What is the queuing theory or waiting lines model?

The waiting lines or queuing theory, consists of the study of waiting line systems in different modalities that serve to define the most effective way to process a queue system.

This theory of mathematical study of the behavior of waiting lines is presented when customers they access a certain place to request a service to a server that reaches a level of attention span. In case the server is available immediately and the client wants to wait, this is when the waiting line is made.

The study of the model of waiting lines or queue theory, serves to facilitate the theoretical basis of the mode of service that the client decides to wait of a given resource, as well as the way the resource can be designed to deliver a given level of service to customers.

Objectives of the waiting lines model or queuing theory

The objectives of this customer service model are:

• Identify the best level of system capacity that can lower the overall cost of that system.
• Form a balance or better balance between qualitative service and quantitative cost considerations.
•  Assess the impact that the possible alternatives for modifying the capacity of the system may have on the total cost.
• It is necessary to make an observation of the time that customers spend in the system or in the queue and the patience they show according to the type of service determined and should be considered to be a situation that may allow the customer to leave the system.

Elements of the waiting line model or queuing theory

The elements of the queue theory are classified as follows:

Basic queuing process

Customers need services that are generated in the entry phase, that is, they enter the system and join the queue. At a certain moment, a participant must be chosen from the queue to provide the service through certain regulations known as service discipline.

After this, the service requested by the client is performed through a service process and in this way the client manages to complete the queuing system.

Client

Is the person that belongs to the population that requires the service.

Population or source of entry

The main characteristic of the input source is its size, which is the number of clients that can request the service at a specific time. The size could be finite or infinite.

Queue discipline

This discipline consists of the order or modality in which clients are chosen to perceive the service or to be served. In the most frequent disciplines are:

• Last in first out (LIFO): Known in the same way as a stack, it is based on serving the customer who came last first.
• Processor Sharing: It is the network capacity that is shared between the clients and thus obtain efficiency or delay in the same way.
• First in first out (FIFO): It consists in serving first the customer who has arrived before and thus will be the first to arrive and the first to leave.
• Random selection of service (RSS): Choose clients circumstantially, according to the order process or according to priority.

Queue capacity

This is the maximum number of clients that queue prior to the beginning of the service in a finite or infinite way.

For simple purposes of calculations, it is easier to assume it to be infinite, however, in real cases it is evident that the capacity of the queue is finite, since the infinite assumption is not restricted if the entrance of clients to the queue cannot be verified for having reached the limit quantity of the herself.

Tail networks

It is the queue system where there are multiple queues and the service flows from one queue to another.

Service mechanism

It is one or more service facilities, where each one has a variety of parallel service channels called servers. To determine this mechanism, you must know the number of servers and the distribution of time that each server takes to perform the service.

Service process

It is the set formed by the queue and the way in which clients are served for the service mechanism, together with the discipline of the queue that indicates the criteria that the client has to choose to pass to said mechanisms of service.

Advantages and disadvantages of the waiting lines model or queuing theory

Within this model of waiting lines or queuing theory there are a series of advantages and disadvantages such as the following:

Advantage

• The results determine the importance of order, probability trend, and benchmark-related modifications.
• They offer favorable dimensions for general stationary systems.
• It allows limited results in stationary situations that are obtained from its application.
• At present there are useful numerical solutions for various systems.
• They are models that incorporate approximations to reality and simplifications to it.

Disadvantages

• Acceptance of these models can be difficult.
• They require high amounts of computational runs to improve solutions, which is often costly.
• The solution of these models could give a false analytical sense of security.
• It is necessary to invest a large amount of time for its development and validation.

The waiting lines or queuing theory It is the study of waiting lines produced by customers who demand a service, waiting in case they are not attended immediately or if they have already been served.

It is a model that has achieved a good development due to its usefulness in the behavior of a large number of phenomena and is can be applied in various problems related to sales through machines, telephone networks, computer centers, among other