Asymptotic analysis for closed multichain queueing networks with bottlenecks

We consider a two-chain exponential queueing network with a large number of customers that consists of one infinite-server (IS) station and two processor-sharing (PS) or first come first served (FCFS) single-server stations. The asymptotic behavior of the partition function is studied for such a network when one or both PS (FCFS) nodes are heavily loaded. The results are derived using methods of multidimensional complex analysis (the theory of homologies and residues) and the saddle-point method.