I. Adan, J. Wessels, and W. Zijm, Analysis of the asymmetric shortest queue problem, Queueing Systems Theory Appl, vol.8, issue.1, pp.1-58, 1991.

C. Banderier and M. Wallner, Lattice paths with catastrophes, Discrete Math. Theor. Comput. Sci, vol.19, issue.1, p.32, 2017.

N. R. Beaton, A. L. Owczarek, and A. Rechnitzer, Exact solution of some quarter plane walks with interacting boundaries, pp.1-34, 2018.

O. Bernardi, M. Bousquet-mélou, and K. Raschel, Counting quadrant walks via Tutte's invariant method. arXiv, 1708, vol.08215, pp.1-54, 2017.

A. Bostan, M. Bousquet-mélou, and S. Melczer, Counting walks with large steps in an orthant. arXiv, 1806, vol.00968, pp.1-60, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01802706

A. Bostan, F. Chyzak, M. Van-hoeij, M. Kauers, and L. Pech, Hypergeometric expressions for generating functions of walks with small steps in the quarter plane, European J. Combin, vol.61, pp.242-275, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01332175

A. Bostan and M. Kauers, The complete generating function for Gessel walks is algebraic, Proc. Amer. Math. Soc, vol.138, issue.9, pp.3063-3078, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00780429

A. Bostan, K. Raschel, and B. Salvy, Non-D-finite excursions in the quarter plane, J. Combin. Theory Ser. A, vol.121, pp.45-63, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00697386

A. Bouaziz, S. Mustapha, and M. Sifi, Discrete harmonic functions on an orthant in Z d, Electron. Commun. Probab, vol.20, issue.52, p.13, 2015.

M. Bousquet-mélou, An elementary solution of Gessel's walks in the quadrant, Adv. Math, vol.303, pp.1171-1189, 2016.

M. Bousquet-mélou, Square lattice walks avoiding a quadrant, J. Combin. Theory Ser. A, vol.144, pp.37-79, 2016.

M. Bousquet-mélou and M. Mishna, Walks with small steps in the quarter plane, Algorithmic probability and combinatorics, vol.520, pp.1-39, 2010.

M. Buchacher and M. Kauers, Inhomogeneous restricted lattice walks, Sém. Lothar. Combin, vol.12, 2019.

T. Budd, Winding of simple walks on the square lattice. arXiv, 1709, vol.04042, pp.1-33, 2017.

J. Cohen and O. Boxma, Boundary value problems in queueing system analysis, North-Holland Mathematics Studies, vol.79, 1983.

D. Denisov and V. Wachtel, Random walks in cones, Ann. Probab, vol.43, issue.3, pp.992-1044, 2015.

T. Dreyfus, C. Hardouin, J. Roques, and M. Singer, On the nature of the generating series of walks in the quarter plane, Invent. Math, vol.213, issue.1, pp.139-203, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01897314

J. Duraj, Random walks in cones: the case of nonzero drift, Stochastic Process. Appl, vol.124, issue.4, pp.1503-1518, 2014.

P. Duren, Univalent functions, Grundlehren der Mathematischen Wissenschaften, vol.259, 1983.

G. Fayolle, Méthodes analytiques pour les files d'attente couplées. Doctorat d'État ès Sciences Mathématiques, 1979.

G. Fayolle and R. Iasnogorodski, Two coupled processors: the reduction to a Riemann-Hilbert problem, Z. Wahrsch. Verw. Gebiete, vol.47, issue.3, pp.325-351, 1979.

G. Fayolle, R. Iasnogorodski, and V. Malyshev, Random walks in the quarter plane, of Probability Theory and Stochastic Modelling, vol.40
URL : https://hal.archives-ouvertes.fr/inria-00572276

G. Fayolle and K. Raschel, Some exact asymptotics in the counting of walks in the quarter plane, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), pp.109-124, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00661541

G. Fayolle and K. Raschel, About a possible analytic approach for walks in the quarter plane with arbitrary big jumps, C. R. Math. Acad. Sci, vol.353, issue.2, pp.89-94, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01021327

R. Foley and D. Mcdonald, Join the shortest queue: stability and exact asymptotics, Ann. Appl. Probab, vol.11, issue.3, pp.569-607, 2001.

F. D. Gakhov, Translated from the Russian, 1990.

R. Iasnogorodski, Problèmes frontières dans les files d'attente. Doctorat d'État ès Sciences Mathématiques, 1979.

, OEIS Foundation Inc. The on-line encyclopedia of integer sequences

I. Kurkova and K. Raschel, Explicit expression for the generating function counting Gessel's walks, Adv. in Appl. Math, vol.47, issue.3, pp.414-433, 2011.

I. Kurkova and K. Raschel, On the functions counting walks with small steps in the quarter plane, Publ. Math. Inst. Hautes Études Sci, vol.116, pp.69-114, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00628424

I. Kurkova and Y. Suhov, Malyshev's theory and JS-queues. Asymptotics of stationary probabilities, Ann. Appl. Probab, vol.13, issue.4, pp.1313-1354, 2003.

J. Lu, Boundary value problems for analytic functions, Series in Pure Mathematics, vol.16, 1993.

V. Malyshev, An analytic method in the theory of two-dimensional positive random walks, Sibirsk. Mat. ?, vol.13, pp.1314-1329, 1421.

M. Mishna and A. Rechnitzer, Two non-holonomic lattice walks in the quarter plane, Theoret. Comput. Sci, vol.410, pp.3616-3630, 2009.

M. Mishna and S. Simon, , 2018.

S. Mustapha, Non-D-finite walks in a three-quadrant cone, Ann. Comb, vol.23, issue.1, pp.143-158, 2019.

K. , Counting walks in a quadrant: a unified approach via boundary value problems, J. Eur. Math. Soc. (JEMS), vol.14, issue.3, pp.749-777, 2012.

W. Tutte, Chromatic sums revisited, Aequationes Math, vol.50, issue.1-2, pp.95-134, 1995.

R. Xu, N. R. Beaton, and A. L. Owczarek, Quarter-plane lattice paths with interacting boundaries: Kreweras and friends, Sém. Lothar. Combin, vol.82, 2019.