Introduction to FSM FSM was introduced to meet requirements of scientific research and engineering FSM, as a mathematical modeling methodology, can be

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1 Chapter 4 FSM (Finite State Machine) Concepts and Extension Prof. Dr. Shaowen Yao School of Software Yunnan University 1

2 Introduction to FSM FSM was introduced to meet requirements of scientific research and engineering FSM, as a mathematical modeling methodology, can be used to describe physical phenomena as well as abstract concepts FSM isn t limited to one scientific field, instead, it can be applied universally When FSM is used to describe one complicated system, the systematic model are abstracted as a black-box, whose input and output are only observable Input System Black box model Output 2

3 A simple example Rotated + door for entry a park Ticket/Unlock Locked Unlocked Pass/Lock 3

4 FSM definition (1) An example State set = {q 0, q 1, q 2 } Input set = {0, 1} Output set = {y, n} Transition = Output Next State 4

5 FSM definition (2) An FSM can be defined as a 5-tuple M = (I, O, S, δ,λ) I: the finite non-empty set of input symbol O: the finite non-empty set of output symbol S: the finite non-empty set of state δ: S X I S, the state transition function λ: S X I O, the output function s δ (s, a) a / λ (s, a) s S a I The number of state of the system is finite. Otherwise, the state-machine is called Turing 5

6 To represent FSM (1) Diagram Table Matrix Diagram representation 6

7 To represent FSM (2) Table representation λ sub-table δ sub-table Diagram representation Output λ (s, a) Next state δ (s, a) s a q 0 n n q 1 q 2 q 1 y n q 1 q 2 q 2 n y q 1 q 2 7

8 To represent FSM (3) Matrix Diagram representation q 0 q 1 q 2 q q q (0/n) (0/y) (0/n) (1/n) (1/n) (1/y) 8

9 Classification of FSM Different output function: Mealy machine λ: S I O Moore machine λ: S O Mealy machine and Moore machine can be conversed to each other Whether the transitioned state and output are determined: DFSM: for specific input and all state, the transitioned state and output determined NFSM: for specific input and an existing state, the transitioned state and output aren t determined 9

10 Examples for Mealy and Moore machine Mealy machine Moore machine Input steam: Output steam: nnnyny Input steam: Output steam:

11 How to design FSM (1) Design strategy Synchronous or asynchronous Synchronous FSM Clock-control mechanism is introduced, input event will be effective when the next clock comes Asynchronous FSM no clock-control mechanism, input event will lead to state change Mealy or Moore DFSM or NFSM Encoding Encode input Encode output Encode State Encode relation of state-transition Design processes 11

12 How to design FSM (2) Design processes (steps to design FSM for a system) FSM FSM FSM FSM 12

13 How to design FSM (3) Design processes (steps to design FSM for a system) FSM FSM 13

14 How to design FSM (4) FSM : FSM, FSM,, FSM FSM FSM FSM 14

15 Extension to FSM (1) FSM FSM FSM CFSM Communicating FSM EFSM (Extended FSM CEFSM Communicating EFSM PFSM (Probability FSM 15

16 Extension to FSM (2) FSM NFSM PFSM FSM EFSM Parameterized EFSM FSM CFSM CEFSM 16

17 R. Miler CCS The Calcula for Communicating System 80 CCS CCS 17

18 CCS 1. P1 a.b.nil NIL P2 a.c.p2 a.c.a.c.p2 18

19 CCS 2 P3 a. c.nil d.nil NIL Q1 = a. b. NIL + c. Q2 Q2 = d. Q1 + e. Q2 P4 Q5 Q6 P5 Q5 Q6 Q7 19

20 CCS CCS Observational Equivalence CCS CCS CCS 20

21 Reliable Data Transfer (RDT) and its FSM RDT is one very important issue. The principle of RDT can be used in App. Layer, TCP and DLL Difference among these scenarios 21

22 Principles of Reliable data transfer important in app., transport, link layers top-10 list of important networking topics! Reliable data transfer:service model and service implementation characteristics of unreliable channel underneath it will determine complexity of reliable data transfer protocol (rdt) 22

23 Reliable data transfer: getting started rdt_send(): called from above, (e.g., by app.). Passed data to deliver to receiver upper layer deliver_data(): called by rdt to deliver data to upper send side receive side udt_send(): called by rdt, to transfer packet over unreliable channel to receiver rdt_rcv(): called when packet arrives on rcv-side of channel 23

24 Reliable data transfer: getting started We ll: incrementally develop sender, receiver sides of reliable data transfer protocol (rdt) consider only unidirectional data transfer but control info will flow on both directions! use finite state machines (FSM) to specify sender, receiver event causing state transition actions taken on state transition state: when in this state next state uniquely determined by next event state 1 event actions state 2 24

25 Rdt1.0: reliable transfer over a reliable channel underlying channel perfectly reliable no bit errors no loss of packets separate FSMs for sender, receiver: all packet flow is from the sender to receiver sender sends data into underlying channel receiver reads data from underlying channel 25

26 Rdt2.0: channel with bit errors underlying channel may flip bits in packet recall: UDP checksum to detect bit errors the question: how to recover from errors: acknowledgements (ACKs): receiver explicitly tells sender that pkt received OK negative acknowledgements (NAKs): receiver explicitly tells sender that pkt had errors sender retransmits pkt on receipt of NAK human scenarios using ACKs, NAKs? new mechanisms in rdt2.0 (beyond rdt1.0): error detection receiver feedback: control msgs (ACK,NAK) rcvr->sender retransmission: if error then retransmission 26

