Abstract
The Wiener-Hopf factorization gives a method to get the Laplace transform of the stationary waiting time of a GI/GI/1 FIFO queue. In practice, see Section 2.5 of Chapter 2, this method consists in locating the poles and the roots of a function in the complex plane. In practice, it is not always easy to get the number of poles and zeros of a complex function in general, and a fortiori to locate them. For this reason, getting some simple qualitative results for the GI/GI/1 FIFO queue may turn out to be quite difficult.
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References
J.F.C. Kingman, Inequalities in the theory of queues, Journal of the Royal Statistical Society B 32 (1970), 102–110.
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Robert, P. (2003). Limit Theorems for GI/GI/1 Queues. In: Stochastic Networks and Queues. Applications of Mathematics, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13052-0_3
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DOI: https://doi.org/10.1007/978-3-662-13052-0_3
Publisher Name: Springer, Berlin, Heidelberg
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