Sufficient conditions for functional-limit-theorem versions of \(L=\lambda W\)

DOI10.1007/BF01149539zbMath0681.60097MaRDI QIDQ1823561

Ward Whitt, Peter W. Glynn

Publication date: 1987

Published in: Queueing Systems (Search for Journal in Brave)

zbMATH Keywords

functional limit theoremslaw of the iterated logarithmcentral-limit theoremregenerative structures

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22)

Related Items (18)

A law of the iterated logarithm for the sojourn time process in queues in series ⋮ On Functional Central Limit Theorems for Semi-Markov and Related Processes ⋮ Little laws for utility processes and waiting times in queues ⋮ Functional law of the iterated logarithm for multi-server queues with batch arrivals and customer feedback ⋮ A law of the iterated logarithm for extreme queue length in multiphase queues ⋮ Asymptotic variability analysis for a two-stage tandem queue. I: The functional law of the iterated logarithm ⋮ Multiple-comparison procedures for steady-state simulations ⋮ The (functional) law of the iterated logarithm of the sojourn time for a multiclass queue ⋮ Extending the FCLT version of \(L=\lambda W\) ⋮ Analysis of initial transient deletion for replicated steady-state simulations ⋮ A functional law of the iterated logarithm for multi-class queues with batch arrivals ⋮ The Brownian approximation for rate-control throttles and the \(G/G/1/C\) queue ⋮ Limit theorems for cumulative processes ⋮ Periodic Little’s Law ⋮ A central-limit-theorem version of the periodic Little's law ⋮ A law of iterated logarithm for multiclass queues with preemptive priority service discipline ⋮ A review of \(L=\lambda W\) and extensions ⋮ On the law of the iterated logarithm in multiserver open queueing networks

Cites Work

• Unnamed Item
• Unnamed Item
• A central-limit-theorem version of \(L=\lambda W\)
• General Irreducible Markov Chains and Non-Negative Operators
• Some Useful Functions for Functional Limit Theorems
• Functional limit theorems for stochastic processes based on embedded processes
• Simulating stable stochastic systems, V: Comparison of ratio estimators
• A splitting technique for Harris recurrent Markov chains
• [https://portal.mardi4nfdi.de/wiki/Publication:4160209 Irr�ductibilit� et r�currence au sens de Harris des �Temps d'attente? des files GI/G/q]
• A New Approach to the Limit Theory of Recurrent Markov Chains
• Simulating Stable Stochastic Systems, I: General Multiserver Queues
• Technical Note—A Last Word on L = λW
• An invariance principle for the law of the iterated logarithm
• Weak Convergence of Probability Measures on the Function Space $C\lbrack 0, \infty)$
• Functional limit theorems for the queue GI/G/1 in light traffic
• Embedded renewal processes in the GI/G/s queue

This page was built for publication: Sufficient conditions for functional-limit-theorem versions of \(L=\lambda W\)