Technical Note—Approximating Systems Fed by Poisson Processes with Rapidly Changing Arrival Rates

DOI10.1287/opre.2020.2031zbMath1486.90076arXiv1807.06805OpenAlexW3174565095MaRDI QIDQ5031645

Zeyu Zheng, Harsha Honnappa, Peter W. Glynn

Publication date: 16 February 2022

Published in: Operations Research (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.06805

zbMATH Keywords

weak convergencestochastic modelingPoisson processcounting processesstochastic model applicationscompensatorinfinite-server queueintensitytotal variation convergence

Mathematics Subject Classification ID

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

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Markov-modulated infinite-server queues with general service times
• Point processes and queues. Martingale dynamics
• An introduction to the theory of point processes
• Uniform acceleration expansions for Markov chains with time-varying rates
• Networks of \(\cdot /\mathrm{G}/\infty \) queues with shot-noise-driven arrival intensities
• Networks of infinite-server queues with nonstationary Poisson input
• Exponential and uniform ergodicity of Markov processes
• Stability of regime-switching stochastic differential equations
• Stability of regime-switching diffusions
• Some limit theorems for Hawkes processes and application to financial statistics
• A Liapounov bound for solutions of the Poisson equation
• Stochastic simulation: Algorithms and analysis
• Markov Chains and Stochastic Stability
• A strong law of large numbers for local martingales
• Asymptotic Formulas for Markov Processes with Applications to Simulation
• Foundations of Modern Probability
• Infinite-server queues with Hawkes input
• Stability of queueing networks and scheduling policies
• On Choosing and Bounding Probability Metrics
• Stability and convergence of moments for multiclass queueing networks via fluid limit models
• Asymptotic Expansions of Singularly Perturbed Systems Involving Rapidly Fluctuating Markov Chains
• Queues Driven by Hawkes Processes
• Spectra of some self-exciting and mutually exciting point processes
• Scaling limits for infinite-server systems in a random environment