BMAP/SM/1 queue with Markovian input of disasters and non-instantaneous recovery

We consider a BMAP/SM/1 system which is exposed to disasters’ arrivals. A disaster causes all customers to leave the system instantaneously. After a disaster appearance the system is recovering during some random time interval. The variants of accumulating and losing customers during the recover period are considered. The embedded and arbitrary time queue length distributions as well as the average output rate and loss probability are calculated. The results are illustrated by numerical examples.