Abstract
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 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.
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Kogan, Y., Yakovlev, A. Asymptotic analysis for closed multichain queueing networks with bottlenecks. Queueing Syst 23, 235–258 (1996). https://doi.org/10.1007/BF01206559
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DOI: https://doi.org/10.1007/BF01206559