# Diffusion approximations for open queueing networks with service interruptions

@article{Chen1993DiffusionAF, title={Diffusion approximations for open queueing networks with service interruptions}, author={Hong Chen and Ward Whitt}, journal={Queueing Systems}, year={1993}, volume={13}, pages={335-359} }

This paper establishes functional central limit theorems describing the heavy-traffic behavior of open single-class queueing networks with service interruptions. In particular, each station has a single server which is alternatively up and down. There are two treatments of the up and down times. The first treatment corresponds to fixed up and down times and leads to a reflected Brownian motion, just as when there are no service interruptions, but with different parameters. To represent long…

## 53 Citations

Brownian Approximations of Multiclass Open-Queueing Networks

- MathematicsOper. Res.
- 2002

A semi-martingale reflected Brownian motion (SRBM) approximation is developed for the performance processes such as workload, queue lengths, and sojourn times of a multiclass open-queueing network with a set of single-server stations.

Heavy-traffic asymptotics for networks of parallel queues with Markov-modulated service speeds

- Mathematics, Computer ScienceQueueing Syst. Theory Appl.
- 2015

It is shown how to numerically compute the joint distributions of the joint workload, waiting-time and queue length processes, by viewing the limit processes as multi-dimensional semi-martingale reflected Brownian motions in the non-negative orthant.

Diffusion approximations for GI/M/s queues with service interruptions

- MathematicsOper. Res. Lett.
- 1993

Fluid limits and diffusion approximations for networks of multi-server queues in heavy traffic

- MathematicsDiscret. Event Dyn. Syst.
- 1994

A Functional Strong-Law-of-Large-Numbers and a Functional Central Limit Theorem are proved for both open and closed networks of multi-server queues in heavy traffic.

Performance analysis of multiclass queueing networks via Brownian approximation

- Mathematics
- 2001

This dissertation illustrates through numerical examples in comparison against simulation that the S R B M model, while not always supported by a heavy traffic l imi t theorem, possesses good accuracy in most cases, even when the systems are moderately loaded.

Diffusion Limits for Open Networks of Finite-Buffer Queues

- Business
- 1996

This paper presents diffusion limits for congestion in networks of finite-buffer queues. We consider both loss networks, such as those in communication systems, and networks with manufacturing…

Two-Moment Analysis of Open Queueing Networks with General Workstation Capabilities

- MathematicsOper. Res.
- 1996

The QNET method for two-moment analysis of multiclass open networks is extended to allow complex workstations of various types and it is explained how the heavy traffic principle can be applied successfully under certain conditions, and shown by example that those conditions are not always met.

Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse

- MathematicsQueueing Syst. Theory Appl.
- 1998

General sufficient conditions are given under which a heavy traffic limit theorem holds for open multiclass queueing networks with head-of-the-line (HL) service disciplines, which, in particular, require that service within each class is on a first-in-first-out (FIFO) basis.

A Heavy-Traffic Limit for the Cycle Counting Process in G/G/1, Optional Interruptions and Elastic Screen Brownian Motion

- MathematicsMath. Oper. Res.
- 1994

A heavy traffic limit theorem is established for the renewal counting process associated with the busy cycles in the underlying queueing system and it is shown that this limit is proportional to the local time at zero of a reflected Brownian motion.

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