Asymptotics of the partition function in large closed BCMP networks with bottlenecks

We consider a two-chain exponential queueing network with a large number of customers, which consists of one infinite-server (lS) station and two processor-sharing (PS) or FCFS single-server stations. 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.<
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