On the application of dynamic screening method to resource queueing system with infinite servers

Infinite-server queues are a widely used modelling tool thanks to their analytical tractability and their ability to provide conservative upper bounds for the corresponding multi-server queueing systems. A relatively new research field is represented by resource queues, in which every customer requires some volume of resources during her staying in the queue and frees it only at the end of the service. In a nutshell, in this paper the joint distribution of the processes describing the number of busy servers and the total volume of occupied resources is derived and the parameters of the corresponding bidimensional Gaussian distribution are explicitly calculated as a function of the arrival process characteristics and the service time and customers capacity distributions. The aim of this paper is twofold: on one side it summarizes in a ready-to-be-used way the main results for different arrival processes (namely, Poisson processes, renewal processes, MAP, and MMPP), on the other it provides a detailed description of the employed methodology, presenting the key ideas at the basis of powerful analysis tools (dynamic screening and asymptotic analysis methods), developed in the last two decades by Tomsk researchers.