Use this URL to cite or link to this record in EThOS:  https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.774761 
Title:  An algebraic perspective on the convergence of vectorbased routing protocols  
Author:  Daggitt, Matthew Lucian 
ORCID:
0000000225523671
ISNI:
0000 0004 7961 9649


Awarding Body:  University of Cambridge  
Current Institution:  University of Cambridge  
Date of Award:  2019  
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Abstract:  
This thesis studies the properties of vectorbased routing protocols whose underlying algebras are strictly increasing. Strict increasingness has previously been shown to be both a sufficient and a necessary condition for the convergence of pathvector protocols. One of the key contributions of this thesis is to link vectorbased routing to a much larger family of asynchronous iterative algorithms. This unlocks a significant body of existing theory, and allows asynchronous protocols to be proved correct by purely synchronous reasoning. As well as applying it to routing protocols, this thesis advances the asynchronous theory in two ways. Firstly it shows that the existing conditions required for convergence may be relaxed. Secondly it proposes the first model for ``dynamic'' asynchronous processes in which both the problem being solved and the set of participants change over time. The thesis' attention then turns to models of routing problems, and presents a new algebraic structure that is simpler and more expressive than the state of the art. In particular this structure is capable of modelling routing problems that underlie both distancevector and pathvector protocols. Consequently these two families of vectorbased protocols may be unified for the first time. The new structure is also capable of modelling protocols that use pathdependent conditional policy. Next the work above is used to construct a model of an abstract vectorbased protocol. This is then used in the first proof of correctness for strictly increasing distancevector protocols and a new proof of correctness for strictly increasing pathvector protocols. The latter is an improvement over previous results as it i) proves that convergence is deterministic ii) does not assume reliable communication between nodes and iii) applies to pathvector protocols with pathdependent conditional policy. The long standing question of the worstcase rate of convergence for a strictly increasing pathvector protocol is then answered by lowering the previous upper bound of $O(n!)$ to a new tight bound of~$\Theta(n^2)$. Finally all of the work has been formalised in the proof assistant Agda. Not only does this significantly increase users' confidence in the validity of the results, the resulting Agda library may also be used to verify the correctness of protocol implementations. To illustrate this, a formal proof of correctness is described for a pathvector protocol which contains many of the features of the Border Gateway Protocol including: local preferences, communities, an expressive conditional policy language and path inflation.


Supervisor:  Griffin, Timothy  Sponsor:  EPSRC  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.774761  DOI:  
Keywords:  Routing protocols ; Agda ; Asynchronous iterations ; Parallel algorithms ; Formal verification ; Algebra ; Convergence ; Vectorbased routing ; Pathvector ; Distancevector ; Routing ; BGP ; RIP  
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