The potential source of customers who enter waiting lines for service is referred to as what?

Queuing theory is the mathematical study of queuing, or waiting in lines. Queues contain customers (or “items”) such as people, objects, or information. Queues form when there are limited resources for providing a service. For example, if there are 5 cash registers in a grocery store, queues will form if more than 5 customers wish to pay for their items at the same time.

A basic queuing system consists of an arrival process (how customers arrive at the queue, how many customers are present in total), the queue itself, the service process for attending to those customers, and departures from the system.

Mathematical queuing models are often used in software and business to determine the best way of using limited resources. Queueing models can answer questions such as: What is the probability that a customer will wait 10 minutes in line? What is the average waiting time per customer? 

The following situations are examples of how queueing theory can be applied:

• Waiting in line at a bank or a store
• Waiting for a customer service representative to answer a call after the call has been placed on hold
• Waiting for a train to come
• Waiting for a computer to perform a task or respond
• Waiting for an automated car wash to clean a line of cars

Queuing models analyze how customers (including people, objects, and information) receive a service. A queuing system contains:

• Arrival process. The arrival process is simply how customers arrive. They may come into a queue alone or in groups, and they may arrive at certain intervals or randomly.
• Behavior. How do customers behave when they are in line? Some might be willing to wait for their place in the queue; others may become impatient and leave. Yet others might decide to rejoin the queue later, such as when they are put on hold with customer service and decide to call back in hopes of receiving faster service. 
• How customers are serviced. This includes the length of time a customer is serviced, the number of servers available to help the customers, whether customers are served one by one or in batches, and the order in which customers are serviced, also called service discipline.
• Service discipline refers to the rule by which the next customer is selected. Although many retail scenarios employ the “first come, first served” rule, other situations may call for other types of service. For example, customers may be served in order of priority, or based on the number of items they need serviced (such as in an express lane in a grocery store). Sometimes, the last customer to arrive will be served first (such s in the case in a stack of dirty dishes, where the one on top will be the first to be washed).
• Waiting room. The number of customers allowed to wait in the queue may be limited based on the space available.

Kendall’s notation is a shorthand notation that specifies the parameters of a basic queuing model. Kendall’s notation is written in the form A/S/c/B/N/D, where each of the letters stand for different parameters.

• The A term describes when customers arrive at the queue – in particular, the time between arrivals, or interarrival times. Mathematically, this parameter specifies the probability distribution that the interarrival times follow. One common probability distribution used for the A term is the Poisson distribution.
• The S term describes how long it takes for a customer to be serviced after it leaves the queue. Mathematically, this parameter specifies the probability distribution that these service times follow. The Poisson distribution is also commonly used for the S term.
• The c term specifies the number of servers in the queuing system. The model assumes that all servers in the system are identical, so they can all be described by the S term above.
• The B term specifies the total number of items that can be in the system, and includes items that are still in the queue and those that are being serviced. Though many systems in the real world have a limited capacity, the model is easier to analyze if this capacity is considered infinite. Consequently, if the capacity of a system is large enough, the system is commonly assumed to be infinite.
• The N term specifies the total number of potential customers – i.e., the number of customers that could ever enter the queueing system – which may be considered finite or infinite.
• The D term specifies the service discipline of the queuing system, such as first-come-first-served or last-in-first-out.

Little’s law, which was first proven by mathematician John Little, states that the average number of items in a queue can be calculated by multiplying the average rate at which the items arrive in the system by the average amount of time they spend in it.

• In mathematical notation, the Little's law is: L = λW
• L is the average number of items, λ is the average arrival rate of the items in the queuing system, and W is the average amount of time the items spend in the queuing system.
• Little’s law assumes that the system is in a “steady state” – the mathematical variables characterizing the system do not change over time.

Although Little’s law only needs three inputs, it is quite general and can be applied to many queuing systems, regardless of the types of items in the queue or the way items are processed in the queue. Little’s law can be useful in analyzing how a queue has performed over some time, or to quickly gauge how a queue is currently performing.

For example: a shoebox company wants to figure out the average number of shoeboxes that are stored in a warehouse. The company knows that the average arrival rate of the boxes into the warehouse is 1,000 shoeboxes/year, and that the average time they spend in the warehouse is about 3 months, or ¼ of a year. Thus, the average number of shoeboxes in the warehouse is given by (1000 shoeboxes/year) x (¼ year), or 250 shoeboxes.

• Queuing theory is the mathematical study of queuing, or waiting in lines.
• Queues contain “customers” such as people, objects, or information. Queues form when there are limited resources for providing a service.
• Queuing theory can be applied to situations ranging from waiting in line at the grocery store to waiting for a computer to perform a task. It is often used in software and business applications to determine the best way of using limited resources.
• Kendall’s notation can be used to specify the parameters of a queuing system.
• Little’s law is a simple but general expression that can provide a quick estimate of the average number of items in a queue.

