Data Flow Modelling. Fault Tolerant Systems Research Group. Budapest University of Technology and Economics

Transcription

1 Data Flow Modelling Budapest University of Technology and Economics Fault Tolerant Systems Research Group Budapest University of Technology and Economics Department of Measurement and Information Systems 1

2 Structure and Behaviour Modelling Structural o Static o Whole and part, components o Connections The main components of the robot vacuum cleaner are the control unit, the roller gear and the vacuum cleaner. Behavioural o Dynamic o Timeliness o State, Process o Reaction to the environment (context) For the command to right changes the roller gear its operational mode to turn. Modelling does not cover all aspects, aspects cannot be separated 2

3 Goal of Data Flow Modelling Nodes and communication o Identify system components and their interactions Nodes specified using a behaviour model o State machine o (Process model?) o DFN Modelling hierarchy 3

4 Communication of Components Loose coupling asynchronous composition Channel o FIFO or random access o Capacity (can be infinite) o Can be associated with a data model (eg. token set) Background technology o E.g. Message queue-based solutions 4

5 Informal Definition Data Flow Network A Data Flow Network is a set of nodes which are connected and communicate over (unbounded) (FIFO) queues. Queues are called channels. The bits of information that are communicated over the channels are called tokens. Nodes read their input channels is a blocking way. Nodes perform some computation on their input, and produce output. To start computing, nodes require enough tokens on their input channels. Nodes consume their input tokens. Nodes are stateless or stateful. Nodes fire one at a time. 5

6 Data Flow Modelling Non-deterministic DFN formalism o [Jonsson, Cannata] Structure o Data flow graph (DFG) nodes directed arcs (FIFO channels) Behaviour o Firing rules: <s0; in=c0; s1; out=c2; > Data o Tokens 6

7 Data Flow Modelling Non-deterministic DFN formalism o [Jonsson, Cannata] Structure o Data flow graph (DFG) Token taken nodes Initial from input directed state arcs (FIFO channels) Behaviour o Firing rules: <s0; in=c0; s1; out=c2; > Data o Tokens Input channel Target state 7 Output channel Priority Token put to output channel

8 Advantages of the method Property Graphical, modular, compact, hierarchical Black and white box model Refinement rules Direct description of information flow Distributed model for both fine and coarse accuracy Data driven operation Call transparency, atomic property, information hiding Mathematical formalism Transformation: TTPN, PA Use case Clear model Early phase of modeling Multilevel modeling Modeling error propagation Asynchron, concurrent events Data driven real-time systems Fault tolerant applications Formal methods Validation, temporal analysis 8

9 Formal Definition Data Flow Network Data Flow Network is a triple (N, C, S ) N : set of nodes C : set of channels o I: input channels o O: output channels o IN: internal channels (between nodes) S : set of states Dataflow channel: Connection to the outside world Connection to the outside world o FIFO channel with unlimited capacity o Linked to one input and one output channel o Channel state: S c = M c token sequence 9

10 Formal Definition Data Flow Network Data flow node: n = (I n,o n,s n,s n0,r n,m n ), where I n set of input channels O n set of output channels S n set of node states s 0 n initial state of node, s 0 n S n M n set of tokens R n set of firing rules, r n R n a structure (s n, X in, s n, X out, ) s n X in states before and after firing, s n S input mapping, X in : I n M n X out output mapping, X out : O n M n priority, N 10

11 in n Example out Channels with one token capacity Network: o DFN = ({n}, {in, out}, {(s,0,0), (s,ok,0), (s,0,ok), (s,ok,ok)}) Nodes: o n = ({in}, {out}, {s}, s, {ok,0}, {r1}) Firing rules: o r1=<s; in=ok; s; out=ok; 0> 11

12 Example in Chennels with one token capacity Network: o DFN = ({n}, {in, out}, {(s,0,0), (s,ok,0), (s,0,ok), (s,ok,ok)}) Nodes: o n = ({in}, {out}, {s}, s, {ok,0}, {r1}) Firing rules: n Set of nodes out o r1=<s; in=ok; s; out=ok; 0> 12

