Extended Coloured Petri Nets with Structured Tokens Formal Method for Distributed Systems

Transcription

1 Extended Coloured Petri Nets with Structured Tokens Formal Method for Distributed Systems Khaoula Al Ali, Wolfgang Fengler, Bernd Däne, Alexander Pacholik Faculty of Computer Science and Automation, Computer Architecture and Embedded Systems Group Alexander Pacholik,

2 Outline Motivation Related work Analysis methods High level Petri nets High Coloured Petri Nets with Structured Tokens (HCPN-ST) Application example / case study Modeling Transformation & analysis Results Conclusion & future work Alexander Pacholik,

3 Motivation Distributed Systems Distributed protocols & algorithms are challenging for validation & verification (e.g. P2P systems) Time modeling (naturals, intervals, statistic distribution) Addressing schemes (relative, absolute, modulo) Statistic parameters Difficult verifiable models Some effects are hard to express (abstract structures, addressing modes) Case-Study: optimized Petri net class for distributed protocols & algorithms Alexander Pacholik,

4 Motivation Distributed Systems Distributed protocols & algorithms are challenging for validation & verification (e.g. P2P systems) Time modeling (naturals, intervals, statistic distribution) Addressing schemes (relative, absolute, modulo) Statistic parameters Difficult verifiable models Some effects are hard to express (abstract structures, addressing modes) Case-Study: optimized Petri net class for distributed protocols & algorithms Alexander Pacholik,

5 Motivation Distributed Systems Distributed protocols & algorithms are challenging for validation & verification (e.g. P2P systems) Time modeling (naturals, intervals, statistic distribution) Addressing schemes (relative, absolute, modulo) Statistic parameters Difficult verifiable models Some effects are hard to express (abstract structures, addressing modes) Case-Study: optimized Petri net class for distributed protocols & algorithms Alexander Pacholik,

6 Related work I Formal techniques Types of formal techniques: 1. Model only main mechanisms & apply exhaustive analysis Petri nets State charts 2. Model all mechanisms in detail & apply simulation, test sequences Estelle Lotos SDL Alexander Pacholik,

7 Related work I Formal techniques Types of formal techniques: 1. Model only main mechanisms & apply exhaustive analysis Petri nets State charts 2. Model all mechanisms in detail & apply simulation, test sequences Estelle Lotos SDL Alexander Pacholik,

8 Related work II Petri net types Petri nets (PN) Flexible method Wide modeling & analysis support Various extensions But: large scale nets become unreadable Coloured Petri nets (CPN) [Jensen92] Abstraction of (similar) structures But: explicit colour transformation rules Predicate/Transition nets (Pr/T-nets)[GenLau81] Implicitly defined colours (based on types) Predicate based transformation rules (each representing sets of colour transformation rules) [Jensen92] K. Jensen, Coloured Petri Nets. Basic Concepts, Analysis Methods and Practical Use. Springer-Verlag, [GenLau81] H. Genrich and K. Lautenbach, System modeling with high-level Petri nets, Theoretical Computer Science, vol. 13, pp , Alexander Pacholik,

9 Related work II Petri net types Petri nets (PN) Flexible method Wide modeling & analysis support Various extensions But: large scale nets become unreadable Coloured Petri nets (CPN) [Jensen92] Abstraction of (similar) structures But: explicit colour transformation rules Predicate/Transition nets (Pr/T-nets)[GenLau81] Implicitly defined colours (based on types) Predicate based transformation rules (each representing sets of colour transformation rules) [Jensen92] K. Jensen, Coloured Petri Nets. Basic Concepts, Analysis Methods and Practical Use. Springer-Verlag, [GenLau81] H. Genrich and K. Lautenbach, System modeling with high-level Petri nets, Theoretical Computer Science, vol. 13, pp , Alexander Pacholik,

10 Specifics of distributed systems modeling Communication protocols: Dynamic environment Heterogeneous system Large node count Distributed algorithms Assignment to node addresses Exchange of messages Time modeling Alexander Pacholik,

11 Specifics of distributed systems modeling Communication protocols: Dynamic environment Heterogeneous system Large node count Distributed algorithms Assignment to node addresses Exchange of messages Time modeling CPN unsuitable Pr/T-net extension required HCPN-ST extension based on: Coloured Petri nets [Jensen92] Predicate/Transition nets [GenLau81] Alexander Pacholik,

