Performance of a Random Number of Complex Systems in the Environment of a Random Number of Competing

The paper makes use of the concept of a random sum of nonnegative random variables and the concept of a minimum of a random number of nonnegative random variables in order to formulate a stochastic model. Sufficient conditions for embedding the formulated stochastic model into an important class of stochastic models are also established. Moreover, the paper establishes applications of the model in investigating the performance of a random number of complex systems being in the environment of a random number of competing and catastrophic information risks.