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A note on the connection between product-form Jackson networks and counting lattice walks in the quarter plane

Abstract : The ultimal goal is to find explicit solutions for counting generating functions (CGF) of some random walks in the quarter plane, starting from the wellknown product-form for the stationary distribution of customers in Jackson's stochastic networks. The first step is to solve a relativety simple boundary value problem (BVP) for the queueing system. Then, by using a variational principle based on the continuity with respect to adequate parameters, it is possible to transform some smooth curves in a continuous fashion and to get explicitly formulas for the conformal mappings of Riemann's theorem. This might be a new way of computing the gluing functions appearing in [1, 3], which are a key ingredient in the explicit formulas for CGFs.
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https://hal.inria.fr/hal-02415746
Contributor : Guy Fayolle <>
Submitted on : Monday, January 6, 2020 - 6:07:25 PM
Last modification on : Friday, April 30, 2021 - 10:01:00 AM
Long-term archiving on: : Tuesday, April 7, 2020 - 11:55:18 PM

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Guy Fayolle. A note on the connection between product-form Jackson networks and counting lattice walks in the quarter plane. 2020. ⟨hal-02415746v2⟩

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