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Stein’s Method for Steady-state Diffusion Approximations: An Introduction through the Erlang-A and Erlang-C Models
16 references·9 citing·32 second hop
Stein’s Method for Steady-state Diffusion Approximations: An Introduction through the Erlang-A and Erlang-C Models (2016)Stein’s Method for Steady-state Diffusion…The G/GI/N queue in the Halfin–Whitt regime (2009)The G/GI/N queue in the Halfi…Validity of heavy traffic steady-state approximations in generalized Jackson networks (2006)Validity of heavy traffic ste…MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic (2004)MaxWeight scheduling in a gen…Telephone Call Centers: Tutorial, Review, and Research Prospects (2003)Telephone Call Centers: Tutor…A Diffusion Approximation for a Markovian Queue with Reneging (2003)A Diffusion Approximation for…State space collapse with application to heavy traffic limits for multiclass queueing networks (1998)State space collapse with app…Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse (1998)Diffusion approximations for …Brownian models of multiclass queueing networks: Current status and open problems (1993)Brownian models of multiclass…A Heavy Traffic Limit Theorem for Networks of Queues with Multiple Customer Types (1991)A Heavy Traffic Limit Theorem…Brownian models of open queueing networks with homogeneous customer populations ∗ (1987)Brownian models of open queue…Open Queueing Networks in Heavy Traffic (1984)Open Queueing Networks in Hea…Heavy-Traffic Limits for Queues with Many Exponential Servers (1981)Heavy-Traffic Limits for Queu…MULTI-DIMENSIONAL DIFFUSION PROCESSES (1980)MULTI-DIMENSIONAL DIFFUSION P…The diffusion approximation for tandem queues in heavy traffic (1978)The diffusion approximation f…Multiple channel queues in heavy traffic. II: sequences, networks, and batches (1970)Multiple channel queues in he…Multiple channel queues in heavy traffic. I (1970)Multiple channel queues in he…Transform Methods for Heavy-Traffic Analysis (2020)Transform Methods for Heavy-T…Steady-State Analysis of the Join-the-Shortest-Queue Model in the Halfin–Whitt Regime (2020)Steady-State Analysis of the …Steady-state analysis of load-balancing algorithms in the sub-Halfin–Whitt regime (2020)Steady-state analysis of load…Optimal Load Balancing with Locality Constraints (2020)Optimal Load Balancing with L…Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime (2019)Economies-of-Scale in Many-Se…Size expansions of mean field approximation: Transient and steady-state analysis (2018)Size expansions of mean field…Stein's Method for Mean-Field Approximations in Light and Heavy Traffic Regimes (2017)Stein's Method for Mean-Field…Stein's Method for Mean Field Approximations in Light and Heavy Traffic Regimes (2017)Stein's Method for Mean Field…Heavy Traffic Approximation for the Stationary Distribution of a Generalized Jackson Network: The BAR Approach (2017)Heavy Traffic Approximation f…The single server queue in heavy traffic (1961)Discrete Flow Networks: Bottleneck Analysis and Fluid Approximations (1991)Logarithmic asymptotics for steady-state tail probabilities in a single-server queue (1994)Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks (1992)Dynamic server allocation to parallel queues with randomly varying connectivity (1993)Achieving 100% throughput in an input-queued switch (2002)Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized cμ-Rule (2004)SCHEDULING IN A QUEUING SYSTEM WITH ASYNCHRONOUSLY VARYING SERVICE RATES (2004)Maximum Pressure Policies in Stochastic Processing Networks (2005)Approximating a Point Process by a Renewal Process, I: Two Basic Methods (1982)An introduction to queueing theory (1993)Designing a Call Center with Impatient Customers (2002)The Modern Call Center: A Multi‐Disciplinary Perspective on Operations Management Research (2007)Networks of Waiting Lines (1957)Brownian Models of Queueing Networks with Heterogeneous Customer Populations (1988)Numerical Methods for Stochastic Control Problems in Continuous Time (1990)Open, Closed, and Mixed Networks of Queues with Different Classes of Customers (1975)Brownian Motion and Stochastic Flow Systems. (1987)Planning Queueing Simulations (1989)Fluctuations of Lévy Processes with Applications (2014)Poisson Arrivals See Time Averages (1982)Introduction to Matrix Analytic Methods in Stochastic Modeling (1999)Statistical Analysis of a Telephone Call Center (2005)Forecasting: theory and practice (2022)Piecewise-Deterministic Markov Processes: A General Class of Non-Diffusion Stochastic Models (1984)On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models (1995)On Customer Contact Centers with a Call-Back Option: Customer Decisions, Routing Rules, and System Design (2004)ARCH models as diffusion approximations (1990)Chapter 49 Arch models (1994)5 Stochastic volatility (1996)Stability of Queueing Networks (2008)Asymptotically tight steady-state queue length bounds implied by drift conditions (2012)
this work references cited by second hop

References

  • 2003Telephone Call Centers: Tutorial, Review, and Research Prospects1,360 cited
  • 1980MULTI-DIMENSIONAL DIFFUSION PROCESSES1,243 cited
  • 1981Heavy-Traffic Limits for Queues with Many Exponential Servers750 cited
  • 2004MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic460 cited
  • 1984Open Queueing Networks in Heavy Traffic449 cited
  • 1970Multiple channel queues in heavy traffic. I438 cited
  • 1987Brownian models of open queueing networks with homogeneous customer populations ∗312 cited
  • 1998State space collapse with application to heavy traffic limits for multiclass queueing networks309 cited
  • 1970Multiple channel queues in heavy traffic. II: sequences, networks, and batches281 cited
  • 1998Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse264 cited
  • 1993Brownian models of multiclass queueing networks: Current status and open problems177 cited
  • 2003A Diffusion Approximation for a Markovian Queue with Reneging166 cited
  • 2009The G/GI/N queue in the Halfin–Whitt regime146 cited
  • 2006Validity of heavy traffic steady-state approximations in generalized Jackson networks146 cited
  • 1978

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The diffusion approximation for tandem queues in heavy traffic
122 cited
  • 1991A Heavy Traffic Limit Theorem for Networks of Queues with Multiple Customer Types103 cited
  • Cited by

    • 2019Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime61 cited
    • 2020Steady-State Analysis of the Join-the-Shortest-Queue Model in the Halfin–Whitt Regime46 cited
    • 2020Steady-state analysis of load-balancing algorithms in the sub-Halfin–Whitt regime38 cited
    • 2020Transform Methods for Heavy-Traffic Analysis34 cited
    • 2018Size expansions of mean field approximation: Transient and steady-state analysis27 cited
    • 2017Heavy Traffic Approximation for the Stationary Distribution of a Generalized Jackson Network: The BAR Approach27 cited
    • 2017Stein's Method for Mean Field Approximations in Light and Heavy Traffic Regimes25 cited
    • 2020Optimal Load Balancing with Locality Constraints22 cited
    • 2017Stein's Method for Mean-Field Approximations in Light and Heavy Traffic Regimes20 cited