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Martingale proofs of many-server heavy-traffic limits for Markovian queues
1 references·16 citing·40 second hopsampled
Martingale proofs of many-server heavy-traffic limits for Markovian queues (2007)Martingale proofs of many-server heavy-tr…Central limit theorems for local martingales (1980)Central limit theorems for lo…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…Universality of Power-of-d Load Balancing in Many-Server Systems (2018)Universality of Power-of-d Lo…Join the Shortest Queue with Many Servers. The Heavy-Traffic Asymptotics (2018)Join the Shortest Queue with …Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues (2018)Functional central limit theo…On the instability of matching queues (2017)On the instability of matchin…Service Systems with Slowdowns: Potential Failures and Proposed Solutions (2015)Service Systems with Slowdown…State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems (2011)State Space Collapse in Many-…A Network of Time-Varying Many-Server Fluid Queues with Customer Abandonment (2011)A Network of Time-Varying Man…Two-parameter heavy-traffic limits for infinite-server queues (2010)Two-parameter heavy-traffic l…Many-server diffusion limits for G/Ph/n+GI queues (2010)Many-server diffusion limits …Law of large numbers limits for many-server queues (2010)Law of large numbers limits f…Admission control for a multi-server queue with abandonment (2010)Admission control for a multi…Real-Time Delay Estimation in Overloaded Multiserver Queues with Abandonments (2009)Real-Time Delay Estimation in…Queue-and-Idleness-Ratio Controls in Many-Server Service Systems (2009)Queue-and-Idleness-Ratio Cont…Dynamic Control of N-Systems with Many Servers: Asymptotic Optimality of a Static Priority Policy in Heavy Traffic (2009)Dynamic Control of N-Systems …Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems (2008)Scheduling Flexible Servers w…Optimality of the shortest line discipline (1977)Heavy-Traffic Limits for Queues with Many Exponential Servers (1981)The power of two choices in randomized load balancing (2001)Universality of Power-of-$d$ Load Balancing in Many-Server Systems (2016)Scalable Load Balancing in Networked Systems: A Survey of Recent Advances (2022)Applied Probability and Queues (1987)Brownian Motion and Stochastic Flow Systems. (1987)Statistical Analysis of a Telephone Call Center (2005)Fluid limits of many-server queues with reneging (2010)Stabilizing Customer Abandonment in Many-Server Queues with Time-Varying Arrivals (2012)The Queueing Network Analyzer (1983)Designing a Call Center with Impatient Customers (2002)The Modern Call Center: A Multi‐Disciplinary Perspective on Operations Management Research (2007)Large-time asymptotics for the G t /M t /s t +GI t many-server fluid queue with abandonment (2011)A many-server fluid limit for the queueing model experiencing periods of overloading (2012)Many-server heavy-traffic limit for queues with time-varying parameters (2014)On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models (1995)Telephone Call Centers: Tutorial, Review, and Research Prospects (2003)Asymptotic analysis of queueing systems with reneging: A survey of results for FIFO, single class models (2011)Introduction to Matrix Analytic Methods in Stochastic Modeling (1999)Customer Abandonment in Many-Server Queues (2010)Diffusion models and steady-state approximations for exponentially ergodic markovian queues (2013)Resource Allocation Problems: Algorithmic Approaches (1989)Stochastic-process limits : an introduction to stochastic-process limits and their application to queues (2002)Blind Fair Routing in Large-Scale Service Systems with Heterogeneous Customers and Servers (2013)Product forms for FCFS queueing models with arbitrary server-job compatibilities: an overview (2020)Brownian Motion and Stochastic Calculus (2007)Service-Level Differentiation in Many-Server Service Systems via Queue-Ratio Routing (2009)Fair Dynamic Routing in Large-Scale Heterogeneous-Server Systems (2010)Control of Patient Flow in Emergency Departments, or Multiclass Queues with Deadlines and Feedback (2015)On Square Integrable Martingales (1967)Diffusion processes with continuous coefficients, I (1969)A Functional Central Limit Theorem for Semimartingales (1981)Stability of strong solutions of stochastic differential equations (1989)Stopping Times and Tightness. II (1989)Theory of Martingales (1989)Join-the-shortest queue diffusion limit in Halfin–Whitt regime: Tail asymptotics and scaling of extrema (2019)Queueing system with impatient customers: A review (2010)Strategic Queueing Behavior and Its Impact on System Performance in Service Systems with the Congestion-Based Staffing Policy (2012)Does the Past Predict the Future? The Case of Delay Announcements in Service Systems (2016)
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References

  • 1980Central limit theorems for local martingales253 cited

Cited by

  • 2009Queue-and-Idleness-Ratio Controls in Many-Server Service Systems148 cited
  • 2010Law of large numbers limits for many-server queues113 cited
  • 2018Join the Shortest Queue with Many Servers. The Heavy-Traffic Asymptotics105 cited
  • 2010Many-server diffusion limits for G/Ph/n+GI queues100 cited
  • 2008Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems88 cited
  • 2009Dynamic Control of N-Systems with Many Servers: Asymptotic Optimality of a Static Priority Policy in Heavy Traffic87 cited
  • 2018Universality of Power-of-d Load Balancing in Many-Server Systems72 cited
  • 2009Real-Time Delay Estimation in Overloaded Multiserver Queues with Abandonments69 cited
  • 2011A Network of Time-Varying Many-Server Fluid Queues with Customer Abandonment67 cited
  • 2011State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems66 cited
  • 2018Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues66 cited
  • 2010Two-parameter heavy-traffic limits for infinite-server queues65 cited
  • 2019Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime

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61 cited
  • 2017On the instability of matching queues60 cited
  • 2015Service Systems with Slowdowns: Potential Failures and Proposed Solutions58 cited
  • 2010Admission control for a multi-server queue with abandonment55 cited