A retrial multi-server queueing model with a Batch Markovian Arrival Process (BMAP) and phase-type (PH-type) service time distribution is analyzed. The rate of individual repeated attempts from the orbit is modulated according to a Markov Modulated Poisson Process (MMPP). The operation of the system is described in terms of continuous time multi-dimensional Markov chain. Stability condition and the algorithm for calculating the stationary state distribution of the chain are obtained. Main performance measures of the system are calculated.