On normalization constants for closed queueing networks with finite local buffers

We present new closed form solutions for partition functions used to normalize the steady-state flow balance equations of certain Markovian type queueing networks. The results focus on single class closed product form networks with state space constraints at the queueing stations. They are achieved by combining the partition function of the open network, having finite local buffers with a delta function in order to fix the number of customers in the system.