Tail asymptotics for busy periods

DOI10.1214/13-SSY098zbMath1310.60130arXiv1112.1815MaRDI QIDQ2921190

Ken R. Duffy, Sean P. Meyn

Publication date: 7 October 2014

Full work available at URL: https://arxiv.org/abs/1112.1815

zbMATH Keywords

sample pathsqueueslarge deviationsbusy periodsintegrated random walks

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Large deviations (60F10) Sample path properties (60G17)

Related Items

Sample path large deviations for Lévy processes and random walks with Weibull increments ⋮ Tail asymptotics for the area under the excursion of a random walk with heavy-tailed increments ⋮ Local asymptotics for the area under the random walk excursion ⋮ Fundamental design principles for reinforcement learning algorithms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Large deviations for the empirical mean of an M/M/\(1\) queue
• Tail behaviour of the area under a random process, with applications to queueing systems, insurance and percolations
• Estimating Loynes' exponent
• How large delays build up in a GI/G/1 queue
• Tail asymptotics for discrete event systems
• Logarithmic asymptotics for a single-server processing distinguishable sources
• Logarithmic asymptotics for the supremum of a stochastic process
• Big queues.
• Large deviations asymptotics and the spectral theory of multiplicatively regular Markov proces\-ses
• Sample path large deviations for queues with many inputs
• Large deviations: From empirical mean and measure to partial sums process
• Large deviation analysis of the single server queue
• Stochastic-Process Limits
• A large deviation principle with queueing applications
• Remarks on Convergence of Random Processes in Non-Separable Metric Spaces and on the Non-Existence of a Borel Measure for Processes in $C(0,\infty )$
• Logarithmic asymptotics for steady-state tail probabilities in a single-server queue
• Variational Analysis
• On the integral of the workload process of the single server queue
• The Large Deviations of Estimating Rate Functions
• Control Techniques for Complex Networks
• [https://portal.mardi4nfdi.de/wiki/Publication:5556859 Verteilungs-invarianzprinzipien f�r das starke gesetz der gro\en zahl]
• Stochastic Abelian and Tauberian theorems
• Single class queueing networks with discrete and fluid customers on the time interval \(\mathbb R\)

This page was built for publication: Tail asymptotics for busy periods