Performance evaluation of Fractal component-based systems

Abstract

Component-based system development is now a well accepted design approach in software engineering. Numerous component models have been proposed, and for most of them, specific software tools allow building component-based systems (CBS). Although these tools perform several checks on the built system, few of them provide formal verification of behavioural properties nor performance evaluation of the resulting system. In this context, we have developed a general method associating to a CBS, a formal model, based on stochastic well formed nets, a class of high-level Petri nets, allowing qualitative behavioural analysis together with performance evaluation of this CBS. The definition of the model heavily depends on the (run time) component model used to describe the CBS. In this paper, we instantiate our method to Fractal CBS and its reference Java implementation Julia. The method starts from the Fractal architectural description of a system and defines rules to systematically generate element models of the CBS and their interactions. We then apply a structured method for both qualitative and performance analysis, taking into account the given implementation of the Fractal model. The main interest of our method is to take advantage of the compositional definition of such systems to carry out an efficient analysis. The paper concentrates on performance evaluation and presents our method step by step with an illustrative example.

Appendix: WN and SWN formal definitions

We remind the reader with the definitions of WN and SWN. A detailed presentation of these models can be found in [10].

Definition 1  (Well-formed Petri net (WN)) A well-formed Petri net S is a tuple

(P, T, C, cd, Pre, Post, Inh, Guard, Pri, M ₀) with:

• P, T: the finite sets of places and transitions,

• C = {C _i / i ∈ I = {1, ⋯ , n}}: the set of basic colour classes; C _i is possibly partitioned into n _i static sub-classes: $C_{i}=\bigcup_{j=1}^{n_{i}}C_{i,j}$,

• cd: P ∪ T→Bag(I). $cd(r)=C_{1}^{e_1}\times C_{2}^{e_2}\times \ldots\times C_{n}^{e_n}$ is the colour domain of a node r; e_i ∈ ℕ is the number of occurrences of C_i in the colour domain of r, where Bag(I) is the set of multisets (bags) on I.

• Pre, Post, Inh: the input, output and inhibition standard colour functions from C(t) to Bag(C(p)).

• Guard(t) : C(t)→{true, false} is a standard predicate associated with the transition t. By default, Guard(t) is the constant function of value True.

• Pri: T→ℕ the priority function. By default, we assume ∀ t ∈ T, Pri(t) = 0;

• M ₀: M ₀(p) ∈ Bag(C(p)) is the initial marking of p.

Definition 2  (Stochastic well-formed net (SWN)) A stochastic well-formed net is a pair (S, θ) such that:

• S is a well-formed net.

• θ a function defined on T such that: $\theta(t): \tilde{cd}(t) \times \prod_{p\in P} Bag(\tilde{C}(p))\longrightarrow R^{+}$.

$\theta(t)(\tilde{c},\tilde{M})$ represents:

• The weight of t for the colour c in the marking M, if π(t) > 0 (t is immediate). the firing probability of t(c) in M is then: $\frac{\theta(t)(\tilde{c}, \tilde{M})}{\sum_{(t',c'), M[t'(c')>} \theta(t')(\tilde{c'},\tilde{M})}$.

• The firing rate of t for the colour c in M, if π(t) = 0 (t is timed): the enabling duration before the firing of t(c,M) follows an exponential probability distribution with mean $\theta(t)(\tilde{c}, \tilde{M})$.

In this definition, $\tilde{c}$ is the representation of the colour c in terms of static sub-classes, and $\tilde{M}(p)$ is the representation of the symbolic marking of p in terms of tuples of static sub-classes. θ(t) depends only on static sub-classes of concerned colours.