12 High Coloured Petri Nets with Structured Tokens (HCPN-ST) Tuple HPCN-ST = (, P, T, F, C, V, K, m, ) 0 dt Σ: finite set of types & colour sets P,T: sets of places, transitions P T = F v ( P T ), prearcs F n ( T P), postarcs C: colour function V: arc expression a F : type( V ( a)) and type( var( V(a))) colour sets K: capacity function m 0 = boolean type : initialization function dt : time function t T : dt( t) = n; n N Alexander Pacholik,

13 HCPN-ST: Example colour set Tuple HCPN-ST: HPCN-ST, P, T, F, C, V, K, Type & colour set: = ( I, Z, A, Plan, Wanderer) 1. Elementary colour set I: set of indices Z: set of pointers Nodeaddress: set of addresses {e} empty position {r} random position = ( Σ m 0, dt ) 2. Structured colour set (protocol specific) Plan := 1A 4243 A L 4A Wanderer : = Z X : = { x i x N times >2 X Plan } length Definition of message elements A: = { a a ( Nodeaddress e r)} Used for construction of tokens representing different types of messages Alexander Pacholik,

14 HCPN-ST: Firing rules Firing rule is expressed by pre- & postarc expressions: Prearc expressions (pre conditions) Postarc expressions (post conditions, modifications) Prearc & postarc expressions built upon: Elementary colour Structured colour Logic expression p1 t p2 Colour transformations (token modifications) defined by postarc expressions. Alexander Pacholik,

15 HCPN-ST: Firing rules Firing rule is expressed by pre- & postarc expressions: Prearc expressions (pre conditions) Postarc expressions (post conditions, modifications) Prearc & postarc expressions built upon: Elementary colour Structured colour Logic expression p1 t 1 2 : p2 1 2 : 1, 2, 3 : Wanderer Colour transformations (token modifications) defined by postarc expressions. Alexander Pacholik,

16 HCPN-ST: Firing rules Firing rule is expressed by pre- & postarc expressions: Prearc expressions (pre conditions) Postarc expressions (post conditions, modifications) Prearc & postarc expressions built upon: Elementary colour Structured colour Logic expression p1 t p2 1 2 : (pos z+1 = e) 1, 2, 3 : Wanderer 1 2 : Colour transformations (token modifications) defined by postarc expressions. Alexander Pacholik,

17 HCPN-ST: Firing rules Firing rule is expressed by pre- & postarc expressions: Prearc expressions (pre conditions) Postarc expressions (post conditions, modifications) Prearc & postarc expressions built upon: Elementary colour Structured colour Logic expression p1 t p2 1 2 (pos z+1 = e) (z:=z+1 Λ pos z := n4) 1 2 : : 1, 2, 3 : Wanderer Colour transformations (token modifications) defined by postarc expressions. Alexander Pacholik,

18 HCPN-ST: Firing rules Firing rule is expressed by pre- & postarc expressions: Prearc expressions (pre conditions) Postarc expressions (post conditions, modifications) Prearc & postarc expressions built upon: Elementary colour Structured colour Logic expression p1 t p2 1 2 (pos z+1 = e) (z:=z+1 Λ pos z := n4) 1 2 : : 1, 2, 3 : Wanderer Colour transformations (token modifications) defined by postarc expressions. Alexander Pacholik,

19 Application Example: Cluster generation by overlapping cycles [UngerWulff02] H. Unger and M. Wulff, Cluster-building in p2p-community networks, ACTA Press, Alexander Pacholik,

20 HCPN-ST example: Cluster generation by overlapping cycles HCPN-ST example model Alexander Pacholik,

21 HCPN-ST example: Cluster generation by overlapping cycles emptynode wanderer HCPN-ST example n1 model n2 : nn killedwr net nodetoremove wrstart nodetoadd fullwr treatmentwr forward Alexander Pacholik, wrtoadd

22 HCPN-ST example: Cluster generation by overlapping cycles emptynode wanderer HCPN-ST example n1 model n2 : nn nettime net killedwr nodetoremovetimer wr nodetoaddtimer kill timeover nodetoremove wrstart nodetoadd noremove addtoplan noadd removefromplan addnoo normforward random wrgenerated fullwr treatmentwr next forward Alexander Pacholik, wrtoadd

