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Queueing theory (spelled queuing theory in the United States) is the mathematical study of waiting lines (or queues). There are several related processes, arriving at the back of the queue, waiting in the queue (essentially a storage process), and being served by the server at the front of the queue. It is applicable in transport and telecommunication. Occasionally linked to ride theory. Agner Krarup Erlang, a Danish engineer who worked for the Copenhagen Telephone Exchange, published the first paper on queueing theory in 1909.
Kendall introduced a A/B/C queueing notation in 1953. It has since been extended to 1/2/3/(4/5/6) where the numbers are replaced with:
- A code describing the arrival process. The codes used are:
- M stands for "Markovian", implying exponential distribution for service times or inter-arrival times.
- D stands for "degenerate" distribution, or "deterministic" service times.
- Ek stands for an Erlang distribution with k as the shape parameter.
- G stands for a "General distribution".
- A similar code representing the service process. The same symbols are used.
- The Number of service channels.
- The Priority order that jobs in the line are served:
- First Come First Served (FCFS) (or First In First Out - FIFO),
- Last Come First Served (LCFS) (or Last In First Out - LIFO),
- Service In Random Order (SIRO)
- The maximum size of the system. The maximum number of customers allowed in the system including those in service. When the number is at this maximum, further arrivals are turned away.
- The size of calling source. The size of the population from which the customers come. This limits the arrival rate. As more jobs queue up there are fewer available to arrive into the system.
The word queue comes from the Latin cauda, meaning tail.
Queueing theory is directly applicable to intelligent transportation systems, call centers, PABXs, networkA wide variety of systems of interconnected components are called networks . Specific examples include: television networks transport networks, roads, railroads, shipping routes and airlines, pipelines (gas, petroleum, water, sewage), electric circuits a telecommunications, serverThis article is about computer servers. For the food service use, see waiter. In computing, a server is: A computer software application that carries out some task on behalf of users. This is usually divided into file serving, allowing users to store and queueing, mainframe computertower of a personal computer. A computer is a device for making calculations or controlling operations that are expressible in numerical or logical terms. While factually accurate, this definition and those found in other dictionaries are so broad that th queueing of telecommunications terminals, and advanced telecommunications systems.
1 See also
- Little's lawIn queueing theory, Little's result theorem or law says: :The average number of customers in a stable system (over some time interval) is equal to their average arrival rate, multiplied by their average time in the system. Although it looks intuitively re
- Queueing delayQueueing delay is a term in computer engineering. It refers to a job that is put into a queue, and has to wait there until it can be executed. The time it waits there before being executed is called the queueing delay. This term is most often used in refe
- Queue areaQueue areas are areas in which people queue ( first in, first out), that is they wait in line for something. Examples include checking out the groceries or other goods that have been collected in a self-service shop, in a shop without self-service, at an
- Random early detection (RED)
- Erlang unit
