The caudal characteristic curve of queues

Many queues and related stochastic models, and in particular those that have a matrix-geometric stationary probability vector, have steady-state queue-length densities that are asymptotically geometric. The graph of the asymptotic rate η of these densities as a function of the traffic intensity ρ is...

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Bibliographic Details
Published in:Advances in applied probability 1986-03, Vol.18 (1), p.221-254
Main Author: Neuts, Marcel F.
Format: Article
Language:English
Subjects:
Applied sciences
Eigenvalues
Eigenvectors
Equation roots
Exact sciences and technology
Kronecker product
Markov processes
Matrices
Operational research and scientific management
Operational research. Management science
Parametric models
Poisson process
Queuing theory. Traffic theory
Stochastic models
Traffic
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Summary:Many queues and related stochastic models, and in particular those that have a matrix-geometric stationary probability vector, have steady-state queue-length densities that are asymptotically geometric. The graph of the asymptotic rate η of these densities as a function of the traffic intensity ρ is the caudal characteristic curve. This is an informative graph from which a number of qualitative inferences about the behavior of the queue may be drawn. The caudal characteristic curve may be computed (by elementary algorithms) for several useful models for which a complete exact numerical solution is not practically feasible. These include queues with certain types of superimposed arrival processes and/or multiple non-exponential servers. The necessary theorems which lead to the algorithmic procedures as well as the interpretation of several numerical examples are discussed.
ISSN:0001-8678
1475-6064
DOI:10.2307/1427244