Multi-service resource queue with the multy-component Poisson arrivals

In many papers devoted to telecommunication systems, multiservice queueing models with heterogeneous customer arrivals are given. As a rule, there is streaming traffic, corresponding to the audio and video conference, and elastic traffic, corresponding to the data and file transmission. Different types of traffic require different quality of service, therefore the multi-service systems are also differentiated service systems. Such papers are aimed at developing a framework for estimating the quality of service indicators in new generation multi-service networks. This paper considers a multiservice resource queueing system with three Poisson arrivals, one of which is splitting. The equation for the probabilities distribution of the total resource amounts on the system blocks is compiling by the dynamic screening method, and using the characteristic function of the stationary distribution, the solution is obtaining. The numerical characteristics of the system performance are obtained by the method of moments using characteristic function. A numerical example shows that arrivals intensity growing increases optimal total resource amounts on system blocks in the system with limited resources, and the splitting arrivals affect the correlation between total resource amounts