23 HCPN-ST example: Cluster generation by overlapping cycles emptynode wanderer HCPN-ST example n1 model n2 : nn nettime net killedwr nodetoremovetimer wr nodetoaddtimer kill timeover nodetoremove wrstart nodetoadd noremove addtoplan noadd removefromplan normforward addnoo random wrgenerated fullwr treatmentwr next forward Alexander Pacholik, wrtoadd

24 emptynode wanderer HCPN-ST example n1 model killedwr HCPN-ST example: Cluster generation by overlapping cycles td < t avg -Δt nodetoremovetimer timeover td=2δt nodetoremove noremove treatmentwr n2 : nn kill (z =1 pos z =) := pos z wr removefromplan (z > 1) next (pos z = ) wrstart (pos z :=e) (z := z+1) td t avg +Δt nodetoaddtimer nodetoadd addtoplan noadd (z x) (pos z = e) pos z ±1 = e (z = x) addnoo net (first (pos i =e):= z := i mod x) nettime normforward (z:=1) (z := z+1) (pos z e pos z r) wr (1,x,, (pos 2..pos x ):= random(e,r)) (pos z := random()) (pos z = r) random forward wrgenerated dt = ttry fullwr Alexander Pacholik, wrtoadd

25 HCPN-ST example: Cluster generation by overlapping cycles nettime emptynode wanderer HCPN-ST example n1 model n2 nn : net (posz = ) wr (1,x,, (pos 2..pos x ):= random(e,r)) td tavg +Δt nodetoaddtimer wr td < tavg -Δt nodetoremovetimer kill (z =1 pos z =) nodetoadd wrstart nodetoremove wrgenerated dt = t try (pos z := random()) (first (posi=e):= z := i mod x) timeover random normforward fullwr td=2δt addtoplan noremove addnoo (z > 1) treatmentwr forward Alexander Pacholik, wrtoadd killedwr noadd (pos z = r) (pos z e pos z r) removefromplan (z:=1) (z x) (z := z+1) (pos z :=e) (z = x) (pos z = e) pos z ±1 = e next (z := z+1) := posz

26 Transformation: HCPN-ST CPN Validation Statistics Parameters Transformation of firing rules Peneca Chromos CPN Simulation HCPN-ST Model CPN Model Transformation of token colours INA Tool CPN Analysis Petri net class (HCPN-ST) verifiable (analyzable + simulatable) Verification of Petri net properties: - Liveliness - Boundedness - Reachability [INA] P. H. Starke, S. Roch: "INA - Integrated Net Analyzer, Version 2.2. Manual" Humboldt-University Berlin 1999 [Chromos] B. Däne, A. Mölders, A. Melber, W. Fengler: "Modeling an Industrial Transportation Facility with Coloured Petri Nets" 18th International Conference on Application and Theorie of Petri Nets. Toulouse, 1997 Alexander Pacholik,

27 First Results CPN-Model: - up to 48 firing modes per transition - up to 192 colours per place Simulation (Peneca Chromos) Analysis (INA) 1. Conflict free (statically and dynamically) 2. Sound simulation (no deadlock during exhaustive test) 3. Behaviour as expected 1. Liveliness: weakly live 2. Boundedness: net is bounded and safe (1-bounded) 3. Reachability: limited state space, no undesired states Alexander Pacholik,

28 Conclusions & Future work Summary Problem oriented Petri net class developed General approach demonstrated, using a complex example Analysis by INA after transformation to CPN Outlook More & detailed examples & results Tool support (Pr/T-nets + custom types +time & probabilities) Extended analysis & verification support Quantitative statistic results Comparison against other simulation approaches (e.g. MLDesigner) Alexander Pacholik,

29 Conclusions & Future work Summary Problem oriented Petri net class developed General approach demonstrated, using a complex example Analysis by INA after transformation to CPN Outlook More & detailed examples & results Tool support (Pr/T-nets + custom types +time & probabilities) Extended analysis & verification support Quantitative statistic results Comparison against other simulation approaches (e.g. MLDesigner) Alexander Pacholik,

30 Questions??????? Alexander Pacholik,