# Queuing Models

## Optimizing Service and Resources

Reduced wait times increase customer satisfaction.

It's 5:30 pm, it seems like everybody has just left work, and you're stuck in a long checkout line at the grocery store. Do you wonder why store management hasn't figured out how many cashiers they need during the evening rush? If you do, you probably have an intuitive appreciation for the importance of queues.

Whether workers wait to use the office copier, airplanes wait to land, or parts wait on an assembly line, queues are an inevitable, and often frustrating, part of life. Waiting lines affect people every day, which is why a primary goal in many businesses is to provide the best level of service possible. Minimizing those waiting lines is a key part of creating a positive experience for the customer.

How can you achieve that in your organization? Well, there's a whole body of mathematical knowledge dedicated to studying, simulating, and analyzing wait times. It's called queuing theory, and it can help minimize the cost to your business of waiting lines.
It does that by helping you determine the best way to use your staff and other resources, while reducing customer wait times.

Queuing models show you how to make sure you have enough staff working, at any given time, to provide a good level of service – without hurting profitability by having people standing around doing nothing.

Queuing models consider the following:

• The average arrival rate of customers.
• The average rate of servicing customers.
• The cost to the business of customer dissatisfaction resulting from waiting time.
• The cost to provide the service points.

## Little's Law

Most queuing models follow the same basic structure: customers arrive for service, they join a line, and they wait to be served. To determine if you have any bottlenecks or other inefficiencies in your queue, you need to figure out what's happening in the queue. Little's Law helps you do this. This theory says that the average length of the queue (L) is equal to the average arrival rate (λ) multiplied by the average waiting time (W).

Here's an example: suppose your call center receives 8,000 calls (L) per quarter (W). You need to figure out the best and most efficient way of providing phone support to your customers. Using Little's Law, you calculate the following:

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