Simulation is the imitation of the operation of a real-world process or system over time.
The first of these two methods is analogous to the real-world process of walking from London to Brighton and counting the steps; the second is not.
This models many real-world processes, and in such cases the choices made by the first few data points have an outsize influence on the rest of the data points.
Such simulation methods, often called stochastic methods, have many applications in computer simulation of real-world processes.
But there are many websites where arguably we don't require the authentication which a real-world process, an inherently offline process requires for someone's identity to be asserted.
It is often useful to use lattice models to approximate real-world processes, such as Brownian motion.
Knowledge acquisition is enabled by direct capture of assertions about real-world processes and events in a form that is most natural for capture.
Each model yields estimates (that can increase insights into the underlying real-world processes) as well as associated goodness-of-fit diagnostics.
Markov chains have many applications as statistical models of real-world processes.
A zero transformation time used in many typical Petri Nets may be mathematically appealing but impractical in representing real-world processes.