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Routeing on trees

Part of: Markov processes Special processes

Published online by Cambridge University Press:  21 June 2016

Maria Deijfen  and
Nina Gantert
Maria Deijfen*
Affiliation:
Stockholm University
Nina Gantert*
Affiliation:
Technische Universität München
*
* Postal address: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden. Email address: mia@math.su.se
** Postal address: Technische Universität München, Boltzmannstr. 3, 85748 Garching, Germany.
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Abstract

We consider three different schemes for signal routeing on a tree. The vertices of the tree represent transceivers that can transmit and receive signals, and are equipped with independent and identically distributed weights representing the strength of the transceivers. The edges of the tree are also equipped with independent and identically distributed weights, representing the costs for passing the edges. For each one of our schemes, we derive sharp conditions on the distributions of the vertex weights and the edge weights that determine when the root can transmit a signal over arbitrarily large distances.

Keywords

Treestransmissionfirst passage percolationbranching random walkMarkov chain

MSC classification

Primary: 60K37: Processes in random environments
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 2 , June 2016 , pp. 475 - 488
Copyright
Copyright © Applied Probability Trust 2016 

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