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5. Analyzing theInteroperabilityMeasurementModel
In section 4.3we have derived a causalmodel for themessage passing behavior of in-
teroperable processes.Wenow investigate themodel behavior in order to decideon the
degree of the calleeās interoperability behavior.Wediscuss themodelās behavior using
probabilities, e.g. there is a probability that an incomingmessageM contains an oper-
ationwhich the dispatcher canmap to a local one. The probability of the complement
means thatM containsanunknownoperation to thedispatcher.
5.1. VariablesDependenciesandd-separation
Theobservationofmessagepassingof interoperableprocesses insection4.2establishes
adependencybetween the incomingandoutgoingmessage through the causal relation-
ships between the variables.We analyze the paths between the nodes in the graphical
causalmodel of ļ¬gure 3 utilizing the process of d-separation,where one can conclude
thevariabledependencies from.Wequote thedeļ¬nitionfromPearlāsbook[15],page46.
Deļ¬nition (d-separation). Apath p isblockedbyasetofnodesZ if andonly if
1. pcontainsachainofnodesAāBāCoraforkAāBāCsuchthat themiddle
nodeB is inZ (i.e.B is conditionedon), or
2. pcontains a colliderAāBāCsuch that the collisionnodeB is not inZ, and
nodescendantofB is inZ.
If Z blocks every path between two nodes X andY are d-separated, conditional on Z,
and thusare independent conditionalonZ.
If two graphās nodes are d-separated, the variables they represent are independent.
In contrast, if twonodes are d-connected, a path exists between them, i.e. the variables
aremost likelydependent.
5.2. d-separationAnalysis
The analysis of d-separation in the causal graph of ļ¬gure 3 let us identify the condi-
tionsformessagedependencies.Concretely, thediscriminatorDshalldeterminethemes-
sageMā²originasa result of the incomingmessageM.Asaconsequence,we formulate:
Problem. Findsetsofnodes in thecausalgraphunderwhichMandDared-connected
ord-separated.
Discussion of the cases, ifM,Dare d-connected. Using an empty conditioning setZ,
then, according to thedeļ¬nitionabove, everypathbetweenM andD formsachainwith
noblockingnode inbetween.So,M andDared-connectedand thereforedependent. In
this case, the incomingmessageM affects the probability ofD. In the context of inter-
operability, it is understood as follows: FormessagesM containing operations known
or unknown to the dispatcher the discriminatorDyieldsD=1orD=0corresponding
to theprobability the incomingmessageM contains anoperationknownorunknown to
thedispatcher.AsingleoccurrenceofmessageM containinganoperationknown to the
dispatcherwill yieldD=1according to thedeļ¬nedcausal relationships in section4.3.
S. Kotstein and C. Decker /AnApproach for Measuring IoT Interoperability 177
Intelligent Environments 2019
Workshop Proceedings of the 15th International Conference on Intelligent Environments
- Title
- Intelligent Environments 2019
- Subtitle
- Workshop Proceedings of the 15th International Conference on Intelligent Environments
- Authors
- AndrƩs MuƱoz
- Sofia Ouhbi
- Wolfgang Minker
- Loubna Echabbi
- Miguel Navarro-CĆa
- Publisher
- IOS Press BV
- Date
- 2019
- Language
- German
- License
- CC BY-NC 4.0
- ISBN
- 978-1-61499-983-6
- Size
- 16.0 x 24.0 cm
- Pages
- 416
- Category
- TagungsbƤnde