  In the present paper the infinite-server MMAPkGk queueing model with random
resource vector of customers, marked MAP arrival and semi-Markov (SM) arrival
of catastrophes is considered. The joint generating functions (PGF) of
transient and stationary distributions of number of busy servers and numbers of
different types served customers, as well as Laplace transformations (LT) of
joint distributions of total accumulated resources in the model at moment and
total accumulated resources of served customers during time interval are found.
The basic differential and renewal equations for transient and stationary PGF
of queue sizes of customers are found.
