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By Peter H. Feiler, Bruce Lewis, Steve Vestal, Ed Colbert (auth.), Pierre Dissaux, Mamoun Filali-Amine, Pierre Michel, François Vernadat (eds.)

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Extra resources for Architecture Description Languages: IFIP TC-2 Workshop on Architecture Description Languages (WADL), World Computer Congress, Aug. 22–27, 2004, Toulouse, France

Example text

When an abstraction is not lumpable, a measure of "near lumpability" has been proposed as a measure of the quality of the approximation. 6 Time Dependent or Transient Solutions For a time dependent analysis, we define safety for an abstract model with partition P as follows. Let x € Ps C 5C be a non-fault or safe set of states and y G Pf C 5C be a "fault occurence" set of states. The abstraction is said to be safe in the time interval [0, T] Psa{Xa{t) = fa) > Px(X(t) G Pf) Vx € Ps and Vt G [0,T].

Theorem 2 is an easily obtained analog for conditions of strong lumpability in a Continuous Time Markov Chain (CTMC). T H E O R E M 2 ( C T M C STRONG LUMPABILITY) Let P be a partition for the CTMC with finite state space 6 and infinitesimal generator matrix A. Let U and V be matrices defined by Equations 4 and 5 with respect to P. The CTMC is said to be strongly lumpable with respect to P if 48 Architecture Description VUD^AV Languages = D~XAV where D = -diag(A). That is, D is a diagonal matrix with (D)u = —(A)a.

11. Kon, F. et alii, "The Case for Adaptive Middleware", Communications of the ACM, pp. 33-38, Vol. 45, No. 6, June, 2002. 12. K. , "Quality Connector: A Pattern Language for Provisioning and Managing Quality-Constrained Services in Distributed Real-Time and Embedded Systems", 9th Conf. , 2002. 13. , Schmerl, B. R. , "Using Gauges for Architecture-Based Monitoring and Adaptation", Work. Conference on Complex and Dynamic Systems Architecture, December, 2001. 14. Sztajnberg, A. , "Bringing QoS to the Architectural Level", ECOOP 2000 Workshop on QoS on Distributed Object Systems, Cannes.

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