In this work we study a retrial queueing system accepting n types of customers who may arrive in the same batch. Customers of type i = 1, 2, ..., p are queued and served according to a non-preemptive priority rule, while customers of type i = p + 1, ..., n who find the server unavailable, leave the system and repeat their demand individually after an exponentially distributed amount of time. We assume that when the server becomes free, he leaves the system for a single vacation. For such a model we obtain the mean number of type i (i = 1, 2, ..., n) customers in steady state and use them to draw conclusions from numerical calculations.
