|
The spelling "queueing" over "queuing" is typically encountered in the academic research field. In fact, one of the flagship journals of the field is ''[[Queueing Systems]]''.
== Practical Applications for Queueing Analysis ==
Queuing theory applies to many fields, such as business logistics, banking and finance, telecommunications, project management, and emergency services.<ref>{{cite web |last1=Investopedia |title=Queuing theory definition, elements, and example |url=https://www.investopedia.com/terms/q/queuing-theory.asp |website=Investopedia |access-date=19 November 2023}}</ref> A queuing analysis predicts areas of congestion based on observable patterns.<ref>{{cite web |last1=Investopedia |title=Queuing theory definition, elements, and example |url=https://www.investopedia.com/terms/q/queuing-theory.asp |website=Investopedia |publisher=Investopedia |access-date=19 November 2023}}</ref> By understanding the current waiting time through queuing analysis, managers make better decisions and work to improve customer satisfaction.
An example of waiting times in a coffee shop exemplifies queuing theory for business logistics well. In simple terms, queuing theory posits that the minutes waiting will equal the number of people in line divided by the number of people served per minute.<ref>{{cite web |last1=Queue-It |title=Queuing theory: Definition, history & real-life applications & examples |url=https://queue-it.com/blog/queuing-theory/#5-the-application-of-queuing-theory |website=Queue-It |access-date=19 November 2023}}</ref> Imagine that ten customers are waiting in line and that the coffee shop consistently serves two people per minute.
''minutes spent waiting = number of people in line / people served per minute
''minutes spent waiting = 10/2''
''minutes spent waiting = 5''
''
This example is simple. If customers spend too long waiting, the coffee shop may lose business. A waiting time of five minutes is typically acceptable in a coffee shop setting. However, if more customers come in at once, the coffee shop should find a way to shorten service times and thus minutes spent waiting. For example, the shop might choose to hire more employees to improve the number of customers served per minute and thus shorten the minutes spent waiting.
Queuing analysis is quintessential to emergency service response time calculations because of the urgency of crisis situations. This example is particularly relevant because, in recent history, emergency departments have been increasing in demand. This increase necessitates improvement and optimization of operational processes.<ref>{{cite web |last1=Elalouf, A. |first1=Wachtel, G |title=Queueing Problems in Emergency Departments: A review of practical approaches and research methodologies |url=https://doi.org/10.1007/s43069-021-00114-8 |website=Operations Research Forum |access-date=19 November 2023}}</ref> Imagine another simplified example. Twenty people need medical
attention in the emergency room. Service occurs at a rate of around four patients per hour.
''hours spent waiting = number of people in line / people per hour''
''hours spent waiting = 20/4
''
''hours spent waiting = 5''
''
This is a higher-stakes example. Though simplified, it shows the importance of queuing analysis by demonstrating extremely high wait times for emergency medical care. Because hospitals cannot control those needing emergency care, they can seek to maximize the number of people served per hour through a variety of measures, such as increasing staffing, building more infrastructure, or adjusting processes.
== Single queueing nodes ==
| 