Sampling at subexponential times, with queueing applications

DOI10.1016/S0304-4149(98)00064-7zbMath0961.60080OpenAlexW2077501147MaRDI QIDQ1593601

Claudia Klüppelberg, Karl Sigman, Soren Asmussen

Publication date: 17 January 2001

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-4149(98)00064-7

zbMATH Keywords

vacation modellarge deviationsPoisson processbusy periodLittle's lawsubexponential distributionMarkov additive process

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Queueing theory (aspects of probability theory) (60K25)

Related Items (42)

Branching processes with immigration in atypical random environment ⋮ Moments and tails in monotone-separable stochastic networks. ⋮ AN IDENTIFICATION PROBLEM IN AN URN AND BALL MODEL WITH HEAVY TAILED DISTRIBUTIONS ⋮ On regenerative estimation of extremal index in queueing systems ⋮ Tail asymptotics for processor-sharing queues ⋮ Log-convexity of counting processes evaluated at a random end of observation time with applications to queueing models ⋮ Tandem queues with subexponential service times and finite buffers ⋮ The queue length in an \(M/G/1\) batch arrival retrial queue ⋮ The DFR Property for Counting Processes Stopped at an Independent Random Time ⋮ Externalities in the M/G/1 queue: LCFS-PR versus FCFS ⋮ Refined tail asymptotic properties for the \(M^X/G/1\) retrial queue ⋮ Tail asymptotics for the \(M_1,M_2/G_1,G_2/1\) retrial queue with non-preemptive priority ⋮ Processor sharing: a survey of the mathematical theory ⋮ Heavy-tailed asymptotics of stationary probability vectors of Markov chains of gi/g/1 type ⋮ Tail asymptotics of the waiting time and the busy period for the \(\mathrm{M}/\mathrm{G}/1/K\) queues with subexponential service times ⋮ A General Class of Closed Fork and Join Queues with Subexponential Service Times ⋮ Tails of random sums of a heavy-tailed number of light-tailed terms ⋮ Tail asymptotics for the fundamental period in the MAP\(/G/1\) queue ⋮ Tail Asymptotics for the Waiting Time in an M/G/1/ROS Vacation Queue with Regularly-Varying Service ⋮ SUBEXPONENTIAL INTERVAL GRAPHS GENERATED BY IMMIGRATION–DEATH PROCESSES ⋮ A sufficient condition for the subexponential asymptotics of GI/G/\(1\)-type Markov chains with queueing applications ⋮ On Exceedance Times for Some Processes with Dependent Increments ⋮ Asymptotics for the First Passage Times of Lévy Processes and Random Walks ⋮ Accelerated consistent estimation of a high load probability in \(M/G/1\) and \(GI/G/1\) queues ⋮ Packet reordering in networks with heavy-tailed delays ⋮ Global and local asymptotics for the busy period of an M/G/1 queue ⋮ Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times ⋮ Accuracy of transformed kernel density estimates for a heavy-tailed distribution ⋮ The supremum of a Gaussian process over a random interval ⋮ Regularly varying tail of the waiting time distribution in M/G/1 retrial queue ⋮ Heavy tails in multi-server queue ⋮ Tail asymptotics for the queue length in an M/G/1 retrial queue ⋮ Sojourn time asymptotics in processor-sharing queues ⋮ Subexponential asymptotics of hybrid fluid and ruin models ⋮ Strong, weak and false inverse power laws ⋮ The Renewal-Based Asymptotics and Accelerated Estimation of a System with Random Volume Customers ⋮ Tails for (max, plus) recursions under subexponentiality ⋮ A Two‐Queue Polling Model with Regularly Varying Service and/or Switchover Times ⋮ Negative ageing properties for counting processes arising in virtual age models ⋮ Improved algorithms for rare event simulation with heavy tails ⋮ Reduced-load equivalence for queues with Gaussian input ⋮ Tail behaviour of the area under the queue length process of the single server queue with regularly varying service times

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Estimates for the probability of ruin with special emphasis on the possibility of large claims
• Large claims approximations for risk processes in a Markovian environment
• Functional large deviation principles for first-passage-time processes
• Transient laws of non-stationary queueing systems and their applications
• Asymptotics for M/G/1 low-priority waiting-time tail probabilities
• Large deviation analysis of the single server queue
• Compound sums and subexponentiality
• The distributional form of Little's law and the Fuhrmann-Cooper decomposition
• Convergence rates for M/G/1 queues and ruin problems with heavy tails
• Technical Note—A Note on the M/G/1 Queue with Server Vacations
• Imbedded Markov Chain Analysis of a Waiting-Line Process in Continuous Time
• The caudal characteristic curve of queues
• Large deviation results for time-dependent queue length distributions
• Subexponential distributions and integrated tails
• On the asymptotic behaviour of the distributions of the busy period and service time in M/G/1
• Equilibrium properties of the M/G/1 queue
• On the tails of waiting-time distributions
• Asymptotic ruin probabilities when exponential moments do not exist
• Subexponential asymptotics of a Markov-modulated random walk with queueing applications
• Asymptotics of palm-stationary buffer content distributions in fluid flow queues
• Densities with Gaussian Tails
• Asymptotics for steady-state tail probabilities in structured markov queueing models
• Logarithmic asymptotics for steady-state tail probabilities in a single-server queue
• Exponential Approximations for Tail Probabilities in Queues II: Sojourn Time and Workload
• Tail probabilities for non-standard risk and queueing processes with subexponential jumps
• Tauberian Results for Densities with Gaussian Tails
• Exponential Approximations for Tail Probabilities in Queues, I: Waiting Times
• A relation between stationary queue and waiting time distributions

This page was built for publication: Sampling at subexponential times, with queueing applications