A unified approach for large queue asymptotics in a heterogeneous multiserver queue

DOI10.1017/apr.2016.84zbMath1425.60078arXiv1510.01034OpenAlexW2962842637MaRDI QIDQ5233164

Masakiyo Miyazawa

Publication date: 16 September 2019

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.01034

zbMATH Keywords

martingalestationary distributiontail asymptoticsheterogeneous serverpiecewise-deterministic Markov processqueue length processheavy-traffic approximationlarge variance

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Processes in random environments (60K37) Continuous-time Markov processes on discrete state spaces (60J27)

Related Items (4)

Stochastic monotonicity and comparability of Markov chains with block-monotone transition matrices and their applications to queueing systems ⋮ Martingale approach for tail asymptotic problems in the generalized Jackson network ⋮ A martingale view of Blackwell’s renewal theorem and its extensions to a general counting process ⋮ A unified approach for large queue asymptotics in a heterogeneous multiserver queue

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A superharmonic vector for a nonnegative matrix with QBD block structure and its application to a Markov-modulated two-dimensional reflecting process
• The \(G/GI/N\) queue in the Halfin-Whitt regime
• A technique for exponential change of measure for Markov processes
• On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models
• Light tail asymptotics in multidimensional reflecting processes for queueing networks
• On Large Delays in Multi-Server Queues with Heavy Tails
• Methods in Diffusion Approximation for Multi-Server Systems: Sandwich, Uniform Attraction and State-Space Collapse
• ASYMPTOTIC BEHAVIOR FOR MArP/PH/2 QUEUE WITH JOIN THE SHORTEST QUEUE DISCIPLINE
• Open Queueing Networks in Heavy Traffic
• Asymptotic behavior of the stationary distributions in the GI/PH/c queue with heterogeneous servers
• Heavy-Traffic Limits for Queues with Many Exponential Servers
• The Representation of Martingales of Jump Processes
• Logarithmic asymptotics for steady-state tail probabilities in a single-server queue
• Applied Probability and Queues
• Heavy traffic theory for queues with several servers. I
• The probability of large queue lengths and waiting times in a heterogeneous multiserver queue I: Tight limits
• The probability of large queue lengths and waiting times in a heterogeneous multiserver queue II: Positive recurrence and logarithmic limits
• Tail Asymptotics of the Stationary Distribution of a Two-Dimensional Reflecting Random Walk with Unbounded Upward Jumps
• A unified approach for large queue asymptotics in a heterogeneous multiserver queue
• DIFFUSION APPROXIMATION FOR STATIONARY ANALYSIS OF QUEUES AND THEIR NETWORKS: A REVIEW
• Heavy traffic approximation for the stationary distribution of a generalized Jackson network: the BAR approach

This page was built for publication: A unified approach for large queue asymptotics in a heterogeneous multiserver queue