Presentation on theme: "Techniques to analyze workflows (design-time)"— Presentation transcript:
1 Petri-net based Analysis of workflows: Verification, validation, and performance analysis
2 Techniques to analyze workflows (design-time) Validation is concerned with the relation between the model and reality.Verification is typically used to answer qualitative questionsIs there a deadlock possible?It is possible to successfully handle a specific case?Will all cases terminate eventually?It is possible to execute two tasks in any order?Performance analysis is typically used to answer quantitative questionsHow many cases can be handled in one hour?What is the average flow time?How many extra resources are required?How many cases are handled within 2 days?
3 Three Analysis Techniques Reachability graphPlace & transition invariantsSimulation
4 Traffic lights are safe! Reachability Graph(0,0,1,1,0,0,0)(1,0,0,0,0,1,0)(1,0,0,1,0,0,1)(0,1,0,1,0,0,0)(1,0,0,0,1,0,0)Five reachable states.Traffic lights are safe!
6 Reachability Graph Graph containing a node for each reachable state. Constructed by starting in the initial state, calculate all directly reachable states, etc.Expensive technique.Only feasible if finitely many statesDifficult to generate diagnostic information.
9 Structural Analysis Techniques To avoid state-explosion problem and bad diagnostics.Properties independent of initial state.We only consider place and transition invariants.Proof the PN is live (transition invariants) and bounded (place invariants)
10 Place Invariant Assigns a weight to each place. The weight of a token depends on the weight of the place.The weighted token sum is invariant, i.e., no transition can change it1 man + 1 woman + 2 couple
11 Other invariants 1 man + 0 woman + 1 couple (Also denoted as: man + couple)2 man + 3 woman + 5 couple-2 man + 3 woman + coupleman – womanwoman – man(Any linear combination of invariants is an invariant.)
14 Transition invariant Assigns a weight to each transition. If each transition fires the number of times indicated, the system is back in the initial state.i.e. transition invariants indicate potential firing sets without any net effect.2 marriage + 2 divorce
15 Other invariants 1 marriage + 1 divorce (Also denoted as: marriage + divorce)20 marriage + 20 divorceAny linear combination of invariants is an invariant, but transition invariants with negative weights have no obvious meaning.
17 Incidence matrix of a Petri net Each row corresponds to a place.Each column corresponds to a transition.Recall that a Petri net is described by (P,T,I,O).N(p,t)=O(t,p)-I(p,t) where p is a place and t a transition.
19 Place invariantLet N be the incidence matrix of a net with n places and m transitionsAny solution of the equation X.N = 0 is a transition invariantX is a row vector (i.e., 1 x n matrix)O is a row vector (i.e., 1 x m matrix)Note that (0,0,... 0) is always a place invariant.
21 Transition invariantLet N be the incidence matrix of a net with n places and m transitionsAny solution of the equation N.X = 0 is a place invariantX is a column vector (i.e., m x 1 matrix)0 is a column vector (i.e., n x 1 matrix)Note that (0,0,... 0)T is always a place invariant.Basis can be calculated in polynomial time.