  A Lindley process arises from classical studies in queueing theory and it
usually reflects waiting times of customers in single server models. In this
note we study recurrence of its higher dimensional counterpart under some mild
assumptions on the tail behaviour of the underlying random walk. There are
several links between the Lindley process and the associated random walk and we
build upon such relations. We apply a method related to discrete subordination
for random walks on the integer lattice together with various facts from the
theory of fluctuations of random walks.
