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Asymptotic analysis of a queueing system by a two-dimensional state space

Published online by Cambridge University Press:  14 July 2016

J. P. C. Blanc
J. P. C. Blanc*
Affiliation:
Centre for Mathematics and Computer Science, Amsterdam
*
∗Present address: Department of Mathematics and Informatics, Delft University of Technology, Julianalaan 132, 2628 BL, Delft, The Netherlands.
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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

CONFORMAL MAPPINGRELAXATION TIME
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 870 - 886
Copyright
Copyright © Applied Probability Trust 1984 

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References

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