Extreme values of birth and death processes and queues

DOI10.1016/0304-4149(87)90043-3zbMath0637.60098OpenAlexW2026989004MaRDI QIDQ1098502

Richard F. Serfozo

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0304-4149(87)90043-3

zbMATH Keywords

queuesFréchet distributionsbirth and death processGumbel distributionstransient and recurrent birth and death processes

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Limit theorems in probability theory (60F99)

Related Items (29)

A law of the iterated logarithm for the sojourn time process in queues in series ⋮ The maximum number of infected individuals in SIS epidemic models: computational techniques and quasi-stationary distributions ⋮ A law of the iterated logarithm for extreme queue length in multiphase queues ⋮ Applications of maximum queue lengths to call center management ⋮ Computational analysis of the maximal queue length in the MAP/\(M\)/\(c\) retrial queue ⋮ Maxima of sojourn times in acyclic Jackson queueing networks ⋮ Heavy-traffic extreme-value limits for queues ⋮ The single server queue with catastrophes and geometric reneging ⋮ Algorithmic analysis of the maximum level length in general-block two-dimensional Markov processes ⋮ Computing the performance measures in queueing models via the method of order statistics ⋮ Estimates of the convergence rate in a limit theorem for geometric sums and some of their applications ⋮ On the cycle maximum of birth-death processes and networks of queues ⋮ On extreme values of the queue length in some queuing systems ⋮ Estimation of the rate of convergence in the limit theorem for extreme values of regenerative processes ⋮ On the global values of the queue length in open queueing networks ⋮ Birth and Death (BDP) Process Models with Applications ⋮ The single server vacation queueing model with geometric abandonments ⋮ On extreme values in open queueing networks ⋮ Analysis of a multiserver queue with setup times ⋮ Heavy-traffic extreme value limits for Erlang delay models ⋮ Algorithmic analysis of the MAP/PH/1 retrial queue ⋮ Maximum Values in Queueing Processes ⋮ Asymptotic behavior of maxima of independent random variables. Discrete case ⋮ A limit theorem for extreme values of discrete random variables and its applications ⋮ On the extreme values of \(M/M/m\) queueing systems ⋮ The laws of iterated and triple logarithms for extreme values of regenerative processes ⋮ Asymptotic behavior of extreme values of queue length in \(M/M/m\) systems ⋮ On extreme values of some regenerative processes ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extremes and related properties of random sequences and processes
• Extreme Values of Queue Lengths in M/G/1 and GI/M/1 Systems
• Extreme value theory for a class of discrete distributions with applications to some stochastic processes
• On the Growth of the Maximum Queue Length in a Stable Queue
• Extreme Values in the GI/G/1 Queue

This page was built for publication: Extreme values of birth and death processes and queues