  In this work, we study Markov-dependent reflected autoregressive processes.
In queueing terms, such processes describe the workload just before a customer
arrival, which makes obsolete a fraction of the work already present, and where
the interarrival time and the service time depend on a common discrete time
Markov chain. Among others, we consider the case where given the state of the
underlying Markov chain, the interarrival time and the service time are
independent, as well as the case where there is also additional dependence
based on the Farlie-Gumbel-Morgenstern copula, the case where the service time
depends on the waiting time of the customer, and the modulated shot-noise queue
where server's speed is workload proportional. The Laplace-Stieltjes transform
of the steady-state workload is derived via a recursive approach. Moreover, we
further consider a Markov-modulated version of the reflected autoregressive
process with more general structure and obtain the Laplace-Stieltjes transform
of the transient distribution of the workload.
