Analysis of the asymmetric shortest queue problem, Queueing Systems Theory Appl, vol.8, issue.1, pp.1-58, 1991. ,
Lattice paths with catastrophes, Discrete Math. Theor. Comput. Sci, vol.19, issue.1, p.32, 2017. ,
Exact solution of some quarter plane walks with interacting boundaries, pp.1-34, 2018. ,
Counting quadrant walks via Tutte's invariant method. arXiv, 1708, vol.08215, pp.1-54, 2017. ,
Counting walks with large steps in an orthant. arXiv, 1806, vol.00968, pp.1-60, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01802706
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
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
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
Discrete harmonic functions on an orthant in Z d, Electron. Commun. Probab, vol.20, issue.52, p.13, 2015. ,
An elementary solution of Gessel's walks in the quadrant, Adv. Math, vol.303, pp.1171-1189, 2016. ,
Square lattice walks avoiding a quadrant, J. Combin. Theory Ser. A, vol.144, pp.37-79, 2016. ,
Walks with small steps in the quarter plane, Algorithmic probability and combinatorics, vol.520, pp.1-39, 2010. ,
Inhomogeneous restricted lattice walks, Sém. Lothar. Combin, vol.12, 2019. ,
Winding of simple walks on the square lattice. arXiv, 1709, vol.04042, pp.1-33, 2017. ,
Boundary value problems in queueing system analysis, North-Holland Mathematics Studies, vol.79, 1983. ,
Random walks in cones, Ann. Probab, vol.43, issue.3, pp.992-1044, 2015. ,
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
Random walks in cones: the case of nonzero drift, Stochastic Process. Appl, vol.124, issue.4, pp.1503-1518, 2014. ,
Univalent functions, Grundlehren der Mathematischen Wissenschaften, vol.259, 1983. ,
, Méthodes analytiques pour les files d'attente couplées. Doctorat d'État ès Sciences Mathématiques, 1979.
Two coupled processors: the reduction to a Riemann-Hilbert problem, Z. Wahrsch. Verw. Gebiete, vol.47, issue.3, pp.325-351, 1979. ,
Random walks in the quarter plane, of Probability Theory and Stochastic Modelling, vol.40 ,
URL : https://hal.archives-ouvertes.fr/inria-00572276
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
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
Join the shortest queue: stability and exact asymptotics, Ann. Appl. Probab, vol.11, issue.3, pp.569-607, 2001. ,
Translated from the Russian, 1990. ,
, Problèmes frontières dans les files d'attente. Doctorat d'État ès Sciences Mathématiques, 1979.
, OEIS Foundation Inc. The on-line encyclopedia of integer sequences
Explicit expression for the generating function counting Gessel's walks, Adv. in Appl. Math, vol.47, issue.3, pp.414-433, 2011. ,
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
Malyshev's theory and JS-queues. Asymptotics of stationary probabilities, Ann. Appl. Probab, vol.13, issue.4, pp.1313-1354, 2003. ,
Boundary value problems for analytic functions, Series in Pure Mathematics, vol.16, 1993. ,
An analytic method in the theory of two-dimensional positive random walks, Sibirsk. Mat. ?, vol.13, pp.1314-1329, 1421. ,
Two non-holonomic lattice walks in the quarter plane, Theoret. Comput. Sci, vol.410, pp.3616-3630, 2009. ,
, , 2018.
Non-D-finite walks in a three-quadrant cone, Ann. Comb, vol.23, issue.1, pp.143-158, 2019. ,
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. ,
Chromatic sums revisited, Aequationes Math, vol.50, issue.1-2, pp.95-134, 1995. ,
Quarter-plane lattice paths with interacting boundaries: Kreweras and friends, Sém. Lothar. Combin, vol.82, 2019. ,