  In this paper, we analyze a retrial queueing system with Batch Markovian
Arrival Processes and two types of customers. The rate of individual repeated
attempts from the orbit is modulated according to a Markov Modulated Poisson
Process. Using the theory of multi-dimensional asymptotically quasi-Toeplitz
Markov chain, we obtain the stability condition and the algorithm for
calculating the stationary state distribution of the system. Main performance
measures are presented. Furthermore, we investigate some optimization problems.
The algorithm for determining the optimal number of guard servers and total
servers is elaborated. Finally, this queueing system is applied to the cellular
wireless network. Numerical results to illustrate the optimization problems and
the impact of retrial on performance measures are provided. We find that the
performance measures are mainly affected by the two types of customers'
arrivals and service patterns, but the retrial rate plays a less crucial role.
