Why is Poisson process, a very special process

Queueing theory is an area where one can find superb applications of various stochastic processes. Here is an adapted visual from Kleinrock that gives a 10,000 ft. view of the various processes. The visual below, at once, explains the reason for Poisson process being so special. It is a process that is an intersection of Semi Markov process, Markov process, Random Walk process, Renewal process and Pure Birth process. It is in the sweet spot, so to speak, of six popular stochastic processes.

Quote for the day

Does anything in nature despair except man? An animal with a foot caught in a trap does not seem to despair. It is too busy trying to survive. It is all closed in, to a kind of still, intense waiting. Is this a key? Keep busy with survival. Imitate the trees. Learn to lose in order to recover, and remember that nothing stays the same for long, not even pain, psychic pain.

Quote for the day

“Music is a proud, temperamental mistress. Give her the time and attention she deserves, and she is yours. Slight her and there will come a day when you call and she will not answer. So I began sleeping less to give her the time she needed.” ― Patrick Rothfusss