KAOS: a KLAIM Extension for Reasoning on Programmable QoS

Transcription

1 KAOS: a KLAIM Extension for Reasoning on Programmable QoS Emilio Tuosto etuosto@di.unipi.it Dipartimento di Informatica Universitá di Pisa In cooperation with: R. De Nicola, G. Ferrari, U. Montanari and R. Pugliese KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.1/15

2 Plan of the talk KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.2/15

3 Plan of the talk WAN Programming with QoS KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.2/15

4 Plan of the talk WAN Programming with QoS A representation of QoS parameters KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.2/15

5 Plan of the talk WAN Programming with QoS A representation of QoS parameters KAOS KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.2/15

6 Plan of the talk WAN Programming with QoS A representation of QoS parameters KAOS KAOS & Hypergraphs: reasoning on QoS issues KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.2/15

7 Plan of the talk WAN Programming with QoS A representation of QoS parameters KAOS KAOS & Hypergraphs: reasoning on QoS issues Details in International Symposium on Verification - Theory and Practice (LNCS) KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.2/15

8 Wide Area Network Programming Issues Absence of centralised control Administrative domains Interoperability Mobility (of resources and computation) Network Awareness Applications are location dependent Locations have different features and allow multiple (security) policies Independently programmed in a distributed environment Service Level Agreement Security... KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.3/15

9 Klaim KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.4/15

10 Klaim Multiple TS KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.4/15

11 Klaim Multiple TS Localities: first class citizens KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.4/15

12 Klaim Multiple TS Localities: first class citizens Process migration KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.4/15

13 Klaim Multiple TS Localities: first class citizens Process migration Q Q a(t)@s R P eval(p )@s R P site s site s KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.4/15

14 Klaim Multiple TS Localities: first class citizens Process migration Q Q a(t)@s R P eval(p )@s R P site s site s KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.4/15

15 Klaim Multiple TS Localities: first class citizens Process migration R Q P a(t)@s eval(p )@s R Q P P ::= nil α.p P 1 P 2 α ::= a@s a ::=... // Klaim actions site s site s ε(p ) KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.4/15

16 KAOS: Gateways KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.5/15

17 KAOS: Gateways Coordinators (super processes) KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.5/15

18 KAOS: Gateways Coordinators (super processes) Dynamic creation of sites KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.5/15

19 KAOS: Gateways Coordinators (super processes) Dynamic creation of sites Gateway connection management KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.5/15

20 KAOS: Gateways Coordinators (super processes) Dynamic creation of sites Gateway connection management Q Q P P R P R site s site s KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.5/15

21 KAOS: Gateways Coordinators (super processes) Dynamic creation of sites Gateway connection management Q Q new(s, P ) P P R P R site s site s KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.5/15

22 KAOS: Gateways Coordinators (super processes) Dynamic creation of sites Gateway connection management Q Q P P R P R site s site s KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.5/15

23 KAOS: Gateways Coordinators (super processes) Dynamic creation of sites Gateway connection management Q Q P ::= γ.p P 1 P 2 γ ::= α κ ν(s κ) κ s R site s P R site s s κ δ l Cost κ abstracts characteristics of connections according to many dimensions (bandwidth, latency, distance, access rights...) KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.5/15

24 Connection costs Algebra on costs: c-semiring. A, +,, 0, 1 is a constraint semiring if A is a set (0, 1 A), and + and are binary operations on A that satisfy the following properties: + is commutative, associative, idempotent, 0 is its unit element and 1 is its absorbing element; is commutative, associative, distributes over +, 1 is its unit element, and 0 is its absorbing element. The additive operation of a c-semiring induces a partial order on A defined as a A b c : a + c = b. The minimal element is thus 0 and the maximal 1 KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.6/15

25 Examples of connection costs N, min, +, +, 0, the c-semiring of natural numbers N where the additive operation is min the multiplicative operation is the sum over natural numbers ({A}),,, A, A}, c-semiring of capabilities A where the additive operation is the multiplicative operation is KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.7/15

26 KAOS: Example 1. message on s t 2. check message s Send msg to t 3. download message KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.8/15

27 KAOS: Example 1. message on s <10,{i,o},2> x <100,{i,o,n},2> t 2. check message s t z <300,{i,o},60> s 3. download message Send msg to t <10,{i},20> y <150,{i,o},2> KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.8/15

28 KAOS: Example 1. message on s <10,{i,o},2> x <100,{i,o,n},2> t 2. check message s t z <300,{i,o},60> s 3. download message Send msg to t Costs are triples κ = d, C, p where <10,{i},20> 1. d is the geographical distance (in Km); y <150,{i,o},2> 2. C {i, o, n} are the capabilities, where i, o and n stand for input, output and creation of new nodes, respectively; 3. p is the price (in euros). KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.8/15

