Asymptotics for M/G/1 low-priority waiting-time tail probabilities
Queueing Systems: Theory and Applications
Generating functions for generating trees
Discrete Mathematics
Processor sharing for two queues with vastly different rates
Queueing Systems: Theory and Applications
Asymptotic analysis of Lévy-driven tandem queues
Queueing Systems: Theory and Applications
Analytic Combinatorics
Tail Decay Rates in Double QBD Processes and Related Reflected Random Walks
Mathematics of Operations Research
Tail asymptotics for a Lévy-driven tandem queue with an intermediate input
Queueing Systems: Theory and Applications
Exact tail asymptotics in a priority queue--characterizations of the preemptive model
Queueing Systems: Theory and Applications
Rare event asymptotics for a random walk in the quarter plane
Queueing Systems: Theory and Applications
Exact tail asymptotics in a priority queue--characterizations of the non-preemptive model
Queueing Systems: Theory and Applications
Analysis of exact tail asymptotics for singular random walks in the quarter plane
Queueing Systems: Theory and Applications
Wireless three-hop networks with stealing II: exact solutions through boundary value problems
Queueing Systems: Theory and Applications
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In this paper, we consider a generalized two-demand queueing model, the same model studied in Wright (Adv. Appl. Prob., 24, 986---1007, 1992). Using this model, we show how the kernel method can be applied to a two-dimensional queueing system for exact tail asymptotics in the stationary joint distribution and also in the two marginal distributions. We demonstrate in detail how to locate the dominant singularity and how to determine the detailed behavior of the unknown generating function around the dominant singularity for a bivariate kernel, which is much more challenging than the analysis for a one-dimensional kernel. This information is the key for characterizing exact tail asymptotics in terms of asymptotic analysis theory. This approach does not require a determination or presentation of the unknown generating function(s).