  In this article a special case of an M/G/2-queue is considered, where the two
servers are exposed to two types of jobs that are distributed among the servers
via a random switch. In this model the asymptotic behaviour of the workload
buffer exceedance probabilities for the two single servers/ both servers
together/ one (unspecified) server is determined. Hereby one has to distinguish
between jobs that are either heavy-tailed or light-tailed. The results are
derived via the dual risk model of the studied M/G/2-queue for which the
asymptotic behaviour of different ruin probabilities is determined.
