Two-parameter process limits for infinite-server queues with dependent service times via chaining bounds

DOI10.1007/S11134-017-9550-1zbMath1390.60336OpenAlexW2764081920MaRDI QIDQ1698763

Guodong Pang, Yuhang Zhou

Publication date: 16 February 2018

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

Full work available at URL: https://doi.org/10.1007/s11134-017-9550-1

zbMATH Keywords

functional limit theoremsmaximal inequalitiesinfinite-server queuetwo-parameter processes\(\rho \)-mixingdependent service timesthe method of chaining

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Queueing theory (aspects of probability theory) (60K25) Functional limit theorems; invariance principles (60F17)

Related Items (3)

Queue length in a queuing system with dependent service times ⋮ Functional Limit Theorems for Shot Noise Processes with Weakly Dependent Noises ⋮ Shot noise processes with randomly delayed cluster arrivals and dependent noises in the large-intensity regime

Cites Work

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• \(\mathrm{G}/\mathrm{GI}/N (+ \mathrm{GI})\) queues with service interruptions in the Halfin-Whitt regime
• The \(G_{t}/GI/s_{t}+GI\) many-server fluid queue
• Two-parameter process limits for an infinite-server queue with arrival dependent service times
• Fluid limits of many-server queues with reneging
• Law of large numbers limits for many-server queues
• Two-parameter heavy-traffic limits for infinite-server queues
• Basic properties of strong mixing conditions. A survey and some open questions
• Asymptotic results for the empirical process of stationary sequences
• The \(G/GI/N\) queue in the Halfin-Whitt regime
• A heavy-traffic analysis of a closed queueing system with a \(GI/\infty\) service center
• Weak convergence and empirical processes. With applications to statistics
• Two-parameter heavy-traffic limits for infinite-server queues with dependent service times
• SPDE limits of many-server queues
• On many-server queues in heavy traffic
• Many-server heavy-traffic limit for queues with time-varying parameters
• Fluid limits of many-server queues with abandonments, general service and continuous patience time distributions
• Stochastic-Process Limits
• G/G/∞ queues with renewal alternating interruptions
• Queues with Many Servers and Impatient Customers
• INFINITE-SERVER QUEUES WITH BATCH ARRIVALS AND DEPENDENT SERVICE TIMES
• Fluid Models for Multiserver Queues with Abandonments
• Central Limit Theorems for dependent variables. I
• An almost sure invariance principle for the empirical distribution function of mixing random variables
• Multiparameter Processes
• Refined Models for Efficiency-Driven Queues with Applications to Delay Announcements and Staffing
• The Generic Chaining
• Upper and Lower Bounds for Stochastic Processes
• On Weak Convergence of Stochastic Processes with Multidimensional Time Parameter
• Convergence Criteria for Multiparameter Stochastic Processes and Some Applications

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