Journal ArticleDOI
Mean-Value Analysis of Closed Multichain Queuing Networks
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It is shown that mean queue sizes, mean waiting times, and throughputs in closed multiple-chain queuing networks which have product-form solution can be computed recursively without computing product terms and normalization constants.Abstract:
It is shown that mean queue sizes, mean waiting times, and throughputs in closed multiple-chain queuing networks which have product-form solution can be computed recursively without computing product terms and normalization constants. The resulting computational procedures have improved properties (avoidance of numerical problems and, in some cases, fewer operations) compared to previous algorithms. Furthermore, the new algorithms have a physically meaningful interpretation which provides the basis for heuristic extensions that allow the approximate solution of networks with a very large number of closed chains, and which is shown to be asymptotically valid for large chain populations.read more
Citations
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Proceedings ArticleDOI
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References
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Journal ArticleDOI
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
TL;DR: Many of the network results of Jackson on arrival and service rate dependencies, of Posner and Bernholtz on different classes of customers, and of Chandy on different types of service centers are combined and extended in this paper.
Journal ArticleDOI
Computational algorithms for closed queueing networks with exponential servers
TL;DR: Methods are presented for computing the equilibrium distribution of customers in closed queueing networks with exponential servers based on two-dimensional iterative techniques which are highly efficient and quite simple to implement.
Journal ArticleDOI
A use of complex probabilities in the theory of stochastic processes
TL;DR: In this paper, the authors generalized Erlang's idea of extending to cover all distributions with rational Laplace transforms; this involves the formal use of complex transition probabilities and properties of the method are considered.
Journal ArticleDOI
Closed Queuing Systems with Exponential Servers
TL;DR: It is found that the distribution of customers in the closed queuing system is regulated by the stage or stages with the slowest effective service rate, which means that closed systems are shown to be stochastically equivalent to open systems in which the number of customers cannot exceed N.
Journal ArticleDOI
A Queueing Network Analysis of Computer Communication Networks with Window Flow Control
TL;DR: A computer communication network with window flow control is modeled by a closed multichain queueing network and the severe computational limitation of previous solution algorithms is overcome with a heuristic derived from the recently found mean value analysis.