Stochastic processes of interacting particles with varying length are
relevant e.g. for several biological applications. We try to explore what kind
of new physical effects one can expect in such systems. As an example, we
extend the exclusive queueing process that can be viewed as a one-dimensional
exclusion process with varying length, by introducing Langmuir kinetics. This
process can be interpreted as an effective model for a queue that interacts
with other queues by allowing incoming and leaving of customers in the bulk. We
find surprising indications for breaking of ergodicity in a certain parameter
regime, where the asymptotic growth behavior depends on the initial length. We
show that a random walk with site-dependent hopping probabilities exhibits
qualitatively the same behavior.Comment: 5 pages, 7 figure
