Markovian arrival processes

Okay, so let's say you are at a candy store and you want to know how many people will come into the store in the next hour. But you can't tell exactly when they will come in or how many will come in at one time. This is where Markovian arrival processes come in handy.

A Markovian arrival process is a way of predicting how many people will arrive at a certain time, based on how many people have arrived in the past. It's like playing with blocks. You know how many blocks you have now, and you can use that to figure out how many you will have in the future.

In a Markovian arrival process, the number of arrivals over a certain time period is random but the probability of a certain number of arrivals happening is based on the number of arrivals in the past. For example, if 5 people arrived in the last hour, there is a higher chance that fewer people will arrive in the next hour than if 50 people arrived in the last hour.

Markovian arrival processes are useful for predicting arrivals in situations where the exact number and time of arrivals is unknown but we have some data about past arrivals. They help us make informed decisions and plan for the future.