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

An infinite-server queueing model MMAPkGk in semi-Markov random environment with marked MAP arrival and subject to catastrophes