Technical Note—On a Formula Dual to Erlang's Loss Formula

For a service system with an infinite number of servers, Poisson arrivals, and negative exponentially distributed service times, this note considers various taboo probabilities, and derives an expression for the probability distribution of the maximum number y of customers simultaneously present during a busy cycle. It turns out that the expression for pr{y = n ∣ y ≧ n} is, in a certain sense, dual to Erlang's loss formula.