Abstract
Although many closed multiclass queuing networks have a product-form solution, evaluating their performance measures remains nontrivial due to the presence of a normalization constant. We propose the application of Monte Carlo summation in order to determine the normalization constant, throughputs, and gradients of throughputs. A class of importance-sampling functions leads to a decomposition approach, where separate single-class problems are first solved in a setup module, and then the original problem is solved by aggregating the single-class solutions in an execution model. We also consider Monte Carlo methods for evaluating performance measures based on integral representations of the normalization constant; a theory for optimal importance sampling is developed. Computational examples are given that illustrate that the Monte Carlo methods are robust over a wide range of networks and can rapidly solve networks that cannot be handled by the techniques in the existing literature.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1110-1135 |
| Number of pages | 26 |
| Journal | Journal of the ACM |
| Volume | 41 |
| Issue number | 6 |
| DOIs | |
| State | Published - Nov 1994 |
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ASJC Scopus subject areas
- Computational Theory and Mathematics
- Computer Graphics and Computer-Aided Design
- Hardware and Architecture
- Information Systems
- Software
- Theoretical Computer Science
Cite this
Monte Carlo summation and integration applied to multiclass queuing networks. / Ross, Keith; Tsang, Danny H K; Wang, Jie.
In: Journal of the ACM, Vol. 41, No. 6, 11.1994, p. 1110-1135.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Monte Carlo summation and integration applied to multiclass queuing networks
AU - Ross, Keith
AU - Tsang, Danny H K
AU - Wang, Jie
PY - 1994/11
Y1 - 1994/11
N2 - Although many closed multiclass queuing networks have a product-form solution, evaluating their performance measures remains nontrivial due to the presence of a normalization constant. We propose the application of Monte Carlo summation in order to determine the normalization constant, throughputs, and gradients of throughputs. A class of importance-sampling functions leads to a decomposition approach, where separate single-class problems are first solved in a setup module, and then the original problem is solved by aggregating the single-class solutions in an execution model. We also consider Monte Carlo methods for evaluating performance measures based on integral representations of the normalization constant; a theory for optimal importance sampling is developed. Computational examples are given that illustrate that the Monte Carlo methods are robust over a wide range of networks and can rapidly solve networks that cannot be handled by the techniques in the existing literature.
AB - Although many closed multiclass queuing networks have a product-form solution, evaluating their performance measures remains nontrivial due to the presence of a normalization constant. We propose the application of Monte Carlo summation in order to determine the normalization constant, throughputs, and gradients of throughputs. A class of importance-sampling functions leads to a decomposition approach, where separate single-class problems are first solved in a setup module, and then the original problem is solved by aggregating the single-class solutions in an execution model. We also consider Monte Carlo methods for evaluating performance measures based on integral representations of the normalization constant; a theory for optimal importance sampling is developed. Computational examples are given that illustrate that the Monte Carlo methods are robust over a wide range of networks and can rapidly solve networks that cannot be handled by the techniques in the existing literature.
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UR - http://www.scopus.com/inward/citedby.url?scp=0028543343&partnerID=8YFLogxK
U2 - 10.1145/195613.195630
DO - 10.1145/195613.195630
M3 - Article
AN - SCOPUS:0028543343
VL - 41
SP - 1110
EP - 1135
JO - Journal of the ACM
JF - Journal of the ACM
SN - 0004-5411
IS - 6
ER -