• Beasley, J. E. “Queuing theory.”
• Boxma, O. J. “Stochastic performance modelling.” 2008.
• Lilja, D. Measuring Computer Performance: A Practitioner’s Guide, 2005.
• Little, J., and Graves, S. “Chapter 5: Little’s law.” In Building Intuition: Insights from Basic Operations Management Models and Principles. Springer Science+Business Media, 2008.
• Mulholland, B. “Little’s law: How to analyze your processes (with stealth bombers).” Process.st, 2017.

Queuing theory is a branch of mathematics that studies how lines form, how they function, and why they malfunction. Queuing theory examines every component of waiting in line, including the arrival process, service process, number of servers, number of system places, and the number of customers—which might be people, data packets, cars, or anything else.

Real-life applications of queuing theory cover a wide range of businesses. Its findings may be used to provide faster customer service, increase traffic flow, improve order shipments from a warehouse, or design data networks and call centers.

As a branch of operations research, queuing theory can help inform business decisions on how to build more efficient and cost-effective workflow systems.

• Queuing theory is the study of the movement of people, objects, or information through a line.
• Studying congestion and its causes in a process is used to help create more efficient and cost-effective services and systems.
• Often used as an operations management tool, queuing theory can address staffing, scheduling, and customer service shortfalls.
• Some queuing is acceptable in business. If there's never a queue, it's a sign of overcapacity.
• Queuing theory aims to achieve a balance that is efficient and affordable.

Queues can occur whenever resources are limited. Some queuing is tolerable in any business since a total absence of a queue would suggest a costly overcapacity.

Queuing theory aims to design balanced systems that serve customers quickly and efficiently but do not cost too much to be sustainable.

At its most basic level, queuing theory involves an analysis of arrivals at a facility, such as a bank or a fast-food restaurant, and an analysis of the processes currently in place to serve them. The end result is a set of conclusions that aim to identify any flaws in the system and suggest how they can be ameliorated.

The origin of queuing theory can be traced to the early 1900s in a study of the Copenhagen telephone exchange by Agner Krarup Erlang, a Danish engineer, statistician, and mathematician. His work led to the Erlang theory of efficient networks and the field of telephone network analysis.

To this day, the fundamental unit of telecommunications traffic in voice systems is called an "erlang."

In queuing theory, the process being studied is broken down into six distinct parameters. These include the arrival process, the service and departure process, the number of servers, the queuing discipline (such as first-in, first-out), the queue capacity, and the size of the client population.

Queues are not necessarily a negative aspect of a business, as their absence suggests overcapacity.

Queuing theory as an operations management technique is commonly used to determine and streamline staffing needs, scheduling, and inventory in order to improve overall customer service. It is often used by Six Sigma practitioners to improve processes.

The psychology of queuing is related to queuing theory. This is the component of queuing that deals with the natural irritation felt by many people who are forced to queue for service, whether they're waiting to check out at the supermarket or waiting for a website to load.

A call-back option while waiting to speak to a customer representative by phone is one example of a solution to customer impatience. A more old-fashioned example is the system used by many delis, which issue customer service numbers to allow people to track their progress to the front of the queue.

Supositorio offers free online queuing theory calculators with a choice of queuing models.

A paper by Stanford Graduate School of Business Professor Lawrence Wein et al. used queuing theory to analyze a variety of possible emergency responses to an airborne bioterrorism attack in a public place. The model pointed to specific actions that could be taken to reduce the wait time for emergency care, thus decreasing the potential number of deaths.

Queuing theory is useful, if not quite so urgent, in guiding the logistics of many businesses. The operations department for a delivery company, for example, is likely to use queuing theory to help it smooth out the kinks in its systems for moving packages from a warehouse to a customer. In this case, the "line" being studied is comprised of boxes of goods waiting to be delivered to customers.

By applying queuing theory, a business can develop more efficient systems, processes, pricing mechanisms, staffing solutions, and arrival management strategies to reduce customer wait times and increase the number of customers that can be served.

Here are the answers to some commonly asked questions about queuing theory.

Queuing theory is used to identify and correct points of congestion in a process. The queue may consist of people, things, or information. In any case, they are being forced to wait for service. That is inefficient, bad for business, and annoying (when the queue consists of people).

Queuing theory is used to analyze the existing process and map out alternatives with a better result.

Agner Krarup Erlang, a Danish mathematician, statistician, and engineer, is credited with creating not only queuing theory but the entire field of telephone traffic engineering.

In the early 20th century, Erlang was head of a technical laboratory at the Copenhagen Telephone Co. His extensive studies of wait time in automated telephone services and his proposals for more efficient networks were widely adopted by telephone companies.

A study of a line using queuing theory would break it down into six elements: the arrival process, the service and departure process, the number of servers available, the queuing discipline (such as first-in, first-out), the queue capacity, and the numbers being served. Creating a model of the entire process from start to finish allows the cause or causes of congestion to be identified and addressed.

Americans stand in line for service (except for New Yorkers, who stand "on line"). British people queue. The word queue comes from an old French noun for an animal's tail.

The computer age has introduced a new usage. An email provider may indicate that your message has been "queued." This means that there is a delay in delivering it but it will be sent ASAP.

Queuing and queueing are both acceptable spellings of the word.