Discrete-time GI/G/1 retrial queues with time-controlled vacation policies

A discrete-time GI/G/1 retrial queue with Bernoulli retrials and time-controlled vacation policies is investigated in this paper. By representing the inter-arrival, service and vacation times using a Markov-based approach, we are able to analyze this model as a level-dependent quasi-birth-and-death (LDQBD) process which makes the model algorithmically tractable. Several performance measures such as the stationary probability distribution and the expected number of customers in the orbit have been discussed with two different policies: deterministic time-controlled system and random time-controlled system. To give a comparison with the known vacation policy in the literature, we present the exhaustive vacation policy as a contrast between these policies under the early arrival system (EAS) and the late arrival system with delayed access (LAS-DA). Significant difference between EAS and LAS-DA is illustrated by some numerical examples.