Corrected asymptotics for a multi-server queue in the Halfin-Whitt regime

DOI10.1007/s11134-008-9070-0zbMath1152.90388OpenAlexW2126583761MaRDI QIDQ943987

Johan S. H. van Leeuwaarden, Bert Zwart, Augustus J. E. M. Janssen

Publication date: 12 September 2008

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

Full work available at URL: https://doi.org/10.1007/s11134-008-9070-0

zbMATH Keywords

Riemann zeta functionLerch's transcendentGaussian random walkSpitzer's identityAll-time maximumCorrected diffusion approximationHalfin-Whitt scalingLambert W FunctionQueues in heavy traffic

Mathematics Subject Classification ID

Queues and service in operations research (90B22)

Related Items

Asymptotics of insensitive load balancing and blocking phases ⋮ Efficiency evaluation for pooling resources in health care ⋮ Gaussian expansions and bounds for the Poisson distribution applied to the Erlang B formula ⋮ Heavy-traffic limits for nearly deterministic queues: Stationary distributions ⋮ Cumulants of the maximum of the Gaussian random walk ⋮ Sharp and simple bounds for the Erlang delay and loss formulae ⋮ Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
• Complete corrected diffusion approximations for the maximum of a random walk
• The \(G/GI/N\) queue in the Halfin-Whitt regime
• On Berry-Esseen results for the compound Poisson distribution
• Ladder heights, Gaussian random walks and the Riemann zeta function
• A simple solution for the M/D/c waiting time distribution
• On the Lambert \(w\) function
• Heavy traffic limits for queues with many deterministic servers
• On Lerch's transcendent and the Gaussian random walk
• Cumulants of the maximum of the Gaussian random walk
• Refining Square-Root Safety Staffing by Expanding Erlang C
• A Combinatorial Lemma and Its Application to Probability Theory
• Dimensioning Large Call Centers
• Corrected diffusion approximations in certain random walk problems
• Heavy-Traffic Limits for Queues with Many Exponential Servers
• The Uniform Asymptotic Expansion of a Class of Integrals Related to Cumulative Distribution Functions
• Some Properties of the Erlang Loss Function
• The multiclass GI/PH/N queue in the Halfin-Whitt regime
• Applied Probability and Queues
• Heavy-Traffic Limits for the G/H₂*/n/mQueue