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Degree-dependent threshold-based random sequential adsorption on random trees

Part of: Time-dependent statistical mechanics (dynamic and nonequilibrium) Special processes Computer system organization Operations research and management science

Published online by Cambridge University Press:  20 March 2018

Thomas M. M. Meyfroyt
Thomas M. M. Meyfroyt*
Affiliation:
Eindhoven University of Technology
*
* Postal address: Eindhoven University of Technology, MetaForum 4.086, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. Email address: [email protected]
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Abstract

We consider a special version of random sequential adsorption (RSA) with nearest-neighbor interaction on infinite tree graphs. In classical RSA, starting with a graph with initially inactive nodes, each of the nodes of the graph is inspected in a random order and is irreversibly activated if none of its nearest neighbors are active yet. We generalize this nearest-neighbor blocking effect to a degree-dependent threshold-based blocking effect. That is, each node of the graph is assumed to have its own degree-dependent threshold and if, upon inspection of a node, the number of active direct neighbors is less than that node's threshold, the node will become irreversibly active. We analyze the activation probability of nodes on an infinite tree graph, given the degree distribution of the tree and the degree-dependent thresholds. We also show how to calculate the correlation between the activity of nodes as a function of their distance. Finally, we propose an algorithm which can be used to solve the inverse problem of determining how to set the degree-dependent thresholds in infinite tree graphs in order to reach some desired activation probabilities.

Keywords

Analytical modelcounter-based gossip protocolinteracting particle systemrandom sequential adsorptionjamming limitrandom tree graph

MSC classification

Primary: 82C22: Interacting particle systems 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 68M10: Network design and communication 90B18: Communication networks
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue 1 , March 2018 , pp. 302 - 326
Copyright
Copyright © Applied Probability Trust 2018 

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