Two-parameter heavy-traffic limits for infinite-server queues with dependent service times

DOI10.1007/s11134-012-9303-0zbMath1264.60068OpenAlexW2119977489MaRDI QIDQ1935510

Ward Whitt, Guodong Pang

Publication date: 18 February 2013

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

Full work available at URL: https://doi.org/10.1007/s11134-012-9303-0

zbMATH Keywords

martingalesfunctional central limit theorems\(S\)-mixing\(\phi \)-mixingtwo-parameter processesinfinite-server queuestime-varying arrivalsgeneralized Kiefer processGaussian (random field) approximationweakly dependent service times

Mathematics Subject Classification ID

Random fields (60G60) Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Random measures (60G57) Functional limit theorems; invariance principles (60F17)

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Cites Work

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• Two-parameter heavy-traffic limits for infinite-server queues
• Asymptotic results for the empirical process of stationary sequences
• Heavy-traffic limits for waiting times in many-server queues with abandonment
• Autocorrelations in infinite server batch arrival queues
• A heavy-traffic analysis of a closed queueing system with a \(GI/\infty\) service center
• Weak convergence and empirical processes. With applications to statistics
• Stochastic-Process Limits
• INFINITE-SERVER QUEUES WITH BATCH ARRIVALS AND DEPENDENT SERVICE TIMES
• Service Interruptions in Large-Scale Service Systems
• Heavy traffic results for single-server queues with dependent (EARMA) service and interarrival times
• An almost sure invariance principle for the empirical distribution function of mixing random variables
• A mixed autoregressive-moving average exponential sequence and point process (EARMA 1,1)
• The M^k/G/∞ batch arrival queue by heterogeneous dependent demands
• Multiparameter Processes
• Convergence Criteria for Multiparameter Stochastic Processes and Some Applications