Asymptotic analysis by the saddle point method of theAnick-Mitra-Sondhi model

[摘要] We consider a fluid queue where the input process consists ofNidenticalsources that turnonandoffat exponential waiting times. The server works at the constantratecand anonsource generates fluid at unit rate.This model was first formulated and analyzed by Anick etal. (1982). We obtain an alternate representation of the jointsteady-state distribution ofthe buffer content and the number ofonsources. This isgiven as a contour integral that we then analyze in the limitN→∞. We give detailed asymptotic results for thejoint distribution as well as the associated marginal andconditional distributions. In particular, simple conditionallimits laws are obtained. These show how the buffer contentbehaves conditioned on the number of active sources and viceversa. Numerical comparisons show that our asymptotic results arevery accurate even forN=20.

[学科分类] 应用数学