# Queuing Theory

#### Description

Queuing theory is the mathematical study of waiting lines. It is applicable in many fields, including traffic engineering, telecommunications (especially call centers), fast food restaurants, and the design of shopping centers, offices, waiting areas, and hospitals.

There are many ways to use queuing theory. However, generally the flow of a process is broken into waiting, moving, and changing phases.  Each phase is then analyzed to determine how it affects the other tasks.

#### Benefits

• Provides insight to potential improvement opportunities
• Helps in understanding crowd and wait times and controls

#### How to Use

• Step 1.  Work with stakeholders to determine acceptable wait times.
• Step 2.  Identify the phases of the process.
• Step 3.  Establish a baseline by estimation or by measuring throughput separately at each phase.
• Step 4.  Calculate distributions based on data collected.
• Step 5.  Enter data into queuing model.
• Step 6.  Change data to reflect possible changes.
• Step 7.  Initiate improvement based on varied inputs.
• Step 8.  Validate impact to quality, customer satisfaction, and financial budgets.

Not Applicable

#### Example

A fast food restaurant is attempting to improve the flow of customers during the lunch rush.

While evaluating the process, the improvement team identifies the following steps:

• The customer enters the restaurant
• The customer enters the waiting line
• The customer orders
• The order is passed to the cooks and assemblers
• The customer pays
• The cooks prepare the food
• Assemblers assemble the order
• The order is presented to the customer

Analysis determines that an excessive amount of time is spent ordering the meals.

Using the appropriate queuing model helps the manager predict that between 71 and 76 people will order double bacon cheeseburgers from 12:00 to 12:30 on Tuesdays. Therefore, preparing the burgers in advance can help decrease the customer wait time.

The team confirmed that preparing the items in advance did not have a negative impact on customer satisfaction.

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