  In this paper the infinite server queue model in semi-Markov random
environment with k Markov arrival streams, random resources of customers, and
catastrophes is considered. After catastrophes occur, all customers in the
model are flashed out and the system jumps into recovery station. After the
recovery time the model works from the empty state. The transient and
stationary joint distributions of numbers of different types of customers in
the model at moment t, numbers of different types of served in some interval
customers, volume of accumulated resources in the model at moment t, and total
volume of served resources in an interval for the model without catastrophes
are found. The transient and stationary joint distributions of numbers of
different types of customers in the model at moment t, and volume of
accumulated resources in the model at moment t and their moments for the model
with catastrophes are obtained. All results are obtained using Danzig
collective marks method and renewal theory methods.
