Quantitative system performance: computer system analysis using queueing network models
Quantitative system performance: computer system analysis using queueing network models
Simple Relationships Among Moments of Queue Lengths in Product form Queueing Networks
IEEE Transactions on Computers
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
Dynamic Scaling and Growth Behavior of Queuing Network Normalization Constants
Journal of the ACM (JACM)
Computational algorithms for state-dependent queueing networks
ACM Transactions on Computer Systems (TOCS)
Computational algorithms for closed queueing networks with exponential servers
Communications of the ACM
On Single-Class Load-Dependent Normalizing Constant Equations
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
A class of tractable models for run-time performance evaluation
ICPE '12 Proceedings of the 3rd ACM/SPEC International Conference on Performance Engineering
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We introduce the Conditional Mean Value Analysis (CMVA) algorithm, an exact solution method for product-form load-dependent closed queueing networks that provides a numerically stable solution of models where the load-dependent Mean Value Analysis (MVA) is numerically unstable. Similarly to the MVA algorithm for constant-rate queues, CMVA performs operations in terms of mean quantities only, i.e., queue-lengths, throughput, response times. Numerical stability derives from a new version of the MVA arrival theorem for load-dependent models which is expressed in terms of mean queue-lengths instead of marginal probabilities. The formula is obtained by the analysis of the conditional state spaces which describe network equilibrium as seen by jobs during their residence times at queues. We also provide a generalization of CMVA to multiclass models that preserves the numerical stability property.