Scaling limits for closed product-form queueing networks

We consider a general class of closed product-form queueing networks, consisting of single-server queues and infinite-server queues. Even if a network is of product-form type, performance evaluation tends to be difficult due to the potentially large state space and the dependence between the individual queues. To remedy this, we analyze the model in a Halfin–Whitt inspired scaling regime, where we jointly blow up the traffic loads of all queues and the number of customers in the network. This leads to a closed-form limiting stationary distribution, which provides intuition on the impact of the dependence between the queues on the network’s behavior. We assess the practical applicability of our results through a series of numerical experiments, which illustrate the convergence and show how the scaling parameters can be chosen to obtain accurate approximations.