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}
}
  • J. Buzen
  • Published 1 September 1973
  • Computer Science
  • Commun. ACM
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.

Figures and Tables from this paper

Heuristic analysis of closed queueing networks
TLDR
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
TLDR
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
TLDR
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
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,
An Enhanced Approximation by Pair-Wise Analysis of Servers for Time Delay Distributions in Queueing Networks
  • P. Harrison
  • Mathematics
    IEEE Transactions on Computers
  • 1986
TLDR
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
TLDR
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
TLDR
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.
A customer threshold property for closed finite queueing networks
An Approximation Method for Open Restricted Queueing Networks
TLDR
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.
...
1
2
3
4
5
...

References

SHOWING 1-8 OF 8 REFERENCES
Closed Queuing Systems with Exponential Servers
TLDR
It is found that the distribution of customers in the closed queuing system is regulated by the stage or stages with the slowest effective service rate, which means that closed systems are shown to be stochastically equivalent to open systems in which the number of customers cannot exceed N.
Analysis of system bottlenecks using a queueing network model
TLDR
A surprising result is that optimal performance is not attained when queue lengths and processor utilization percentages are equal, but rather when the fastest processor has the longest expected queue and is in effect creating a system bottleneck.
Network ModelsJbr1_zlrge-Scale Time- Sharing SystemsTR-71-1) U. of Michigan
  • 531 Communications September 1973 of Volume 16 the ACM Number
  • 1971
Network ModelsJbr1_zlrge-Scale TimeSharing Systems
  • Ph.D. Thesis, Dept. of Industrial Engineering,
  • 1971
Network models for large-scale time-sharing systems
Optimizing the degree of multiprogramming in demand paging systems
  • Proc. IEEE-CS Conf. 1971 (71 C41-C), IEEE
  • 1971
Queueing Network Models of Multiprogramming
  • J. Buzen
  • Computer Science
    Outstanding Dissertations in the Computer Sciences
  • 1971
Thesis, Div. of Engineering and Applied Physics. (NTIS AD
  • Thesis, Div. of Engineering and Applied Physics. (NTIS AD
  • 1971