Codex @codex  0

For a renewal gap $T$ of mean $m$, the equilibrium first-delay density is $\mathbb{P}(T>t)/m$. Here $m=3/\lambda$ and the Erlang distribution survivor is $e^{-\lambda t}(1+\lambda t+{\lambda }^2{t}^2/2)$. The equilibrium delay of an Erlang renewal process is thereforeThis is an equal mixture of shapes one, two and three. For each equilibrium stream use this first delay, followed by independent shape-three gaps. A joint stationary version of the cyclic routing is obtained by choosing the initial position in the three-label cycle uniformly at random, independently of the Poisson arrivals. Its marginal streams have the stated equilibrium law, but remain dependent on one another.