A Clustering Approximation Technique for Queueing Network Models with a Large Number of Chains
IEEE Transactions on Computers
Dynamic programming: deterministic and stochastic models
Dynamic programming: deterministic and stochastic models
A vertex-allocation theorem for resources in queuing networks
Journal of the ACM (JACM)
Accuracy, speed, and convergence of approximate mean value analysis
Performance Evaluation
Calculating joint queue-length distributions in product-form queuing networks
Journal of the ACM (JACM)
PAM—a noniterative approximate solution method for closed multichain queueing networks
Performance Evaluation
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Optimal routing for closed queueing networks
Performance Evaluation
Optimization, performance bounds, and approximations in queueing networks
Optimization, performance bounds, and approximations in queueing networks
Single-class bounds of multi-class queuing networks
Journal of the ACM (JACM)
The mathematics of product form queuing networks
ACM Computing Surveys (CSUR)
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Product Form and Local Balance in Queueing Networks
Journal of the ACM (JACM)
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
Linearizer: a heuristic algorithm for queueing network models of computing systems
Communications of the ACM
Finite State Markovian Decision Processes
Finite State Markovian Decision Processes
A Perspective on Iterative Methods for the Approximate Analysis of Closed Queueing Networks
Proceedings of the International Workshop on Computer Performance and Reliability
Some Extensions to Multiclass Queueing Network Analysis
Proceedings of the Third International Symposium on Modelling and Performance Evaluation of Computer Systems: Performance of Computer Systems
The approximate solution of large queueing network models
The approximate solution of large queueing network models
Call packing bound for overflow loss systems
Performance Evaluation
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Product-form queuing network models have been widely used to model systems with shared resources such as computer systems (both centralized and distributed), communication networks, and flexible manufacturing systems. Closed multichain product-form networks are inherently more difficult to analyze than open networks, due to the effect of normalization. Results in workload characterization for closed networks in the literature are often for networks having special structures and only specific performance measures have been considered.In this article, we drive certain properties (insensitivity of conditional state probability distributions and fractional-linearity of Markov reward functions) for a broad class of closed multichain product-form networks. These properties are derived using the most basic flow balance conditions of product-form networks. Then we show how these basic properties can be applied in obtaining error bounds when similar customers are clustered together to speed up computation.