# Computational algorithms for closed queueing networks with exponential servers

@article{Buzen1973ComputationalAF, title={Computational algorithms for closed queueing networks with exponential servers}, author={Jeffrey P. Buzen}, journal={Commun. ACM}, year={1973}, volume={16}, pages={527-531} }

Methods are presented for computing the equilibrium distribution of customers in closed queueing networks with exponential servers. [... ] Key Method The computational algorithms are based on two-dimensional iterative techniques which are highly efficient and quite simple to implement. Implementation considerations such as storage allocation strategies and order of evaluation are examined in some detail. Expand

## 905 Citations

Heuristic analysis of closed queueing networks

- Mathematics
- 1983

An iterative approximation procedure, based on a decomposition approximation, is proposed for closed queueing networks having M single server queueing stations with arbitrary interconnections and general service time distributions.

HAM: the heuristic aggregation method for solving general closed queueing network models of computer systems

- MathematicsSIGMETRICS '82
- 1982

An approximate analytical method for estimating performance statistics of general closed queueing network models of computing systems is presented, based on the aggregation theorem (Norton's theorem) of Chandy, Herzog and Woo.

Simple bounds for closed queueing networks

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- 1999

This work establishes simple closed form bounds on the network throughput (both lower and upper), which are sharper than those that are currently available.

A Discrete Time technique for Solving Closed Queueing Network Models of Computer Systems

- MathematicsMMB
- 1983

We give a discrete-time model for a central server computer system, and show that the equilibrium distribution is of product-form Given the requests for workload at the different stations of a cycle,â€¦

An Enhanced Approximation by Pair-Wise Analysis of Servers for Time Delay Distributions in Queueing Networks

- MathematicsIEEE Transactions on Computers
- 1986

An approximation for the distribution of time delays experienced by a customer in a network of queues is presented and it is proved that the correlation between the sojourn times at successive servers on a customer's path in a closed queueing network with exponential servers is negative.

The Evaluation of Normalizing Constants in Closed Queueing Networks

- MathematicsOper. Res.
- 1990

The present paper describes an alternative method of obtaining Harrison's result, and can usefully be applied to other closed networks of queues, particularly those in which irregular constraints bound the state space.

Performance Evaluation of Closed Queueing Networks with Limited Capacities

- Business
- 2006

An algorithm was developed for performance evaluation of single class closed queueing networks with configurations likely to occur in real-world manufacturing systems, i.e. limited waiting spaces, split-merge topologies, and stations with multiple servers that proved to be accurate, efficient and very consistent.

Performance Sensitivity Formulae, Algorithms and Estimates for Closed Queueing Networks with Exponential Servers

- MathematicsPerform. Evaluation
- 1996

A customer threshold property for closed finite queueing networks

- MathematicsPerform. Evaluation
- 2006

An Approximation Method for Open Restricted Queueing Networks

- BusinessOper. Res.
- 1980

It is found that this method provides a fairly good approximation procedure for obtaining system performance measures such as blocking probabilities, output rates, etc., in open restricted queueing networks.

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