29 KAOS: Example Costs are elements of the cartesian product of 1. (N, min, +, +, 0), 2. ( ({i, o, n}), glb,, {i, o, n}, {i, o, n}), 3. (Q, min, +, +, 0). proved to be a c-semiring [BMR97] Operations and + are d, C, p d, C, p = d + d, C C, p + p d, C, p + d, C, p = min{d, d }, glb{c, C }, min{p, p }. Accordingly, the neutral elements of and +, respectively are defined as 1 = 0, {i, o, n}, 0 and 0 = +,, +. KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.9/15

30 Hypergraphs Programming model 2 Tackling new non-functional computational phenomena of systems using SHR. The metaphor is WAN systems as Hypergraphs WAN computations as SHR In other words: Components are represented by hyperedges Systems are bunches of (connected) hyperedges Computing means to rewrite hyperedge......according to a synchronisation policy KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.10/15

31 Hyperedges and Hypergraphs Syntax A hyperedge generalises edges: It connects more than two nodes L : 3, L(y, z, x), y x 3 L 1 2 z KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.11/15

32 Hyperedges and Hypergraphs Syntax A hyperedge generalises edges: It connects more than two nodes L : 3, L(y, z, x), y x 3 L 1 2 z G ::= nil ν y.g L( x) G G KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.11/15

33 Hyperedges and Hypergraphs Syntax A hyperedge generalises edges: It connects more than two nodes L : 3, L(y, z, x), y x 3 L 1 2 z G ::= nil ν y.g L( x) G G Syntactic Judgement Γ G, fn(g) Γ KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.11/15

34 Hyperedges and Hypergraphs Syntax A hyperedge generalises edges: It connects more than two nodes L : 3, L(y, z, x), y x 3 L 1 2 z G ::= nil ν y.g L( x) G G Syntactic Judgement Γ G, fn(g) Γ An example: L : 3, M : 2 x, y ν z.(l(y, z, x) M(y, z)) KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.11/15

35 Hyperedges and Hypergraphs Syntax A hyperedge generalises edges: It connects more than two nodes L : 3, L(y, z, x), y x 3 L 1 2 z G ::= nil ν y.g L( x) G G Syntactic Judgement Γ G, fn(g) Γ An example: y L : 3, M : 2 x, y ν z.(l(y, z, x) M(y, z)) x L M z KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.11/15

36 Replacement of Hyperedges L G KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.12/15

37 Replacement of Hyperedges L G G G L 3 G2 G2 KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.12/15

38 Replacement of Hyperedges L G G2 G1 G L KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.12/15

39 Replacement of Hyperedges L G G2 G1 G L Edge replacement: local Synchronisation as distributed constraint solving New node creation Node fusion: mobility model KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.12/15

40 Replacement of Hyperedges L G Edge replacement: local G1 1 2 G L G2 Synchronisation as distributed constraint solving New node creation Node fusion: mobility model Benefits: Powerful model of system composition (π, π-i, fusion) LTS for Ambient......and for Klaim and path reservation for KAOS KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.12/15

41 KAOS & Hypergraphs [[ s :: L P ]] = Γ (ν x, p)([[ P ]] p s m,n ( u, x, p) n j=1 G κ j t j (x j, v j )) ζ ζ G G ζ P... G G KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.13/15

42 KAOS & Hypergraphs [[ s :: L P ]] = Γ (ν x, p)([[ P ]] p s m,n ( u, x, p) n j=1 G κ j t j (x j, v j )) ζ ζ... G G [ nil ] p = nil [ o t ] p = L o t (p) [ γ.p ] p = L γ.p (p) ζ [ ε(p )@s ] p = (ν u)(ε T s (P ) (u, p) S P (u)) P G G [ P 1 P 2 ] p = [ P 1 ] p [ P 2 ] p [ rec X. P ] p = [ P [ rec X. P / X ] ] p.... KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.13/15

43 Graph for the message example t G κ tx x x x G κ zx x G κ xz t G κ xt t G κ ty ε T s S Ff,t z G κzs z G κ sz y y y G κ yz z z z s s s L bigfile,file KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.14/15

44 KAOS Graph semantics: pros & cons KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.15/15

45 KAOS Graph semantics: pros & cons Many productions (recently reduced :-) KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.15/15

46 KAOS Graph semantics: pros & cons Many productions (recently reduced :-) + Determines the optimal path (also KAOS) KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.15/15

47 KAOS Graph semantics: pros & cons Many productions (recently reduced :-) + Determines the optimal path (also KAOS) + Path reservation KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.15/15

48 KAOS Graph semantics: pros & cons Many productions (recently reduced :-) + Determines the optimal path (also KAOS) + Path reservation + Path routing KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.15/15

49 KAOS Graph semantics: pros & cons Many productions (recently reduced :-) + Determines the optimal path (also KAOS) + Path reservation + Path routing Theorem KAOS remote actions are routed on paths with minimal cost (wrt the c-semiring operations) KAOS: a KLAIM ExtensionforReasoning on Programmable QoS p.15/15