In this article, we prove that for any probability distribution µ on N one can construct a stationary version of the infinite-bin model –an interacting particle system introduced by Foss and Konstantopoulos– with move distribution µ. Using this result, we obtain a new formula for the speed of the front of infinite-bin models, as a series of positive terms. This implies that the growth rate C(p) of the longest path in a Barak-Erd˝ os graph of parameter p is analytic on (0, 1].