Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Linearizer: a heuristic algorithm for queueing network models of computing systems
Communications of the ACM
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
Incorporating load dependent servers in approximate mean value analysis
SIGMETRICS '84 Proceedings of the 1984 ACM SIGMETRICS conference on Measurement and modeling of computer systems
Asymptotic expansion for large closed queuing networks
Journal of the ACM (JACM)
Asymptotic Expansions for Large Closed Queueing Networks with Multiple Job Classes
IEEE Transactions on Computers
Monte Carlo summation and integration applied to multiclass queuing networks
Journal of the ACM (JACM)
Towards a polynomial-time randomized algorithm for closed product-form networks
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Solving product form stochastic networks with Monte Carlo summation
WSC' 90 Proceedings of the 22nd conference on Winter simulation
On the asymptotic behaviour of closed multiclass queueing networks
Performance Evaluation
Product Form Queueing Networks
Performance Evaluation: Origins and Directions
Exact Asymptotic Analysis of Closed BCMP Networks with a Common Bottleneck
ASMTA '08 Proceedings of the 15th international conference on Analytical and Stochastic Modeling Techniques and Applications
A unified framework for the bottleneck analysis of multiclass queueing networks
Performance Evaluation
A generalized method of moments for closed queueing networks
Performance Evaluation
Operations Research Letters
Closed Queueing Networks Under Congestion: Nonbottleneck Independence and Bottleneck Convergence
Mathematics of Operations Research
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A method is presented for calculating the partition function, and from it, performance measures, for closed Markovian stochastic networks with queuing centers in which the service or processing rate depends on the center's state or load. The analysis on which this method is based is new and a major extension of our earlier work on load-independent queuing networks. The method gives asymptotic expansions for the partition function in powers of 1/N, where N is a parameter that reflects the size of the network. The expansions are particularly useful for large networks with many classes, each class having many customers. The end result is a decomposition by which expansion coefficients are obtained exactly by linear combinations of partition function values of small network constructs called pseudonetworks. Effectively computable bounds are given for errors arising from the use of a finite number of expansion terms. This method is important because load dependence is at once an essential element of sophisticated network models of computers, computer communications, and switching, teletraffic, and manufacturing systems, and the cause of very intensive computations in conventional techniques. With this method, very large load-dependent networks can be analyzed, whereas previously only small networks were computationally tractable.