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Goal & Method
Goal
Enable the Software Architecture Model (SAM)
to model and analyze both functional properties and common non-functional properties
Method
Extend SAM with stochastic constructs Transform SAM model to SRN model
Dependability Analysis Using SAM Tianjun Shi, Xudong He School of - - PowerPoint PPT Presentation
Dependability Analysis Using SAM Tianjun Shi, Xudong He School of - - PowerPoint PPT Presentation
Dependability Analysis Using SAM Tianjun Shi, Xudong He School of Computer Science Florida International University {tshi01, hex}@cs.fiu.edu Goal & Method Goal Enable the Software Architecture Model (SAM) to model and analyze both
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The SAM Model
A SAM model: {C, h}
A set of compositions C = {C1, C2, …, Ck} A hierarchical mapping h relating compositions.
A composition: Ci = {Cmi, Cni, Csi}
Cmi: a set of components Cni : a set of connectors Csi : a set of composition constraints
Components / Connectors: Cij = {Bij , Sij}
Bij : behavior model (a Petri net) Sij : property specification ( a temporal logic formula)
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The SAM model (Cont’d)
A graphic view of a SAM architecture model
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Predicate Transition Net (PrT net)
A PrT net is a class of high level Petri net, and is defined as a tuple (N, Spec, ins), where
N = (P, T, F), the net structure Spec = (S, OP, Eq), the underlying specification ins = (ϕ, L, R, M0), the net inscription associating
a net element in N with its denotation in Spec.
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Stochastic Reward Net (SRN)
SRN is an extension to Stochastic Petri Net
A firing rate for each transition, which could be
marking dependent
Enabling Function for each transition Priority for each transition
Tools for SRNs
SPNP SMART
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Extension on SAM
Add a stochastic construct into the behavior model expressed in a PrT net
A special variable RATE is used in the constraint
- f a transition to specify the firing rate.
Firing rate is not necessarily constant
Formally specify non-functional property requirements using Probabilistic real time Computation Tree Logic (PCTL)
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Transformation from SAM to SRN
Unfold the behavior model to a low level Petri net.
Unfold each transition T into a set of transitions based on the set of
constant substitution that satisfy the constraint of T.
Places are connected to the unfolded transitions according to the
substitution.
Remove the dead transitions and combine equivalent elements if
any.
Assign the firing rate to each transition based on the stochastic construct. Solve the transformed SRN to evaluate dependability.
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An example: the multiprocessor system
P1 M1 D11 D12 D1m P2 M2 D21 D22 D2m Pn Mn Dn1 Dn2 Dnm Sn B Mg
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The behavior model of the example system
TP TGM TLM TD T1 T2 T3 T5 T4 PPf PGMf PLMf PDf i i i r r r i i <i, j> X i Psub PSf X’ PBf r r r X X’ i i r <i, j> i TB r r PP PGM PLM PD PB PS r r
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The SRN model of the example system
TPi TGM TLMi t1i t2i PPfi PGMf PLMfi t3i TDi1 TDi2 PDfi1 PDfi2 PF1 PF2 PF3 t1 t2 t3 t4 PSf PBf TB
(a) (b)
PPi PGM PLMi PDi1 PDi2 PB PS PFi λP λGM λLM λD λD λB
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Analysis Results
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 5000 10000 15000 20000 25000
Time (in hours) Probability of system down
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