Experiences with Sample Clauses

Experiences with stochastic Event-B In this section we reflect on the use of stochastic Event-B for mod- xxxxxx dependable systems, particularly in comparison to the existing ap- proaches described in Section 2. Both options for stochastic Event-B, illustrated by the emergency brake case study above, provide a clean and useful method for combining stochastic and logical reasoning. The use of rates and the exponential dis- tribution allow an intuitive model of the case study, where-as using prob- abilistic choice alone (as with pB) is rather more complicated. As a con- sequence the stochastic Event-B models are smaller than those possible in pB, with fewer proof steps required to analyse the expectations. With a simpler notation and shorter proofs, more complex problems should be easier to analyse. Finally, using the expectation approach allows an algebraic analysis of the model. Algebraic solutions reveal the precise relationship between parameters of the model and the stochastic require- ments, thus making the impact of design decisions more transparent. n n Some valuable lessons were also learnt whilst analysing the emer- gency brake scenario in the proposed stochastic version of Event-B. In- terestingly, it would seem that the way an expectation is formulated has an impact on the algebraic solution obtained. For example, for option 1, an alternative (semantically equivalent) expectation was initially anal- ysed, 0 ≡⟩ λmax − c × λreq, and gave the result p ≤ c . Whilst the two solutions are not contradictory (different variables of the model are re- ferred to in each), the solution presented in Section 4.3 is clearly more useful for finding a suitable design for the system. Therefore the way in which expectations are formulated seems to impact on the usefulness of the results obtained. Option 2 should also be used with some caution, as a couple of subtle issues were noticed when analysing/implementing such a model. There are rounding issues to consider when obtaining an observation from a continuous probability distribution, i.e. when implementing a statement such as time := time + exp(λ). Also the statement (x := 1 p⊕ x := 2) || time := time + exp(λ) would not be equivalent to (x := 1 || time := time + exp(λ)) p⊕ (x := 2 || time := time + exp(λ)) || in general. This parallel substitution rule is valid for probabilistic pro- grams. However, if there is a stochastic assignment on the right-hand side of there needs to be some constraint in place to prevent different values...
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