  Motivated by queueing applications, we study various reflected autoregressive
processes with dependencies. Amongst others, we study cases where the
interarrival and service times are proportionally dependent with additive
and/or subtracting delay, as well as cases cases where interarrival times
depends on whether the service duration of the previous arrival exceeds or not
a random threshold. Moreover, we study cases where the autoregressive parameter
is constant as well as a discrete or a continuous random variable, as well as
cases where . More general dependence structures are also discussed. Our
primary aim is to investigate a broad class of recursions of autoregressive
type for which several independence assumptions are lifted, and for which a
detailed exact analysis is provided. We provide expressions for the Laplace
transform of the waiting time of a customer in the system in terms of an
infinite product of known Laplace transforms. An integer-valued reflected
autoregressive process that can be used to model a novel retrial queueing
system with orbital searching time to depend on whether the last busy period
starts with an empty or a non empty orbit queue, is also discussed. For such a
model the probability generating function of the stationary orbit queue length
is given as an infinite product of known generating functions. A first attempt
towards multidimensional setting is also analyzed. Some additional
generalizations with more general dependence structure are also discussed.
