Asymptotic analysis for closed multichain queueing networks with bottlenecks (Q1362314)

The authors obtain explicit asymptotic expressions for the partition function for a large two-chain network consisting of one infinite server and two processor-sharing on FMFS single server stations. The key step in asymptotic evaluation of the multidimensional contour integral is its transformation to the saddle-point contour integral, which has an explicit asymptotic expression. This approach requires one to find the saddle-point contour, move the initial integration contour to the saddle-point contour, pick-up the residues between these two contours and find the term providing the main contribution to the asymptotic expansion of the partition function. This paper generalizes the results of the one-dimensional case discussed by \textit{A. Birman} and \textit{Y. Kogan} [Commun. Stat., Stochastic Models 8, No. 3, 543-563 (1992; Zbl 0756.60087)].