We consider Markovian multiserver retrial queues where a blocked customer hastwo opportunities for abandonment: at the moment of blocking or at thedeparture epoch from the orbit. In this queueing system, the number ofcustomers in the system (servers and buffer) and that in the orbit form alevel-dependent quasi-birth-and-death (QBD) process whose stationarydistribution is expressed in terms of a sequence of rate matrices. Using asimple perturbation technique and a matrix analytic method, we derive Taylorseries expansion for nonzero elements of the rate matrices with respect to thenumber of customers in the orbit. We also obtain explicit expressions for allthe coefficients of the expansion. Furthermore, we derive tail asymptoticformulae for the joint stationary distribution of the number of customers inthe system and that in the orbit. Numerical examples reveal that the tailprobability of the model with two types of nonpersistent customers is greaterthan that of the corresponding model with one type of nonpersistent customers.
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