## Probability automaton modelling

In order to predict the behavior of more complex systems that are affected by random factors, you can use modeling. For example, the **probability automaton modeling method** allows us to make a model in the form of interconnected automatons whose states are changing in time simultaneously and discretely. The automaton receives some input signal, has an internal state that includes the state generated by a random value, and is capable of producing an output signal.

Let's consider a simple model of an ATM and its implementation in Mathematica. Let's assume that there is an ATM, which is replenished every `t`

interval by a constant `r`

value. The ATM is approached at random intervals by customers, who withdraw a random amount of money. If there is no money, the ATM receives a negative feedback with a value, `v`

, and to deliver the money, you need to spend certain variables. At the same time, the bank receives income for every unit of time that amounts to an α percent of...