Asymptotic analysis of multi-arrival heterogenous resource queueing system $\mathrm{MMPP/GI(2)/}\infty$ in a random Markovian environment

This paper proposes to study a mathematical model of multimodal information transfer in the form of a heterogeneous service system with an infinite resource of servers. This model allows taking into account the random volume of resources required for processing (transferring) data and the influence of the stochastic environment on the intensity of incoming flows. Three Markov modulated flows with requirements for resources of different types for a random time are received at the input.
To analyze the total resources occupied in the system, a modification of the asymptotic analysis method is proposed, applicable under the limit condition of increasing the intensity of the incoming flow and frequent changes in the state of the random environment. Theorems on the two-dimensional Gaussian approximation of total resource requests in the models under consideration are proved. These approximations are determined by the moments of the first and second order of the incoming flow and the service time parameters.