27 rdt2.0: FSM specification sender FSM receiver FSM Rdt 2.0-A protocol for a channel with bit errors 27

28 rdt2.0: in action (no errors) sender FSM receiver FSM 28

29 rdt2.0: in action (error scenario) sender FSM receiver FSM 29

30 rdt2.0 has a fatal flaw! What happens if ACK/NAK corrupted? sender doesn t know what happened at receiver! can t just retransmit: possible duplicate What to do? sender ACKs/NAKs receiver s ACK/NAK? What if sender ACK/NAK lost? Add enough checksum bit to detect and recover bit errors retransmit, but this might cause retransmission of correctly received pkt! Handling duplicates: sender adds sequence number to each pkt sender retransmits current pkt if ACK/NAK garbled receiver discards (doesn t deliver up) duplicate pkt stop and wait Sender sends one packet, then waits for receiver response 30

31 rdt2.1: sender, handles garbled ACK/NAKs 31

32 rdt2.1: receiver, handles garbled ACK/NAKs 32

33 rdt2.1: discussion Sender: seq # added to pkt two seq. # s (0,1) will suffice. Why? must check if received ACK/NAK corrupted twice as many states state must remember whether current pkt has 0 or 1 seq. # Receiver: must check if received packet is duplicate state indicates whether 0 or 1 is expected pkt seq # note: receiver can not know if its last ACK/NAK received OK at sender 33

34 rdt2.2: a NAK-free protocol same functionality as rdt2.1, using ACKs only instead of NAK, receiver sends ACK for last pkt received OK receiver must explicitly include seq # of pkt being ACKed duplicate ACK at sender results in same action as NAK: retransmit current pkt! sender FSM 34

35 rdt3.0: channels with errors and loss New assumption: underlying channel can also lose packets (data or ACKs) checksum, seq. #, ACKs, retransmissions will be of help, but not enough Q: how to deal with loss? sender waits until certain data or ACK lost, then retransmits drawbacks? Approach: sender waits reasonable amount of time for ACK retransmits if no ACK received in this time if pkt (or ACK) just delayed (not lost): retransmission will be duplicate, but use of seq. # s already handles this receiver must specify seq # of pkt being ACKed requires countdown timer 35

36 rdt3.0 sender 36

37 rdt3.0 in action 37

38 rdt3.0 in action 38

39 Performance of rdt3.0 rdt3.0 works, but performance stinks example: 1 Gbps link, 15 ms e-e prop. delay, 1KB packet: T transmit = 8kb/pkt 10**9 b/sec =8 microsec/pkt fraction of time Utilization = U = = 8 microsec sender busy sending msec = KB pkt every 30 msec -> 33kB/sec thruput over 1 Gbps link network protocol limits use of physical resources! 39

40 Pipelined protocols Pipelining: sender allows multiple, in-flight, yet-to-be-acknowledged pkts range of sequence numbers must be increased buffering at sender and/or receiver Two generic forms of pipelined protocols: go-back-n, selective repea 40

41 Go-Back-N Sender: k-bit seq # in pkt header window of up to N, consecutive unack ed pkts allowed ACK(n): ACKs all pkts up to, including seq # n - cumulative ACK may receive duplicate ACKs (see receiver) timer for each in-flight pkt timeout(n): retransmit pkt n and all higher seq # pkts in window 41

42 GBN: sender extended FSM 42

43 GBN: receiver extended FSM receiver simple: ACK-only: always send ACK for correctly-received pkt with highest in-order seq # may generate duplicate ACKs need only remember expectedseqnum out-of-order pkt: discard (don t buffer) -> no receiver buffering! ACK pkt with highest in-order seq # 43

44 GBN in action N=4 44

45 Selective Repeat receiver individually acknowledges all correctly received pkts buffers pkts, as needed, for eventual in-order delivery to upper layer sender only resends pkts for which ACK not received sender timer for each unacked pkt sender window N consecutive seq # s again limits seq #s of sent, unacked pkts 45

46 Selective repeat: sender, receiver windows 46

47 Selective repeat sender data from above : if next available seq # in window, send pkt timeout(n): resend pkt n, restart timer ACK(n) in [sendbase,sendbase+n]: mark pkt n as received if n smallest unacked pkt, advance window base to next unacked seq # receiver pkt n in [rcvbase, rcvbase+n-1] send ACK(n) out-of-order: buffer in-order: deliver (also deliver buffered, in-order pkts), advance window to next not-yet-received pkt pkt n in [rcvbase-n,rcvbase-1] ACK(n) otherwise: ignore 47

48 Selective repeat in action 48

49 Selective repeat: dilemma Example: seq # s: 0, 1, 2, 3 window size=3 receiver sees no difference in two scenarios! incorrectly passes duplicate data as new in (a) Q: what relationship between seq # size and window size? 49

穨control.PDF

穨control.PDF TCP congestion control yhmiu Outline Congestion control algorithms Purpose of RFC2581 Purpose of RFC2582 TCP SS-DR 1998 TCP Extensions RFC1072 1988 SACK RFC2018 1996 FACK 1996 Rate-Halving 1997 OldTahoe