Queuing Theory

What is the Queuing Theory?

The Queuing Theory is concerned with studying all the various dynamics of lines – or “queues” – and how they may be made to operate more efficiently. It is essentially the study of “waiting in line,” including how people behave when they have to queue up to make a purchase or receive a service, what types of queue organization move people through a line most efficiently, and how many people can a specific queuing arrangement process through the line within a given time frame.

Queuing theory is also applied to moving objects or information through a “line.” For example, an auto manufacturer may look to queuing theory for guidance on the most efficient way to set up its assembly lines. A transport company, such as FedEx or UPS, can use queuing theory to determine the most operationally efficient manner of transferring packages from one transport vehicle to another.

In the world of business, queuing theory can help a company’s executives determine the best way to set up and organize business operations so as to maximize both sales and customer service satisfaction.

Financial analysts may construct models based on queuing theory to make projections about how changing an operational variable may improve queuing efficiency and, as a result, bottom-line profitability. The use of queuing theory has become so popular that there are now online queuing calculators available that can do a basic analysis of a given queuing setup.

The Basics of Queuing Theory

Queuing theory is essentially a vehicle for cost analysis. It would be prohibitively expensive, or indicative of not having very many customers, for most businesses to operate in a manner so that none of their customers or clients ever had to wait in line. As a simplistic example, for a movie theater to eliminate the circumstance of people having to wait in line to purchase a movie ticket, it would likely need to set up fifty to a hundred ticket booths. However, the theater obviously could not afford to pay a hundred ticket sellers.

Therefore, businesses use information gleaned from queuing theory in order to set up their operational functions so as to strike a balance between the cost of servicing customers and the inconvenience to customers caused by having to wait in line.

The basics of queuing include the people waiting in line and the performance of the service that they’re waiting to receive. In studies on queuing, it is usually broken down into four categories, as follows:

• Arrival – The process by which customers arrive at the line/queue
• The Queue – The nature or operation of the queue itself (How does the line move along?)
• Service – The process of providing the service that a customer is waiting on (for example, being seated and then being served in a restaurant – note that the restaurant has to consider the dynamics of two separate queues, the queue of people waiting to be seated, and then the queue of people already seated who are waiting to be served. The latter might be further broken down into the two queues of waiting to have your order taken and waiting for your food to arrive at your table).
• Leaving – The process of departing from the queue location (for example, businesses that offer a drive-through service have to consider how people leaving the drive-through may impact people entering the business’ parking lot)

Factors of Queuing – Arrival

Queuing models analyze the operational aspects and variables involved in each of the four categories of queuing outlined above. Following are some of the variables that can affect the functioning and operational efficiency of each part of a queue, and that, therefore, should be considered by the business where a queue forms.

Factors to consider in relation to the arrival of people at the queuing location include such things as the number of people, on average, who arrive within a given time frame, such as one hour. A related factor is that of substantial fluctuations in the amount of traffic/arrivals that occurs at different times of the day and/or on different days of the week or month.

Grocery stores know, for example, that in order to avoid queues getting backed up, they need to have more employees working during rush hour on a Friday than, say, on Wednesday mornings between 10 a.m. and noon.

Factors of Queuing – The Queue

How does the line move along? For example, does it work better for a bank to have just one line of customers waiting for the next available teller or cashier, or to have separate lines for each teller? Characteristics of human behavior become an important part of queuing theory when posing such a question. While one line of customers being fed to four different teller stations versus four separate lines at each teller station may not have a significant effect on how quickly or efficiently customers are served, it may well have an impact on customer satisfaction.

Although ultimately, the wait time to be served may be roughly the same regardless of the line arrangement, customers may feel, or perceive, that they are being served more quickly if they only have to wait in line behind two or three people (each teller station has its own queue) as opposed to having to stand in line behind 10 or 12 people (one line of customers being fed to all four teller stations).

There are also basic practicalities to consider: If the business office is relatively small, will using just a single line result in a line so long that it extends back out the door? Many people seeing a situation like that may well be discouraged from doing business there. They may instead choose to go to a competitor that appears to offer less wait time.

Note the part about “appears” to offer less wait time. Doing business with the competitor may, in fact, involve approximately the same amount of time waiting in line. The only difference may be that the competitor chose to go with separate lines for each service station rather than one single line for all the stations, thus avoiding having a line that extends back out the door. Here, you can see that there are aesthetics of queues to be considered in addition to any operational efficiency factors.

Factors of Queuing – Service

There are also variables that exist in relation to the actual provision of service. A common example is the “express lane” in grocery stores, reserved for customers who are only purchasing a small number of items. (Typically, express lanes are designated for customers with “12 items or less” or “20 items or less”). The reason such express lanes exist is that grocery stores using queuing theory have found that customer satisfaction is improved by enabling customers who are only buying a few things to check out more quickly, as opposed to having to wait in line behind other customers with full carts of groceries.

Other factors that impact actually providing service include how long, on average, it takes to provide service to each customer or client, the number of servers required for maximum operational and cost efficiency, and the rules governing the order in which customers are served. While most queues operate on a “first-come, first-served” basis, it is not appropriate for some businesses.

A classic example is the waiting area at a hospital emergency room. Rather than using a “first arrival” basis for service orders, patients are served based on the severity of their illness or injury. It necessitates adding a service step known as “triage,” whereby a nurse evaluates each patient in terms of the severity of their emergency to decide where in the line of receiving service that patient is placed.

Factors of Queuing – Leaving

The elements associated with customers departing a queue location are commonly basic logistical matters. The example related above shows how businesses with drive-through operations have to take into account how people leaving the drive-through may affect incoming traffic to the location.

Another example of a departure-related factor is a restaurant determining whether to have servers present bills and collect payment at a customer’s table or to have customers pay their bill to a cashier on their way out.

More Resources

CFI offers the Financial Modeling & Valuation Analyst (FMVA®) certification program for those looking to take their careers to the next level. To keep learning and developing your knowledge base, please explore the additional relevant resources below:

• Decision Analysis
• Operations Management
• Demand Theory
• Logistics
• See all accounting resources