Which Type of Queuing Model Would Be Best for Analyzing an Automated Car Wash?

which type of queuing model would be best for analyzing an automated car wash

Through the use of one of the queuing theory’s queuing models, businesses can be able to identify and avoid the causes of congestion. Thus, ultimately achieving customer satisfaction.

If you’re an automated car wash owner wondering which type of queuing model would be best for analyzing an automated car wash, the answer is the Poisson queue model.

How Does the Poisson Queue Model Work?

The Poisson queue model predicts how many times customers avail of service, referred to as an event, in a specific time period. And it finds the probability of the waiting time until the occurrence of another event.

Why Use Poisson for Analyzing Automated Car Wash Queuing


This model is perfect for an automated car wash business because the events in a car wash are independent but identical. Its queuing pattern meets the criteria required for Poisson:

  • The events happen independently.
  • The events can be identified in whole numbers.
  • The frequency of events in a specific time period is known.

How to Analyze an Automated Car Wash Queuing With Poisson

Below is how we can solve for automated car wash queuing analysis using Poisson:


To explain it simply, in analyzing car wash queuing, you would first have to identify the following:

  • Events or the known average of vehicles per hour
  • Specific time period
  • Number of cars that actually get a car wash in a specific time period, which is the k in the formula

Afterward, you would compute the (events/time) x time. Then you take that result to finally solve the formula.

Poisson only works with discrete values. So if the result is a decimal, just round it off.

The result would show how many times the number of cars would actually get a car wash within 100 observations.

Cons of the Poisson Queue Model

Poisson is apt for an automated car wash’s queuing pattern. But there are some disadvantages to it.

In Poisson, a strong assumption would be formulated on underlying data distribution. That is specifically on the value of the mean and average, which would be assumed equal. Although appropriate for some situations, it may not always be the case.

Also, Poisson is not always reliable in approximation, particularly in the upper limit, wherein little is known. In a car wash setup, Poisson’s validity in approximation is only limited to conditions that are up to the facility’s full capacity.

What happens is that the variance becomes higher than the mean. In that situation, it would be more appropriate to use the normal distribution analysis.


When choosing which type of queuing model would be best for analyzing an automated car wash, Poisson is the best option. It’s because a car wash’s queuing pattern complies with its criteria.

Thankfully, through the Poisson, car wash owners will be able to manage their business efficiently and keep customers satisfied. Furthermore, We have gathered a number of articles related to automatic car washes, you can refer to such as how long does an automatic car wash take and what is a touchless car wash. 

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