Quantitative system performance: computer system analysis using queueing network models
Quantitative system performance: computer system analysis using queueing network models
RECAL—a new efficient algorithm for the exact analysis of multiple-chain closed queuing networks
Journal of the ACM (JACM)
Data networks
Simple Relationships Among Moments of Queue Lengths in Product form Queueing Networks
IEEE Transactions on Computers
Mean Value Analysis by Chain of Product form Queueing Networks
IEEE Transactions on Computers
The placement optimization program: a practical solution to the disk file assignment problem
SIGMETRICS '89 Proceedings of the 1989 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
Optimal Selection of CPU Speed, Device Capacities, and File Assignments
Journal of the ACM (JACM)
Optimal Design of Linear Storage Hierarchies
Journal of the ACM (JACM)
Comparative Models of the File Assignment Problem
ACM Computing Surveys (CSUR)
Optimal routing in closed queuing networks
ACM Transactions on Computer Systems (TOCS)
Computational algorithms for closed queueing networks with exponential servers
Communications of the ACM
Computer Performance Modeling Handbook
Computer Performance Modeling Handbook
Convexity and Concavity Properties of Analytic Queuing Models for Computer Systems
Performance '84 Proceedings of the Tenth International Symposium on Computer Performance Modelling, Measurement and Evaluation
Load Balancing in Distributed Systems with Multiple Classes and Site Constraints
Performance '84 Proceedings of the Tenth International Symposium on Computer Performance Modelling, Measurement and Evaluation
A Decision Model for Closed Queuing Networks
IEEE Transactions on Software Engineering
Storage optimization for large-scale distributed stream-processing systems
ACM Transactions on Storage (TOS)
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This paper is concerned with the parameter optimization in closed product-form queueing networks. Our approach is to combine the techniques of the calculus of variations with the mean value analysis (MVA) recursion of closed queueing networks. We view the MVA recursion as nonlinear difference equations describing a multi-stage system, wherein a stage corresponds to the network population, and the response times at each node constitute the state variables of the multi-stage system. This viewpoint leads to a two-point boundary value problem , in which the forward system corresponds to the MVA recursion and the backward system corresponds to an MVA-like adjoint recursion. The method allows for a very general class of objective functions, and the adjoint equations provide the necessary information to compute the gradient of the cost function. The optimization problem can then be solved by any of the gradient-based methods. For the special case when the objective function is the network delay function, the gradient vector is shown to be related to the moments of the queue lengths. In addition, the adjoint vector offers the potential for the on-line adaptive control of queueing networks based on the state information (e.g., actual degree of multi-programming, response times at the devices.) The theory is illustrated via application to the problem of determining the optimal disk routing probabilities in a large scale, modern I/O (Input/Output) subsystem. A subsequent paper will deal with extensions of the theory to multi-class networks.