an:06000225
Zbl 1235.60132
Li, Hui; Zhao, Yiqiang Q.
Tail asymptotics for a generalized two-demand queueing model -- a kernel method
EN
Queueing Syst. 69, No. 1, 77-100 (2011).
00287336
2011
j
60K25 30E15
generalized two-demand queueing model; generating functions; stationary probabilities; kernel method; asymptotic analysis; dominant singularity; exact tail asymptotics; random walks in the quarter plane
Summary: We consider a generalized two-demand queueing model (the same model was studied in [\textit{P. E. Wright}, Adv. Appl. Probab. 24, No.~4, 986--1007 (1992; Zbl 0760.60093)]). 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. This approach does not require a determination or presentation of the unknown generating function(s).
Zbl 0760.60093