Robustness of queuing network formulas
Journal of the ACM (JACM)
RECAL—a new efficient algorithm for the exact analysis of multiple-chain closed queuing networks
Journal of the ACM (JACM)
Mean Value Analysis by Chain of Product form Queueing Networks
IEEE Transactions on Computers
A perspective on queueing models of computer performance
Performance Evaluation
The mathematics of product form queuing networks
ACM Computing Surveys (CSUR)
Monte Carlo summation and integration applied to multiclass queuing networks
Journal of the ACM (JACM)
Matrix computations (3rd ed.)
Capacity planning for Web performance: metrics, models, and methods
Capacity planning for Web performance: metrics, models, and methods
Queueing networks and Markov chains: modeling and performance evaluation with computer science applications
Application of the Diffusion Approximation to Queueing Networks I: Equilibrium Queue Distributions
Journal of the ACM (JACM)
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)
The Operational Analysis of Queueing Network Models
ACM Computing Surveys (CSUR)
Linearizer: a heuristic algorithm for queueing network models of computing systems
Communications of the ACM
Balanced job bound analysis of queueing networks
Communications of the ACM
Computational algorithms for product form queueing networks
Communications of the ACM
Computational algorithms for closed queueing networks with exponential servers
Communications of the ACM
On the asymptotic behaviour of closed multiclass queueing networks
Performance Evaluation
A Unifying Framework for the Approximate Solution of Closed Multiclass Queuing Networks
IEEE Transactions on Computers
A New Recursive Algorithm for Computing Generating Functions in Closed Multi-Class Queueing Networks
MASCOTS '04 Proceedings of the The IEEE Computer Society's 12th Annual International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems
An analytical model for multi-tier internet services and its applications
SIGMETRICS '05 Proceedings of the 2005 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
QoS management in service-oriented architectures
Performance Evaluation
CoMoM: Efficient Class-Oriented Evaluation of Multiclass Performance Models
IEEE Transactions on Software Engineering
A generalized method of moments for closed queueing networks
Performance Evaluation
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Performance evaluation of distributed systems and service-oriented architectures is often based on stochastic models, such as closed queueing networks which are commonly solved by the Mean Value Analysis (MVA) algorithm. However, the MVA is unable to solve models with hundreds or thousands of users accessing services of multiple classes, a configuration that is often useful to predict the performance of real-world applications. This paper introduces the Method of Moments (MoM), the first exact algorithm for solving closed queueing networks with large population sizes. Compared to the MVA algorithm, which is based on a recursive evaluation of mean queue-lengths, MoM defines a recursion on higher-order moments of queue-lengths that is solved at each step by a linear system of equations. This approach dramatically decreases the costs of an exact analysis compared to the MVA approach. We prove that MoM requires log-quadratic time and log-linear space in the total population size, whereas MVA complexity expressions grow combinatorially as the product of class populations. This extends the feasibility of exact methods to a much larger family of multiclass performance models than those that can be solved by the MVA algorithm.