In this paper, we introduce a bivariate Markov process {X(t), t [≥] 0} = {(C(t), Q(t)), t[≥] 0} whose state space is a lattice semistrip E = {0, 1, 2, 3} × Z+. The process {X(t), t [≥] 0} can be seen as the joint process of the number of servers and waiting positions occupied, and the number of customers in orbit of a generalized Markovian multiserver queue with repeated attempts and state dependent intensities. Using a simple approach, we derive closed form expressions for the stationary distribution of {X(t), t [≥] 0} when a sufficient condition is satisfied. The stationary analysis of the M/M/2/2 + 1 and M/M/3/3 queues with linear retrial rates is studied as a particular case in this process.
