Convergence of a queueing system in heavy traffic with general patience-time distributions

DOI10.1016/j.spa.2011.07.003zbMath1230.60098OpenAlexW2121404777MaRDI QIDQ719770

Chihoon Lee, Ananda P. N. Weerasinghe

Publication date: 11 October 2011

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

Full work available at URL: https://doi.org/10.1016/j.spa.2011.07.003

zbMATH Keywords

stochastic controldiffusion approximationscustomer abandonmentcustomer impatiencerenegingheavy traffic theorycontrolled queueing systems

Mathematics Subject Classification ID

Communication networks in operations research (90B18) Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Performance evaluation, queueing, and scheduling in the context of computer systems (68M20)

Related Items (10)

On a class of singular stochastic control problems for reflected diffusions ⋮ A Unified Approach to Diffusion Analysis of Queues with General Patience-Time Distributions ⋮ Diffusion approximations for open Jackson networks with reneging ⋮ Abandonment versus blocking in many-server queues: asymptotic optimality in the QED regime ⋮ Dynamic scheduling of a \(GI/GI/1+GI\) queue with multiple customer classes ⋮ Diffusion Models for Double-ended Queues with Renewal Arrival Processes ⋮ Stationary distribution convergence of the offered waiting processes in heavy traffic under general patience time scaling ⋮ Diffusion approximations for double-ended queues with reneging in heavy traffic ⋮ Optimal service rate perturbations of many server queues in heavy traffic ⋮ General hazard-type scaling of abandonment time distribution for a \(\mathrm{G}/\mathrm{Ph}/n+\mathrm{GI}\) queue in the Halfin-Whitt heavy-traffic regime

Cites Work

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• Abandonment versus blocking in many-server queues: asymptotic optimality in the QED regime
• Drift rate control of a Brownian processing system
• Optimal buffer size and dynamic rate control for a queueing system with impatient customers in heavy traffic
• Call centers with impatient customers: Many-server asymptotics of the M/M/\(n+G\) queue
• Proofs of the martingale FCLT
• The Skorokhod problem in a time-dependent interval
• Heavy-traffic limits for waiting times in many-server queues with abandonment
• Point processes and queues. Martingale dynamics
• Heavy traffic analysis of open processing networks with complete resource pooling: asymptotic optimality of discrete review policies
• A diffusion approximation for a Markovian queue with reneging
• Scheduling a multi class queue with many exponential servers: asymptotic optimality in heavy traffic.
• Diffusion approximation for open state-dependent queueing networks in the heavy traffic situation
• Many-server diffusion limits for \(G/Ph/n+GI\) queues
• An explicit formula for the Skorokhod map on \([0,a\)]
• Scheduling control for queueing systems with many servers: asymptotic optimality in heavy traffic
• A diffusion approximation for a GI/GI/1 queue with balking or reneging
• On the Rosenthal's inequality for locally square integrable martingales.
• Stochastic-Process Limits
• Queues with Many Servers: The Virtual Waiting-Time Process in the QED Regime
• Approximating the GI/GI/1+GI Queue with a Nonlinear Drift Diffusion: Hazard Rate Scaling in Heavy Traffic
• Customer Abandonment in Many-Server Queues
• Dynamic Control of a Multiclass Queue with Thin Arrival Streams
• Dynamic Control of a Queue with Adjustable Service Rate
• Asymptotically Optimal Admission Control of a Queue with Impatient Customers
• Multiple channel queues in heavy traffic. I
• Admission control for a multi-server queue with abandonment

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