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Boundary value problems in queueing theory. (English) Zbl 0662.60098
Certain types of random walks on \(\{0,1,2,...\}^ 2\) lead to the study of functional equations which can be transformed into Riemann boundary value problems. The author starts by outlining this procedure as well as the solution of the boundary value problem. He continues by illustrating this techniques with a typical random walk example and further shows that the corresponding functional equation can also be studied in terms of a Riemann-Hilbert boundary value problem or - yet another alternative - a Fredholm integral equation. A discussion of the application to queueing models with a “two-dimensional” state space and an extensive list of references is included.
Reviewer: R.Schaßberger

MSC:
60K25 Queueing theory (aspects of probability theory)
60G50 Sums of independent random variables; random walks
45B05 Fredholm integral equations
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