Asymptotic analysis of a queueing system by a two-dimensional state space
- 1 December 1984
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 21 (4) , 870-886
- https://doi.org/10.2307/3213703
Abstract
A technique is developed for the analysis of the asymptotic behaviour in the long run of queueing systems with two waiting lines. The generating function of the time-dependent joint queue-length distribution is obtained with the aid of the theory of boundary value problems of the Riemann–Hilbert type and by introducing a conformal mapping of the unit disk onto a given domain. In the asymptotic analysis an extensive use is made of theorems on the boundary behaviour of such conformal mappings.Keywords
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