 Conditional limit theorems for queues with Gaussian input, a weak convergence approachA.B. Dieker Stochastic Processes and their Applications, 2005, vol. 115, issue 5, 849-873 Abstract: We consider a buffered queueing system that is fed by a Gaussian source and drained at a constant rate. The fluid offered to the system in a time interval (0,t] is given by a separable continuous Gaussian process Y with stationary increments. The variance function of Y is assumed to be regularly varying with index 2H, for some 0 [infinity]. In addition, we study how a busy period longer than T typically occurs as T-->[infinity], and we find the logarithmic asymptotics for the probability of such a long busy period. The study relies on the weak convergence in an appropriate space of to a fractional Brownian motion with Hurst parameter H as [alpha]-->[infinity]. We prove this weak convergence under a fairly general condition on [sigma]2, sharpening recent results of Kozachenko et al. (Queueing Systems Theory Appl. 42 (2002) 113). The core of the proof consists of a new type of uniform convergence theorem for regularly varying functions with positive index. Keywords: Weak; convergence; Large; deviations; Gaussian; processes; Overflow; probability; Busy; period; Metric; entropy; Regular; variation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:115:y:2005:i:5:p:849-873 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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