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Asymptotic stationarity of multichannel queues

Part of: Probability theory on algebraic and topological structures Special processes

Published online by Cambridge University Press:  01 July 2016

Władysław Szczotka
Władysław Szczotka*
Affiliation:
Wrocław University
*
∗Postal address: Mathematical Institute, Wroclaw University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland.
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Abstract

The paper deals with asymptotic stationarity of the process where is a vector in with non-negative coordinates, is an -valued process, S is a separable metric space and all operations in are meant in the coordinate-wise sense. It is shown that a type of asymptotic stationarity of (X, Y), together with some conditions, implies the same type of asymptotic stationarity of (w, X, Y). This result is applied to analyze asymptotic stationarity of multichannel queues. It may also be used to analyze asymptotic stationarity of series of multichannel queues.

Keywords

VECTOR OF WAITING TIMESSTATIONARY REPRESENTATIONWEAK CONVERGENCESTRONG CONVERGENCECONVERGENCE IN VARIATION

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60B10: Convergence of probability measures 60B12: Limit theorems for vector-valued random variables (infinite-dimensional case)
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 1 , March 1993 , pp. 203 - 220
Copyright
Copyright © Applied Probability Trust 1993 

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