We consider an M/G/1 retrial queueing system with two types
of calls which models a telephone switching system. In the case that
arriving calls are blocked due to the channel being busy, the outgoing
calls are queued in priority group whereas the incoming calls enter the
retrial group in order to try service again after a random amount of time.
In this paper we find the Laplace-Stieltjes transform of the distribution of
the virtual waiting time for an incoming call. When the arrival rate of
outgoing calls is zero, it is shown that our result is consistent with the
known result for a retrial queueing system with one type of call.