  We consider Markovian multiserver retrial queues where a blocked customer has
two opportunities for abandonment: at the moment of blocking or at the
departure epoch from the orbit. In this queueing system, the number of
customers in the system (servers and buffer) and that in the orbit form a
level-dependent quasi-birth-and-death (QBD) process whose stationary
distribution is expressed in terms of a sequence of rate matrices. Using a
simple perturbation technique and a matrix analytic method, we derive Taylor
series expansion for nonzero elements of the rate matrices with respect to the
number of customers in the orbit. We also obtain explicit expressions for all
the coefficients of the expansion. Furthermore, we derive tail asymptotic
formulae for the joint stationary distribution of the number of customers in
the system and that in the orbit. Numerical examples reveal that the tail
probability of the model with two types of nonpersistent customers is greater
than that of the corresponding model with one type of nonpersistent customers.
