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Dependencies in Markovian networks

Part of: Special processes Multivariate analysis Stochastic processes

Published online by Cambridge University Press:  01 July 2016

H. Daduna  and
R. Szekli
H. Daduna*
Affiliation:
Hamburg University
R. Szekli*
Affiliation:
Wrocław University
*
* Postal address: Institute of Mathematical Stochastics, Hamburg University, Bundesstrasse 55, 20146 Hamburg, Germany.
** Postal address: Mathematical Institute, Wrocław University, P1. Grunwaldzki 2/4, 50–384 Wrocław, Poland.
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Abstract

Monotonicity and correlation results for queueing network processes, generalized birth–death processes and generalized migration processes are obtained with respect to various orderings of the state space. We prove positive (e.g. association) and negative (e.g. negative association) correlations in space and positive correlations in time for different situations, in steady state as well as in the transient phase of the system. This yields exact bounds for joint probabilities in terms of their independent versions.

Keywords

QUEUEING NETWORKSGENERALIZED BIRTH–DEATH PROCESSESMONOTONICITYCORRELATION INEQUALITIESORDERINGPOINT PROCESSES

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60G55: Point processes 62H20: Measures of association (correlation, canonical correlation, etc.)

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 1 , March 1995 , pp. 226 - 254
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Research carried out while this author held an Alexander von Humboldt Fellowship at Hamburg University.

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