Be careful with Queuing theory, there are only very limited situations where the assumptions needed to apply an analytical solution exist.

It is my opinion that QT is probably the most well-known but misapplied OR technique that is popular with non-OR people.

In this particular case:

1. DMV arrivals are typically NOT independent. Most states have indirectly set up a system where there will be batches of people either with the same birthday [Florida] or same original registration date [Oregon] which effectively sets up a pseudo-scheduled system and not an independent random arrival situation.

2. Arrival rates and Service times are almost NEVER normally distributed when a human interaction is involved and the needs are not homogenous. Arrival rates are typically exponential and service times Erlang. But I have seen so many non-OR people mess this up by slapping normal distributions on observations and inappropriately applying very simplistic QT equations and making decisions based on faulty assumptions.

Now that begin said the use of run charts can be useful, but you got to make sure they even make sense. You have a LCL of a negative cycle time????

My point is analytical QT equation usage is very dangerous because a lot of the time the equations are taught and the general insights are explained [i.e. 100% utilization is not the goal, etc. etc.]. But it seems very few people pay attention to the extreme restrictions in place to actually use the analytical equation’s results to make decisions in real world situations.

In addition, the “Cult of the Normal Distribution” that is prevalent in “improvement” or “business analytical” professionals is going to be its downfall. Only things that are not influenced by any special cause have a possibility of being described by such a distribution – and there are very few of those in the real world.
Posted by William “Ike” Eisenhauer