Infinite-Server Resource Queueing Systems with Different Types of Markov-Modulated Poisson Process and Renewal Arrivals

In this paper, we propose models that significantly expand the scope of practical applications, namely, queueing systems with various nodes for processing heterogeneous data require arbitrary resource capacities their service. When a customer arrives in system, typeis randomly selected according to set probabilities. Then goes server corresponding device type, where its service is performed during random time period distribution function depending on type customer. Moreover, each requires amount resources, which also depends but independent time. The aim research was develop system an unlimited number servers and arrival process form Markov-modulated Poisson or stationary renewal process, requests resources. We have analysis under conditions growing intensity process. Here formulate theorems prove high-load conditions, joint asymptotic probability n-dimensional total amounts occupied resources multidimensional Gaussian parameters are dependent As result numerical simulation experiments, conclusions drawn limits applicability obtained results. dependence convergence experimental results (including distributions capacity) studied. approximations may be applied estimating optimal limited