Page - 178 - in Intelligent Environments 2019 - Workshop Proceedings of the 15th International Conference on Intelligent Environments

More formal, letMop an incomingmessage specifying an operation the dispatcher canmap toa localone, i.e.op∈FM∩FP.ThenP(M=Mop) is theprobability thatMop is received by the callee, andP(M=Mop) is the probability of an incomingmessage, whichcannotbemappedbythedispatcher.Due tod-separation thediscriminatoralways dependson the incomingmessageaccording to thecausal relationships, i.e. P(D=1 |M=Mop)=P(D=0 |M=Mop)=1 (1) P(D=0 |M=Mop)=P(D=1 |M=Mop)=0 (2) Asa result, it isderived P(D=1)= ∑ M∈{Mop;Mop} P(D=1 |M)P(M)=P(M=Mop) (3) P(D=0)= ∑ M∈{Mop;Mop} P(D=0 |M)P(M)=P(M=Mop) (4) Discussionof the cases, ifM,Dared-separated. UsingZ={M′}will block the path betweenM andD, renderingD independent fromM, i.e. P(D |M′,M)=P(D |M′). Givenwefilter forM′=Rwemayalwaysobserve interoperability.ForM=Mop it is the resultof thecausal relations .ForM=Mop, contrary toequation4, there isanexogenous factorwhichchangesM′ toM′=R.A technical example couldbea fail-safeoperation, whichcatches thedispatcher’sUP result andcreatesanon-arbitrary responseM′=R. P(D |M′=R,M)=P(D |M′=R)= { 1 , forD=1 0 , forD=0 (5) For thecomplementaryevent,P(D |M′ =R) inverts the results fromequation5. 5.3. Degreeof Interoperability Table2summarizes thed-separationanalysis forM andDand relates it to thedegreeof interoperability.Using theequations3,4and5,wecanfinallyprobabilisticallymeasure the degree of the interoperable behavior of the callee proccess. The probabilityP(D= 1) is themetric quantitywhich states how often the the callee shows an interoperable behaviorunderarbitrary incomingmessagesM. 6. ConclusionandOutlook In this paper,we investigated the call of operations bymessagepassing as a special as- pect of interoperability.We designed a causal model formalizing this behavior. It en- ables us to quantify the degree of interoperability, that is howsuccessful the dispatcher calls aprocess’soperationaccording toan incomingmessage. It is assumed that there is anoperational communicationbetweenprocesses.Ourapproachcontributes toprevious work onC4IF byPersisteras andTarabanis; it can be embedded into theConsolidation interoperability levelof their framework. S. Kotstein and C. Decker /AnApproach for Measuring IoT Interoperability178