I asked this on math.stackexchange but have yet to get an answer, so will try here too…
In their monograph “Queues“, Cox and Smith state (paraphrased – this is p5):
In interval (t,t+Δt) the probability of no arrivals in a completely random process is 1−αΔt+o(Δt), for one arrival αΔt+o(Δt) and for more than one arrival o(Δt) where α is the mean rate of arrival.
I cannot follow this… here is my thinking – we take N to be the probability of no arrivals, W to be the probability of one arrival, Z to be the probability of more than one arrival, and A to be the probability of any arrivals.
By my understanding of Cox and Smith:
1=1−αΔt+o(Δt)+αΔt+o(Δt)+o(Δt) =1+3o(Δt) which is surely nonsense.
So, what have I got wrong here?