# The Queueing Network Analyzer

@article{Whitt1983TheQN, title={The Queueing Network Analyzer}, author={Ward Whitt}, journal={The Bell System Technical Journal}, year={1983}, volume={62}, pages={2779-2815} }

This paper describes the Queueing Network Analyzer (QNA), a software package developed at Bell Laboratories to calculate approximate congestion measures for a network of queues. The first version of QNA analyzes open networks of multiserver nodes with the first-come, first-served discipline and no capacity constraints. An important feature is that the external arrival processes need not be Poisson and the service-time distributions need not be exponential. Treating other kinds of variability is…

## 1,032 Citations

Performance of the Queueing Network Analyzer

- MathematicsThe Bell System Technical Journal
- 1983

The examples here demonstrate the importance of the variability parameters used in QNA to describe non-Poisson arrival processes and nonexponential service-time distributions and show that QNA performs much better than the standard Markovian algorithm, which does not use variability parameters.

A Robust Queueing Network Analyzer Based on Indices of Dispersion

- Mathematics
- 2020

We develop a robust queueing network analyzer algorithm to approximate the steady-state performance of a single-class open queueing network of single-server queues with Markovian routing. The…

A Robust Queueing Network Analyzer Based on Indices of Dispersion

- MathematicsArXiv
- 2020

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.

Dependence in packet queues

- BusinessIEEE Trans. Commun.
- 1989

This study indicates that all three kinds of dependence should be considered in the analysis and measurement of packet queues involving variables packet lengths, and indicates how to predict expected packet delays under heavy loads.

The QNET method for two-moment analysis of open queueing networks

- Computer ScienceQueueing Syst. Theory Appl.
- 1990

A cruder approach to two-moment network analysis, called ΠNET, is described and investigated, which is based on a product form approximation, or decomposition approximation, to the stationary distribution of the Brownian system model.

Decomposition of general tandem queueing networks with MMPP input

- Computer SciencePerform. Evaluation
- 2001

A robust queueing network analyzer based on indices of dispersion

- MathematicsNaval Research Logistics (NRL)
- 2021

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.

Decomposition of General Tandem Queueing Networks with MMPP Input

- Computer ScienceComputer Performance Evaluation / TOOLS
- 2000

The internal traffic processes are described as semi-Markov processes (SMPs) and Markov modulated Poisson processes (MMPPs) and correlations in the traffic streams, which are known to have a considerable impact on performance, are taken into account to some extent.

Departures from a Queue with Many Busy Servers

- MathematicsMath. Oper. Res.
- 1984

This paper shows that the stationary departure process is approximately Poisson when there are many busy slow servers in a large class of stationary G/GI/s congestion models having s servers, infinite waiting room, the first-come first-served discipline, and mutually independent and identically distributed service times that are independent of a stationary arrival process.

Diffusion Approximations for Time-Dependent Queueing Systems

- Computer Science, BusinessIEEE J. Sel. Areas Commun.
- 1986

A parametric-decomposition method of the time-dependent analysis of queueing networks which makes possible the analysis of various aspects of computer-communication systems, especially the adaptive routings, the strategies of flow and congestion control, the influence of short overload peaks and other time-varying phenomena in such systems.

## References

SHOWING 1-10 OF 66 REFERENCES

Performance of the Queueing Network Analyzer

- MathematicsThe Bell System Technical Journal
- 1983

The examples here demonstrate the importance of the variability parameters used in QNA to describe non-Poisson arrival processes and nonexponential service-time distributions and show that QNA performs much better than the standard Markovian algorithm, which does not use variability parameters.

Departures from a Queue with Many Busy Servers

- MathematicsMath. Oper. Res.
- 1984

This paper shows that the stationary departure process is approximately Poisson when there are many busy slow servers in a large class of stationary G/GI/s congestion models having s servers, infinite waiting room, the first-come first-served discipline, and mutually independent and identically distributed service times that are independent of a stationary arrival process.

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An approximate method for the analysis of general queuing networks is proposed, based on the method of decomposition where the total network is broken up into subsystems; e.g., queuing stations of the type GI/G/1 or subnets.

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- 1982

New results are presented which contribute to the foundations of a tool to support performance analysis and modeling activities and obtain a Little's Law type of relation between delay moments and queue size factorial moments.

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The range of possible values can be reduced dramatically by imposing realistic shape constraints on the interarrival-time distribution with given first two moments and found extremal distributions in the presence of shape constraints by restricting attention to discrete distributions with all mass on a fixed finite set of points.

Heavy-Traffic Limits for Queues with Many Exponential Servers

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Two different kinds of heavy-traffic limit theorems have been proved for s -server queues and the resulting approximation is better than the earlier ones for many-server systems operating at typically encountered loads.

A class of approximations for the waiting time distribution in a GI/G/1 queueing system

- Computer Science, MathematicsThe Bell System Technical Journal
- 1982

A class of approximations for the waiting time distribution in single server queueing systems with general independent (renewal) input and general (independent) service time distributions is presented.

On approximations for queues, I: Extremal distributions

- Mathematics, Computer ScienceAT&T Bell Laboratories Technical Journal
- 1984

This work calculates the set of possible values for the mean queue length in a GI/M/1 queue and shows how it depends on the traffic intensity and the second moment, and uses extremal distributions to compare alternative parameters for approximations.

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Bounds are found for various measures of performance in certain classes of the GI//G1 queue in terms of the mean and variance of the interarrival, service, and idle distributions.

A Light-Traffic Theorem for Multi-Server Queues

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It is shown that as the traffic goes to zero, the probability of delay depends only on the mean of the service-time distributions and that the delay when positive converges in distribution to the minimum of c independent equilibrium-excess service-times is zero.