), mass demand for various services often arises. The term «mass» implies the multiple repeatability and statistical stability of the process as a whole.

Service — this is direct interaction with a customer, aimed at satisfying their demand.

A queueing system (QS) is a system in which:

• mass demands arise for the performance of some kinds of services
• these demands are satisfied — service

The main feature of queueing processes is their randomness. Two interacting parties are distinguished, one of which serves, while the other acts as the one being served. The presence of randomness in the behavior of one of the parties leads to a random course of the entire service process. The causes of randomness lie in the mass character of the needs, as well as in the randomness of the operation of the serving system.

Classification of QS

Classification of QS

By the number of service channels:

• 1. Single-channel QS - a QS with one service channel.
• 2. Multichannel QS - a QS with several service channels.

By the time customers spend in the queue before service begins

• 1 Loss systems (QS with losses) - a QS in which a customer arriving at a moment when all channels are busy is refused, leaves the QS, and does not participate further in the service process (for example, a telephone network, in which a call request leaves the QS in the case where the channel is busy.).
• 2. Delay systems (QS with waiting/queue) - a QS in which a customer arriving at a moment when all channels are busy does not leave, but joins the queue for service.

In turn, QS with waiting (a queue) are subdivided into:

• — QS with a finite queue.
• — QS with an infinite queue.
• — QS with a limited waiting time (a customer that arrives to find all devices busy joins the queue and waits for service for a limited time. If it does not receive service within the set time, the customer leaves the system).
• — QS with an unlimited waiting time.

III. By service priority
1. QS with statistical priority - a QS in which service is performed in order of customer arrival.
2. QS with relative priority - a QS in which a high-priority customer waits for the service of a lower-priority customer to finish (a QS where a more important customer only gets a «better» place in the queue).
3. QS with absolute priority — a QS in which a high-priority customer, upon arrival, preempts a lower-priority customer.
4. QS with mixed priority — a QS in which absolute priority is used if the lower-priority customer has been served for a time less than the critical value, and relative priority is used otherwise.

IV. By service principle
1. QS with service based on the principle "first come - last served" (for example, a QS with service based on the principle "first come - last served")
2. QS with service based on the principle "first come - last served"

V. Depending on the way customers are generated
1. Open QS - a QS in which a finite, usually constant, number of customers circulates, which return to the source after service is completed.
2. Closed QS - a QS in which the source generates an infinite number of customers.

The classification of QS given above is conditional.
In practice, QS most often act as mixed systems. For example, customers wait for service to begin up to a certain moment, after which the system starts working as a loss system. A classification of queueing systems
is given in Diagram 1

By service possibility:

• QS with losses;
• QS with an infinite queue;
• QS with an infinite number of channels.

By presence of a queue:

• QS with a queue;
• QS without a queue.

By waiting time in the queue:

• QS with a limited waiting time;
• QS with an unlimited waiting time.

By number of customers in the system:

• closed QS with a queue;
• QS with an infinite number of customers.

By the nature of service:

• QS with mutual assistance and a queue;
• QS without mutual assistance.

By number of service channels:

• single-channel QS;
• multichannel QS;
• QS with an infinite number of channels.

Fig. 1. Classification of QS

See also

• QS

• Modeling

• System

• Inventory management system.

• Petri nets