Large finite population queueing systems: The single-server model

DOI10.1016/0304-4149(94)90060-4zbMath0823.60088OpenAlexW1965789271MaRDI QIDQ1338765

Guy Louchard

Publication date: 20 September 1995

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

Full work available at URL: https://doi.org/10.1016/0304-4149(94)90060-4

zbMATH Keywords

Brownian motiondiffusion approximationsasymptotic in heavy trafficsingle-server model

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22)

Related Items

Strong Embeddings for Transitory Queueing Models, Heavy-Traffic Analysis Through Uniform Acceleration of Queues with Diminishing Populations, Finite-pool queueing with heavy-tailed services, Rare events of transitory queues, A queueing model with independent arrivals, and its fluid and diffusion limits

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Refining diffusion approximations for queues
• The Brownian excursion area: A numerical analysis
• On the joint distribution of the maximum and its location for a linear diffusion
• Transient behavior of the M/M/1 queue: Starting at the origin
• Weak convergence inapplied probability
• Functional central limit theorems for random walks conditioned to stay positive
• Excursions in Brownian motion
• Weak convergence of compound stochastic process. I
• On a probability problem connected with railway traffic
• Kac's formula, levy's local time and brownian excursion
• The maximum of a random walk whose mean path has a maximum
• Asymptotic Analysis of the Time Dependent M/M/1 Queue
• The first-passage density of a continuous gaussian process to a general boundary
• Transient behavior of regulated Brownian motion, I: Starting at the origin
• Transient behavior of regulated Brownian motion, II: Non-zero initial conditions
• Transient behavior of the M/M/1 queue via Laplace transforms
• On some time-non-homogeneous diffusion approximations to queueing systems
• Large finite population queueing systems part i: the infinite server model.
• The maximum of a Gaussian process whose mean path has a maximum, with an application to the strength of bundles of fibres
• Brownian Excursion, the M/M/1 Queue and Their Occupation Times
• Queues with time-dependent arrival rates I—the transition through saturation
• Queues with time-dependent arrival rates. II — The maximum queue and the return to equilibrium
• Queues with time-dependent arrival rates. III — A mild rush hour
• Multiple channel queues in heavy traffic. II: sequences, networks, and batches
• Multiple channel queues in heavy traffic. I
• Solutions for some diffusion processes with two barriers