Boundary value problems in queueing theory
Queueing Systems: Theory and Applications
Analytic Combinatorics
Tail Decay Rates in Double QBD Processes and Related Reflected Random Walks
Mathematics of Operations Research
Rare event asymptotics for a random walk in the quarter plane
Queueing Systems: Theory and Applications
Tail asymptotics for a generalized two-demand queueing model--a kernel method
Queueing Systems: Theory and Applications
Understanding and tackling the root causes of instability in wireless mesh networks
IEEE/ACM Transactions on Networking (TON)
First response to letter of G. Fayolle and R. Iasnogorodski
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
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We study the stationary distribution of a random walk in the quarter plane arising in the study of three-hop wireless networks with stealing. Our motivation is to find exact tail asymptotics (beyond logarithmic estimates) for the marginal distributions, which requires an exact solution for the bivariate generating function describing the stationary distribution. This exact solution is determined via the theory of boundary value problems. Although this is a classical approach, the present random walk exhibits some salient features. In fact, to determine the exact tail asymptotics, the random walk presents several unprecedented challenges related to conformal mappings and analytic continuation. We address these challenges by formulating a boundary value problem different from the one usually seen in the literature.