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Revisiting the Tail Asymptotics of the Double QBD Process: Refinement and Complete Solutions for the Coordinate and Diagonal Directions
16 references·1 citing·33 second hop
Revisiting the Tail Asymptotics of the Double QBD Process: Refinement and Complete Solutions for the Coordinate and Diagonal Directions (2012)Revisiting the Tail Asymptotics of the Do…Tail Asymptotics of the Stationary Distribution of a Two-Dimensional Reflecting Random Walk with Unbounded Upward Jumps (2014)Tail Asymptotics of the Stati…Stationary distribution of a two-dimensional SRBM: geometric views and boundary measures (2013)Stationary distribution of a …Tail asymptotics for a generalized two-demand queueing model—a kernel method (2011)Tail asymptotics for a genera…Reflecting Brownian Motion in Two Dimensions: Exact Asymptotics for the Stationary Distribution (2011)Reflecting Brownian Motion in…Light tail asymptotics in multidimensional reflecting processes for queueing networks (2011)Light tail asymptotics in mul…Rare event asymptotics for a random walk in the quarter plane (2010)Rare event asymptotics for a …Tail Decay Rates in Double QBD Processes and Related Reflected Random Walks (2009)Tail Decay Rates in Double QB…Tail asymptotics for a Lévy-driven tandem queue with an intermediate input (2009)Tail asymptotics for a Lévy-d…Exact tail asymptotics in a priority queue—characterizations of the preemptive model (2009)Exact tail asymptotics in a p…Large deviations of a modified Jackson network: Stability and rough asymptotics (2005)Large deviations of a modifie…Bridges and networks: Exact asymptotics (2005)Bridges and networks: Exact a…The stationary tail asymptotics in the GI/G/1-type queue with countably many background states (2004)The stationary tail asymptoti…Explicit Solutions for Variational Problems in the Quadrant (2001)Explicit Solutions for Variat…Ideology of induced chains (1995)Ideology of induced chainsTwo Parallel Queues Created by Arrivals with Two Demands I (1984)Two Parallel Queues Created b…Two queues in parallel (1977)Two queues in parallelExact asymptotic formulae of the stationary distribution of a discrete-time two-dimensional QBD process (2018)Exact asymptotic formulae of …Two Similar Queues in Parallel (1961)J.comput. appl. math (1990)A compensation approach for two-dimensional Markov processes (1993)The stability of a queue with non-independent inter-arrival and service times (1962)Applied Probability and Queues (1987)Markovian arrivals in stochastic modelling: a survey and some new results (2010)Introduction to Stochastic Processes (2014)The Single Server Queue (1983)The fork-join queue and related systems with synchronization constraints: stochastic ordering and computable bounds (1989)The stochastic rendezvous network model for performance of synchronous client-server-like distributed software (1995)Order-Fulfillment Performance Measures in an Assemble-to-Order System with Stochastic Leadtimes (1999)Structured Stochastic Matrices of M/G/1 Type and Their Applications. (1991)Fundamentals of Queueing Networks (2001)Asymptotics for the stationary distribution in a discrete-time two-dimensional quasi-birth-and-death process (2012)A superharmonic vector for a nonnegative matrix with QBD block structure and its application to a Markov-modulated two-dimensional reflecting process (2015)Optimization in operations research (1997)Join the shortest queue: stability and exact asymptotics (2001)Exact asymptotics for the stationary distribution of a Markov chain: a production model (2009)The Value of Partial Resource Pooling: Should a Service Network Be Integrated or Product-Focused (2009)Brownian models of open queueing networks with homogeneous customer populations ∗ (1987)Multidimensional Reflected Brownian Motions Having Exponential Stationary Distributions (1987)Stochastic Networks Theory and Applications (1996)Boundary Value Problems in Queueing System Analysis (1983)Large Deviations For Performance Analysis: Queues, Communication and Computing (1995)A TWO-CLASS RETRIAL SYSTEM WITH COUPLED ORBIT QUEUES (2017)Reflected Brownian Motion on an Orthant (1981)A time-reversed representation for the tail probabilities of stationary reflected Brownian motion (2002)Efficient simulation of buffer overflow probabilities in jackson networks with feedback (2005)Matrix-Geometric Solutions to Stochastic Models (1984)Introduction to Matrix Analytic Methods in Stochastic Modeling (1999)Large Deviations For Performance Analysis (2019)The M / G /1 queue with two service speeds (2001)Fast Jackson Networks with Dynamic Routing (2002)
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References

  • 1984Two Parallel Queues Created by Arrivals with Two Demands I309 cited
  • 1977Two queues in parallel153 cited
  • 2011Reflecting Brownian Motion in Two Dimensions: Exact Asymptotics for the Stationary Distribution96 cited
  • 1995Ideology of induced chains86 cited
  • 2004The stationary tail asymptotics in the GI/G/1-type queue with countably many background states74 cited
  • 2009Tail Decay Rates in Double QBD Processes and Related Reflected Random Walks72 cited
  • 2011Light tail asymptotics in multidimensional reflecting processes for queueing networks59 cited
  • 2005Large deviations of a modified Jackson network: Stability and rough asymptotics44 cited
  • 2001Explicit Solutions for Variational Problems in the Quadrant40 cited
  • 2010Rare event asymptotics for a random walk in the quarter plane39 cited
  • 2013Stationary distribution of a two-dimensional SRBM: geometric views and boundary measures37 cited
  • 2011Tail asymptotics for a generalized two-demand queueing model—a kernel method36 cited
  • 2005Bridges and networks: Exact asymptotics33 cited
  • 2009Exact tail asymptotics in a priority queue—characterizations of the preemptive model29 cited
  • 2014Tail Asymptotics of the Stationary Distribution of a Two-Dimensional Reflecting Random Walk with Unbounded Upward Jumps

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27 cited
  • 2009Tail asymptotics for a Lévy-driven tandem queue with an intermediate input24 cited
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    • 2018Exact asymptotic formulae of the stationary distribution of a discrete-time two-dimensional QBD process17 cited