weird queue process results

For a queue generating process with an underlying uniform distribution, the steady state probability of a given queue state depends exclusively on the number of distinct elements in that queue. Notably, the number of repetitions of a given value in a queue does not influence that queue's steady state probability.

For the same process with a single outcome's probability increased by some amount, the steady state probability of a given queue state depends exclusively on the number of distinct elements in that queue and whether it contains the higher probability outcome. Notably, the number of repetitions of a given value in a queue still does not influence that queue's steady state probability.