Аннотация:Abstract This paper extends Neuts' M/G/l paradigm to continuous-time bivariate Markov processes with the skip-free to the left property. The process takes values in [0, ∞) and takes a finite number of values. The process may either decrease linearly or have upward jump discontinuities. We also make some additional assumptions so that the bivariate Markov process is a natural continuous analog of Markov chains of the M/G/l type. The steady-state distribution is characterized by a vector Laplace transform. As applications of the result, we show that the MAP/G/l queue with state-dependent services and the MAP/G/l vacation queue are treated in a unified way
