We consider the control of discrete component $ n_t a switching Markov process x_t = ( z_t, n_t) when there is running cost and an immediate c(i, j) for from i to j $. study minimization ergodic (or long-term average) total cost. Essentially, this paper treats case where, n_t=n fixed, z_t reflected diffusion or with jumps, being, fixed z $, continuous-time chain. Using vanishing discount approa...