We study a multitype branching process in varying environment which describes an aged structure population, when the maximal age of individuals may vary over generations and go to infinity. We prove a Kesten Stigum type theorem, namely the a.s. convergence of the successive size of the population normalized by its mean. The technic developed is inspired by the spine approach for multitype branching processes and from geometric ergodicity along the spine using a Doeblin condition. We also obtain the a.s. convergence of the distribution of the ages among the population. Adding an immigration, this process is connected to a queuing system for buses which serve stations indexed by $\N$. We can then determine the asymptotic behavior of a single bus and when two buses are going to merge with probability one.