13 Example in Chennels with one token capacity Network: o DFN = ({n}, {in, out}, {(s,0,0), (s,ok,0), (s,0,ok), (s,ok,ok)}) Nodes: o n = ({in}, {out}, {s}, s, {ok,0}, {r1}) Firing rules: n Set of nodes out o r1=<s; in=ok; s; out=ok; 0> Set of channels 13

14 Example in Chennels with one token capacity Network: o DFN = ({n}, {in, out}, {(s,0,0), (s,ok,0), (s,0,ok), (s,ok,ok)}) Nodes: o n = ({in}, {out}, {s}, s, {ok,0}, {r1}) Set of states Firing rules: n Set of nodes out o r1=<s; in=ok; s; out=ok; 0> Set of channels 14

15 Example in n out Chennels with one token capacity Set of input channels o DFN = ({n}, {in, out}, {(s,0,0), (s,ok,0), (s,0,ok), (s,ok,ok)}) Network: Nodes: o n = ({in}, {out}, {s}, s, {ok,0}, {r1}) Firing rules: o r1=<s; in=ok; s; out=ok; 0> 15

16 Example in n out Chennels with one token capacity Set of input Set of output channels channels o DFN = ({n}, {in, out}, {(s,0,0), (s,ok,0), (s,0,ok), (s,ok,ok)}) Network: Nodes: o n = ({in}, {out}, {s}, s, {ok,0}, {r1}) Firing rules: o r1=<s; in=ok; s; out=ok; 0> 16

17 Example in n out Chennels with one token capacity Set of input Set of output channels channels o DFN = ({n}, {in, out}, {(s,0,0), (s,ok,0), (s,0,ok), (s,ok,ok)}) Network: Nodes: o n = ({in}, {out}, {s}, s, {ok,0}, {r1}) Firing rules: o r1=<s; in=ok; s; out=ok; 0> Set of node states 17

18 Example in n out Chennels with one token capacity Set of input Set of output channels channels o DFN = ({n}, {in, out}, {(s,0,0), (s,ok,0), (s,0,ok), (s,ok,ok)}) Network: Nodes: o n = ({in}, {out}, {s}, s, {ok,0}, {r1}) Firing rules: oset r1=<s; of tokens in=ok; s; out=ok; 0> Set of node states 18

19 Example in n out Chennels with one token capacity Set of input Set of output channels channels o DFN = ({n}, {in, out}, {(s,0,0), (s,ok,0), (s,0,ok), (s,ok,ok)}) Network: Nodes: o n = ({in}, {out}, {s}, s, {ok,0}, {r1}) Firing rules: oset r1=<s; of tokens in=ok; s; out=ok; 0> Set of node states Set of firing rules 19

20 Example - Counter Design the Counter node of a DFN o Input: and input tokens o Output: w00t token when reading 3 s in a row. Counter 20

21 Example - Referee Design the Referee node of a DFN. o Input 1: result of a coin toss o Input 2: the player s guess o Output: if the toss and the guess match, otherwise. Referee Toss Guess {Toss.1, Guess. } 21

22 Execution Model How the model will be executed? o State based models event handling o Process based models keeping track of the current state of the instances o Data flow based models independent/concurrent execution of all nodes nodes only care for their own input/output channels Applications: o E.g. data processing, form processing, LabView, 22

23 Example Food Ordering System 23

24 Example Food Ordering System 24

25 Example Fashion Supplies 25

26 Example Warning Triangle Manufacturing 1. Two machines o One produces light-resistant side panels, and places them on the conveyor belt. o The other one takes the panels off the belt, and besides produces an assembled triangle every once in a while. 2. First machine sometimes produces deformed side panels. 3. The assembler machine contains a testing equipment wired before the original functionality, that is able to get rid of the deformed panels. 4. After discarding deformed panels the assembler machine always waits until three light-resistant panels have arrived and assembles a triangle out of them. 26

27 Example Error Propagation Analysis Modelling the system as a data flow network The nodes are the system components o their behaviour is modelled in a state based way o states: correct operation, different erroneous operation modi o state transitions: corruption, repair o error handling features can be modelled error detection, error correction, error confinement The channels are the communication channels where errors can propagate The tokens are messages: correct or erroneous ones o the content of the messages is not considered The big question: What kind of errors can be propagated to the output? 27