Multiclass GI/GI/\(\infty \) Queueing Systems with Random Resource Requirements

In the paper we consider a GI/GI/\(\infty \) queuing system with n types of customers under the assumptions that customers arrive at the queue according to a renewal process and occupy random resource amounts, which are independent of their service times. Since, in general, the analytical solution of the corresponding Kolmogorov differential equations is not available, we focus on the amount of resources occupied by each class of customers under the assumption of infinitely growing arrival rate, and derive its first and second-order asymptotic approximations. In more detail, we show that the n-dimensional probability distribution of the total resource amount is asymptotically n-dimensional Gaussian, and we verify the accuracy of the asymptotics (in terms of Kolmogorov distance) by means of discrete event simulation.