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Queue at the Eiffel Tower (2007)

A queue ( English queue, line ; French queue ) forms when more requests per unit of time are directed to a system than it can process in the same time, i.e. the demand exceeds the maximum performance of the system. A queue of waiting usually forms due to a lack of adaptation on both sides.

Queue in front of a grocery store in Berlin-Mitte (1923)
Even when it rains, there is discipline in the British queue
Queue in Friedland Camp (February 1958)


In queuing systems, the event types include arrival in the queue, start and end of processing / service and leaving the system. The queue creates a sequence , with the last person in line being served last. Conversely, the person who queued first will be served first ( English First In - First Out ). Waiting times arise here by capacity shortages , production bottlenecks , the bottleneck or long service time.

From a queue, depending on the arrival and service rate, the load or the degree of utilization , the average waiting time , the average throughput time , the average queue length and the average order backlog in the system can be derived. If larger queues are expected, these can be better organized using a meander people guidance system.


While in Anglo-Saxon countries ( United Kingdom , Ireland , USA , Canada ) there is self-discipline in queues, in Germany there is occasional jostling. If a crowd arises, its dangers (costs) can be higher than the disciplined waiting demands of everyone, the advantages (performance) of which, however, lie in rewarding the strongest crowd. A queue is also formed if more offers are sent to a system per time unit than it can accept in the same period of time, i.e. the offer exceeds the performance of the system. Such a queue is always set up if the costs for the supplier's waiting are lower than the costs for the customer's waiting or if the conditions are accordingly agreed. Such a queue is set up to stabilize system operation. The formation of a physical queue can be avoided if a call system is set up or the number of people to be processed is known and the offer places (advice, cash registers, service providers) are increased in good time. From a technical point of view, queues have buffer functions in discrete systems. They are a prerequisite for a system's ability to vibrate, although vibrations are usually undesirable.

Scientific treatment

In the field of computer science , the queue is a special data structure , i.e. a series of elements (tasks, operations) that wait for an event (processing, service, forwarding) in front of an operator station and are processed there serially.

In mathematics , queuing theory is used to research how the waiting time is distributed or how many customers / parts wait on average. The study by the mathematician Thomas Hanschke shows that queues in front of systems with high utilization show strong similarities to molecules under the influence of Brownian motion . On the basis of this model, there are a number of measures that lead to a considerable increase in efficiency.

The queue is an object of knowledge of the queue theory , in the framework of which the mapping of queues is dealt with, based on this in business administration in operations research . In traffic theory , a certain traffic model (communication technology) also leads to the concept of the queue. In sociology , unexpectedly huge queues (> 10,000 queues) have been studied.

Queues in business

In the service sector (such as authorities , restaurants , credit institutes , cinemas , logistics , theaters ) or in retail (at the cash desk ) , queues form because the staffing capacity of the operating staff ( consultants , cashiers , waiters , servers or counter staff ) is too low for the existing number of customers is. The business administration therefore demands in the queuing theory that the number of staff must be based on the expected average workload . Accordingly, there are no queues up to this degree of utilization ; If, on the other hand, the capacity is aligned with the maximum utilization, then with all lower utilization there are empty capacities , which lead to unnecessary idle costs .

The last one in a queue - for example at the cinema box office - initially only has the disadvantage of a longer waiting time compared to the people in front, but the disadvantage can also have material consequences if the service for the last person is fully booked or the product is out of stock .

In the financial market , the uninformed investors form their expectations about the solvency of the credit institutions by observing the behavior of the informed investors. Informed investors withdraw their savings as soon as they receive bad news about their bank. If the uninformed depositors observe this, they will interpret a queue in front of the bank counter as a signal of imminent bankruptcy and a bank run will ensue .

In call centers , a caller is distributed to a free employee by Automatic Call Distribution . If several calls come into the call center at the same time, queues arise. You will encounter a telephone queue that only ends as soon as, for example, information is requested that is required to process the request, regardless of whether this is done by means of an automated dialogue or by a natural person.

Queues in traffic

Queue in an airport ( meander guidance system)

The traffic areas for traffic routes are scarce , so that the increasing number of means of transport leads to queues, which are known as traffic jams . Roads on land, waterways or sea ​​routes on water and airways in the air are affected by the risk of congestion. The disruption of the traffic flow on these traffic routes is called traffic jams in road traffic and traffic jams in shipping . Queues are formed which result in the delay of affected road users . The storage research tries especially on the road to explore leading to congestion causes and find solutions.

