Jean Mairesse Random walks on groups and queues Consider a transient nearest-neighbor random walk on a plain group, i.e. a free product of a finitely-generated free group and finitely many finite groups. Elements of the group can be set in bijection with a regular language L over the alphabet of generators. The random walk can be viewed as a random sequence of words of L, with a local dynamic affecting only one of the extremities of the words, say the right one. We now change the model by assuming that both extremities can be modified, the right one according to the random walk mechanism, and the left one by cancellation of one symbol. If the rate at which the left end gets modified is large enough, then the model becomes a positive recurrent Markov chain on L. First, we prove that the stationary distribution exhibits a simple multiplicative form. Second, we show that the model admits a very natural interpretation in terms of queueing theory. In particular, we obtain a wide generalization of the classical theory of `product form networks`.