Gaussian Limits for a Fork-Join Network with Nonexchangeable Synchronization in Heavy Traffic

DOI10.1287/moor.2015.0740zbMath1342.60157OpenAlexW2207360139MaRDI QIDQ2806818

Hongyuan Lu, Guodong Pang

Publication date: 19 May 2016

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

Full work available at URL: https://semanticscholar.org/paper/18ec5c108d6654a84f964fb3eeb1ffb2bee6e8b7

zbMATH Keywords

functional central limit theoremgeneralized Kiefer processGaussian limitsfork-join networksmultiparameter martingalemultiparameter sequential empirical processmany-server heavy-traffic regimenonexchangeable synchronization

Mathematics Subject Classification ID

Related Items (8)

Heavy-traffic limits for an infinite-server fork-join queueing system with dependent and disruptive services ⋮ Stochastic bounds in Fork-Join queueing systems under full and partial mapping ⋮ Control of Fork-Join Processing Networks with Multiple Job Types and Parallel Shared Resources ⋮ Large Fork-Join Queues with Nearly Deterministic Arrival and Service Times ⋮ Tail asymptotics for the delay in a Brownian fork-join queue ⋮ A functional central limit theorem for Markov additive arrival processes and its applications to queueing systems ⋮ On the Control of Fork-Join Networks ⋮ Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime

Uses Software

• MapReduce

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An empirical process central limit theorem for multidimensional dependent data
• Asymptotics of subexponential max plus networks: the stochastic event graph case
• An empirical central limit theorem with applications to copulas under weak dependence
• Two-parameter heavy-traffic limits for infinite-server queues
• Synchronized queues with deterministic arrivals
• Generalized parallel-server fork-join queues with dynamic task scheduling
• Heavy-traffic limits for waiting times in many-server queues with abandonment
• The \(G/GI/N\) queue in the Halfin-Whitt regime
• A note on strong approximations of multivariate empirical processes
• Processing networks with parallel and sequential tasks: Heavy traffic analysis and Brownian limits
• The trouble with diversity: Fork-join networks with heterogeneous customer population
• Two-parameter heavy-traffic limits for infinite-server queues with dependent service times
• On many-server queues in heavy traffic
• Tails for (max, plus) recursions under subexponentiality
• A fork-join queueing model: Diffusion approximation, integral representations and asymptotics
• Strong approximation of the empirical distribution function for absolutely regular sequences in \({\mathbb R}^d\)
• Strong approximation of empirical copula processes by Gaussian processes
• Queues with Many Servers and Impatient Customers
• INFINITE-SERVER QUEUES WITH BATCH ARRIVALS AND DEPENDENT SERVICE TIMES
• Exact Monte Carlo simulation for fork-join networks
• Queues with Many Servers: The Virtual Waiting-Time Process in the QED Regime
• Random Walk: A Modern Introduction
• Acyclic fork-join queuing networks
• Almost sure approximation theorems for the multivariate empirical process
• The function space D([O, ∞)ρ, E)
• The Physics of the Mt/G/∞ Queue
• Parallel queues with resequencing
• The synchronization of Poisson processes and queueing networks with service and synchronization nodes
• Multiparameter Processes
• Refined Models for Efficiency-Driven Queues with Applications to Delay Announcements and Staffing
• Response times in M/M/s fork-join networks
• The fork-join queue and related systems with synchronization constraints: stochastic ordering and computable bounds
• Sojourn times in G/M/1 fork‐join networks
• A Multivariate Exponential Distribution
• On Weak Convergence of Stochastic Processes with Multidimensional Time Parameter
• Convergence Criteria for Multiparameter Stochastic Processes and Some Applications
• Heavy-traffic limit for the initial content process
• On a synchronization queue with two finite buffers
• A simple and effective component procurement policy for stochastic assembly systems

This page was built for publication: Gaussian Limits for a Fork-Join Network with Nonexchangeable Synchronization in Heavy Traffic