This paper considers a two node tandem queueing system with phase-type servers and Bernoulli arrivals where the servers operate in discrete-time and are subject to blocking and failures. The invariant probability vector of the underlying finite state Quasi-Birth-and-Death process is shown to admit a matrix-geometric representation for all values of the arrival parameter λ. The corresponding rate matrix is given explicitly in terms of the model parameters and the resulting closed-form expression provides the basis for an efficient calculation of the invariant probability vector. The cases λ=1 and λ<1 are studied separately and the irreducibility of the underlying Markov chain is investigated in each situation. The continuous-time formulation is briefly discussed and only major differences with the discrete-time results are pointed out. Some numerical examples are also provided.
