Heavy-traffic limits for stationary network flows

@article{Whitt2020HeavytrafficLF,
  title={Heavy-traffic limits for stationary network flows},
  author={Ward Whitt and Wei You},
  journal={Queueing Systems},
  year={2020},
  volume={95},
  pages={53-68}
}
This paper studies stationary customer flows in an open queueing network. The flows are the processes counting customers flowing from one queue to another or out of the network. We establish the existence of unique stationary flows in generalized Jackson networks and convergence to the stationary flows as time increases. We establish heavy-traffic limits for the stationary flows, allowing an arbitrary subset of the queues to be critically loaded. The heavy-traffic limit with a single bottleneck… Expand
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References

SHOWING 1-10 OF 79 REFERENCES
Open Queueing Networks in Heavy Traffic
  • M. Reiman
  • Mathematics, Computer Science
  • Math. Oper. Res.
  • 1984
TLDR
These limit theorems state that properly normalized sequences of queue length and sojourn time processes converge weakly to a certain diffusion as the network traffic intensity converges to unity. Expand
Validity of heavy traffic steady-state approximations in generalized Jackson networks
We consider a single class open queueing network, also known as a generalized Jackson network (GJN). A classical result in heavy-traffic theory asserts that the sequence of normalized queue lengthExpand
Stationary Distribution Convergence for Generalized Jackson Networks in Heavy Traffic
TLDR
This note provides an alternative proof of this result assuming (in addition to natural heavy traffic and stability assumptions) only standard independence and square integrability conditions on the network primitives that are commonly used in heavy traffic analysis. Expand
Heavy-Traffic Limit of theGI/GI/1 Stationary Departure Process and Its Variance Function
Heavy-traffic limits are established for the stationary departure process from a GI/GI/1 queue and its variance function. The limit process is a function of the Brownian motion limits of the arrivalExpand
Multiple channel queues in heavy traffic. II: sequences, networks, and batches
Abstract : Sequences of queueing facilities with r parallel arrival channels and s parallel service channels are studied under the conditions of heavy traffic: the associated sequences of trafficExpand
A Robust Queueing Network Analyzer Based on Indices of Dispersion
TLDR
A robust queueing network analyzer algorithm to approximate the steady-state performance of a single-class open queueingnetwork of single-server queues with Markovian routing with heavy-traffic limits is developed. Expand
Queues with superposition arrival processes in heavy traffic
To help provide a theoretical basis for approximating queues with superposition arrival processes, we prove limit theorems for the queue-length process in a [Sigma] GIi/G/s model, in which theExpand
Ergodicity of queuing networks
We consider an open Jackson-type service network with single-channel stations. It is shown that if the load on each station is less than i, the process defined by the length of the queue satisfies anExpand
Discrete Flow Networks: Bottleneck Analysis and Fluid Approximations
TLDR
The analysis presupposes only the existence of long-run averages, and is based on a continuous fluid approximation to the network in terms of these averages, providing functional strong laws of large-numbers for stochastic Jackson queueing networks since they apply to their sample paths with probability one. Expand
Heavy traffic approximation for the stationary distribution of a generalized Jackson network: The BAR approach
In the seminal paper of Gamarnik and Zeevi [17], the authors justify the steady-state diffusion approximation of a generalized Jackson network (GJN) in heavy traffic. Their approach involves theExpand
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