About Probability Characteristics Evaluation in Queuing System with Limited Resources and Random Requirements

Mobile data traffic increases on everyday basis for the last decade and is going to keep this trend in the near future. Exponential growth of data traffic in wireless networks accelerates the development of new technologies and the transition to 5G networks. The ongoing improvements will allow to increase the channels throughput and will allow devices to simultaneously support both cellular and Wi-Fi networks, and even allow direct device-to-device (D2D) connection without any base station involved. Evolving heterogeneous networks promise more efficient radio resources usage by a macro cell traffic offloading to the small cells and uplink and downlink decoupling (DUDe). A resource-sharing model in heterogeneous networks is for the first time proposed to be analyzed in terms of queuing system with random requirements. We suggest a multiserver queuing network with limited resources where each class of customers requires a random vector of resources to be served. It has been proved that stationary probabilities of the system with aggregated flow of customers with mean-weighted requirement are equal to the stationary probabilities of the suggested system. The analytical method for the key probability characteristics evaluation requires calculating all k-fold convolutions for each set of vectors requirements. We propose a recurrent computation algorithm for normalization constant evaluation and efficient formulas for blocking probability, mean volume and variance of the occupied resources.