In air traffic queues hot hold , prior to the start ( English airport slot ) and before the landing queue (in the narrow sense, English holding pattern ). They arise when several aircraft are heading for the runway ready to take off at the same time or several aircraft that are ready for landing have to be staggered by air traffic controllers . Since the capacity of some airports is exhausted due to high demand, the airlines are given tight time windows during which they can use the airport to take off or land an aircraft. When landing, priority is given to the aircraft with the longest flight route and / or with a low tank of fuel. Reasons for holding patterns are excessive traffic, blocked runways (other aircraft during take-off / landing, snow removal) or bad weather conditions.

Queues in information technology

In information technology, the queue is used to describe the accumulation of several tasks in terms of throughput ( data throughput ), which manifests itself in a longer response time . More servers would increase the throughput because tasks could be processed in parallel. However, this does not affect the response time until the operational load is kept constant and the waiting time in the queues is reduced by more network resources . The problem is known above all when several personal computers are connected to a single network printer in a computer network and this printer receives and has to process several print jobs in parallel .

Health care queues

Waiting patients in Nepal

Healthcare queues mean patients are not getting the medical service they want right away. There is a time lag between the demand for a service and its use. This type of rationing plays a major role in the health system, as the consumption of many medical services is very time-consuming and the costs are covered by health insurance. Queues can arise in front of doctors' offices, hospitals, but also at national or international level, such as for transplants.

In general, a distinction can be made between two principles: The "first-come-first-serve" principle gives preference to the patients who appeared first. A family doctor , for example, uses this system in his waiting room. If the waiting room is occupied, there is a queue. The weak point of this system, however, is that the patients are not assessed for urgency. In the worst case, the result of this principle can mean the death of a patient in the queue. The second principle is based on the urgency of the treatment. In the emergency room of a hospital, for example, triage instruments are used, according to which every incoming patient is assessed and categorized according to the severity of the illness. Emergencies are then given priority, while non-urgent cases are dealt with according to the time of arrival. This can lead to difficulties with the classification, as the urgency is assessed relatively and subjectively. This creates the danger of arbitrariness and injustice.

The treatment sequence can be handled efficiently in various medical fields when the patient personal responsibility for instance in a clinic , select the sector that comes to them in question. Touchscreen terminals that can be flexibly adapted in terms of content to the treatment and advice options are well suited for this. These issue tickets that have an identification number and the place of treatment.

In the area of ​​the expected treatment, a monitor then provides information on the sequence of treatment and other subject-specific or organizational issues.

The principle of queuing in hospitals and large doctor's offices is often referred to as inefficient because it does not make any statement about the benefit that a patient expects from the medical service. Rather, it shows how long a person in need is able to wait and be patient. The optimization reserves in this area are enormous. In clinical outpatient departments alone, it is expected that around 30% higher efficiency can be achieved.

See also


  • Snakes. In: Lars Clausen : Krasser social change. Leske + Budrich, Opladen 1994, ISBN 3-8100-1141-X .
  • H. Kühn: Ethical problems of economically rationalized medicine. (= WZB discussion papaer . P96-207). Public Health Working Group, Berlin 1996, DNB 949383082 .
  • T. Kopetsch: On the rationing of medical services within the framework of statutory health insurance. Nomos-Verlag, Baden-Baden 2001, ISBN 3-7890-7142-0 .

Web links

Commons : Queues  - collection of images, videos, and audio files
Wiktionary: Queue  - explanations of meanings, word origins, synonyms, translations

Individual evidence

  1. Leena Suhl / Taïeb Mellouli, Optimization Systems: Models, Processes, Software, Applications , 2006, p. 14
  2. Alexander Kumpf, Requirements-based modeling of material flow systems for planning-accompanying simulation , 2001, p. 40
  3. Stefan Dege: Society - Corona: Why we don't like to wait , dw.com , May 30, 2020, accessed on May 30, 2020
  4. ^ Mathematics of queuing - "When we wait, we are like molecules" sueddeutsche.de December 20, 2007
  5. Timm Gudehus, Logistics: Basics - Strategies - Applications , 2010, p. 494
  6. Monika Lindner-Lehmann, Regulation and Control of Banks , 2001, p. 50 f.
  7. Andreas Meier, eDemocracy & eGovernment , 2009, p. 191
  8. Axel Schulz / Susanne Baumann / Simone Wiedenmann, Flughafen-Management , 2010, p. 128
  9. ^ John L. Hennessy / David A. Patterson, Computer Architecture: Analysis, Design, Implementation, Evaluation , 1994, p. 508