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Types of Nodes and Centrality Measures in Networks Read chapter Read first chapter

2019 | OriginalPaper | Chapter

3. Routing on a Ring Network

Authors : Ramya Burra, Chandramani Singh, Joy Kuri, Eitan Altman

Published in: Game Theory for Networking Applications

Publisher: Springer International Publishing

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Abstract

We study routing on a ring network in which traffic originates from nodes on the ring and is destined to the center. The users can take direct paths from originating nodes to the center and also multihop paths via other nodes. We show that routing games with only one and two hop paths and linear costs are potential games. We give explicit expressions of Nash equilibrium flows for networks with any generic cost function and symmetric loads. We also consider a ring network with random number of users at nodes, all of them having same demand, and linear routing costs. We give explicit characterization of Nash equilibria for two cases: (i) General i.i.d. loads and one and two hop paths, (ii) Bernoulli loads. We also analyze optimal routing in each of these cases.

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previous chapter The Time-Consistent Shapley Value for Two-Stage Network Games with Pairwise Interactions
next chapter Performance of Dynamic Secure Routing Game
Footnotes
1
Clearly, the addition here is modulo N.
 
2
\([x]^b_a := \min \{\max \{x,a\},b\}\).
 
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Metadata
Title
Routing on a Ring Network
Authors
Ramya Burra
Chandramani Singh
Joy Kuri
Eitan Altman
Copyright Year
2019
Book
Game Theory for Networking Applications

Print ISBN: 978-3-319-93057-2

Electronic ISBN: 978-3-319-93058-9

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-93058-9_3