Queueing systems with many servers: null controllability in heavy traffic

DOI10.1214/105051606000000358zbMath1121.60092arXivmath/0507342OpenAlexW2000731707MaRDI QIDQ997402

Rami Atar, Gennady Shaikhet, Avishai Mandelbaum

Publication date: 6 August 2007

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0507342

zbMATH Keywords

heavy trafficnull controllabilityscheduling and routingmulticlass queueing systemssingular control of diffusions

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) Stochastic scheduling theory in operations research (90B36) Performance evaluation, queueing, and scheduling in the context of computer systems (68M20) Impulsive optimal control problems (49N25)

Related Items (7)

Optimal admission control for many-server systems with QED-driven revenues ⋮ Scheduling parallel servers in the nondegenerate slowdown diffusion regime: asymptotic optimality results ⋮ Gaussian expansions and bounds for the Poisson distribution applied to the Erlang B formula ⋮ Optimal control of parallel server systems with many servers in heavy traffic ⋮ Necessary condition for null controllability in many-server heavy traffic ⋮ Control of systems with flexible multi-server pools: a shadow routing approach ⋮ Critically loaded queueing models that are throughput suboptimal

Cites Work

• Two workload properties for Brownian networks
• A diffusion model of scheduling control in queueing systems with many servers
• Scheduling a multi class queue with many exponential servers: asymptotic optimality in heavy traffic.
• Heavy traffic resource pooling in parallel-server systems
• Scheduling control for queueing systems with many servers: asymptotic optimality in heavy traffic
• Stochastic differential equations with reflecting boundary conditions
• Heavy-Traffic Limits for Queues with Many Exponential Servers
• The multiclass GI/PH/N queue in the Halfin-Whitt regime
• Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized cμ-Rule
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