Journal ArticleDOI
Open and closed models for networks of queues
TLDR
This paper investigates ways to use open models to approximate closed models with specified expected equilibrium populations, especially effective for approximately solving large closed models, where “large” may mean many nodes or many jobs.Abstract:
This paper investigates the relationship between open and closed models for networks of queues. In open models, jobs enter the network from outside, receive service at one or more service centers, and then depart. In closed models, jobs neither enter nor leave the network; instead, a fixed number of jobs circulate within the network. Open models are analytically more tractable, but closed models often seem more realistic. Hence, this paper investigates ways to use open models to approximate closed models. One approach is to use open models with specified expected equilibrium populations. This fixed-population-mean method is especially effective for approximately solving large closed models, where “large” may mean many nodes or many jobs. The success of these approximations is partly explained by limit theorems: Under appropriate conditions, the fixed-population-mean method is asymptotically correct. In some cases the open-model methods also yield bounds for the performance measures in the closed models.read more
Citations
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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.
Book
Principles of random walk
TL;DR: In this article, a very special class of random processes, namely to random walk on the lattice points of ordinary Euclidean space, is studied, and the author considered this high degree of specialization worth while because of the theory of such random walks is far more complete than that of any larger class of Markov chains.
Journal ArticleDOI
Negative Association of Random Variables with Applications
Kumar Joag-Dev,Frank Proschan +1 more
TL;DR: In this article, negative association is defined as the property that a random variable is negatively associated (NA) if for every pair of disjoint subsets $A_1, A_2$ of Ω(1, 2, \cdots, k, k) of a function f(X, i, i = 1, 3, 4, k), f(G, g), g, g, j, j \in A_1), g(G), g), rbrack \leq 0, for all nondecreasing
Journal ArticleDOI
The Queueing Network Analyzer
TL;DR: This paper describes the Queueing Network Analyzer (QNA), a software package developed at Bell Laboratories to calculate approximate congestion measures for a network of queues and uses two parameters to characterize the arrival processes and service times.