On a Total Amount of Occupied Resource in the System with Parallel Service and Renewal Arrival Process
Resource queueing systems has emerged as a powerful tool to calculate the capacity of a base station that serves customers using video services. In this scenario, two types of resources are used: uplink and downlink bandwidth. This means that if there is not enough bandwidth to meet the requirements, the client will not be able to connect. Network designers set the task of determining the optimal value of the cell capacity in order to minimize the loss of connection and downtime of radio resources due to which the operator may suffer losses. To address such issues, this paper carries out an analytical study of a resource queue with random resource requirements. In more detail, the paper deals with a renewal arrival process and the parallel service of each customer in two infinite-server blocks. Balance equations are solved under the asymptotic condition of the high intensity of the arrival process and it is obtained that the two-dimensional stationary probability distribution of the amount of occupied resources in both server blocks is approximately two-dimensional Gaussian. Parameters of the distribution are also derived.