Fractal Network Technology Tutorial

Transcription

1 Verification of a MAC-Layer Protocol for Wireless Sensor Network Faranak Heydarian Faranak Heydarian Frits Vaandrager Radboud University Nijmegen

2 Outline Introduction Mac Model UPPAAL Model A Synchronized Network UPPAAL Numerical Results Theorem of having a Synchronized Network Conclusion & Future Work 2

3 Introduction A Wireless Sensor Network (WSN) is a wireless network consisting of spatially distributed autonomous devices using sensors to cooperatively monitor physical or environmental conditions, such as temperature, sound, vibration, pressure, motion or pollutants, at different locations. 3

4 MAC Model Time is considered as a sequence of Time Frames. ATimeFrame Ati time frame is composed of a fixed number (C) of ftime Slots. tsn RX TX RX idle idle idle idle In a time slot the hardware clock of the sensor node ticks a fixed number (k ) of times. 4

5 Synchronization When the nodes are powered on, they are all unsynchronized. In order to get synchronized, a node needs information about the relative time frame start, called T moment. The clock synchronization is requested each time a node receives a message, keeping the internal oscillator to not drift from the given T moment. Whenever a message is received, the transmitter T moment is adopted by the receiver nodes. 5

6 Guard Time A is allocated at the beginning i of each TX slot to TX Time Slot accommodate timing skew among the oscillators of the nodes. It is also required after the message to Guard Time allow the transmitter to return to a quiescent state. t RX Time Slot Guard Time 6

7 UPPAAL Model A Wireless Sensor Node Clock START_TX clk[id]==guardtime start_message! SENDING X x<=max x>=min tick[id]! x:=, csn[id]==tsn[id] urg! csn[id]!=tsn[id] tick[id]? clk[id]==k -guardtime tick[id]! Synchronizer clk[id]:=(clk[id]+1)%k INIT WAIT S csn[id]<=n S 1 start_message? clk[id]== urg! csn[id]:=(csn[id]+1)%c tick[id]? clk[id]:=guardtime+1 7

8 A Synchronized Network A wireless sensor network is synchronized if no two nodes transmit, simultaneously and the receiver nodes are able to get the message of the transmitter in RX slots with the same slot number as the transmitter. A B C 1 2 TX 3 Colliison 1 TX only if: A fully-connected wireless sensor network is synchronized if and ( i, j Nodes)( NODE( i). SENDING csn[ i] = csn[ j]) 8

9 Numerical Results Nodes Nodes C C 6 n 4 n 4 k 1 k 1 g 2 g min min max max Nodes C 6 n 4 k g 2 min max

10 Theorem A fully-connected wireless sensor network is synchronized if and only if: ( C d) k g min < ( d = tsn ( ) k 1 max tsn max C d k min ) 1

11 Necessity Proof by Counter Example ( C d). Imagine: k g ( C d). k 1 min max Suppose a wireless sensor network in which there exist one very slow sensor node (clock tick length max) and one very fast node (clock tick length min): Fast g+1 g F End of Frame Slow g S 11

12 Necessity Proof Fast g+1 g F End of Frame Slow g S (( C d). 1) F = min. k max. ( ( C d). k g ) S = ) = ( C d). k ( C d). k g 1 min max max. (( C d). k g) min. (( C d). k 1) S F 12

13 Sufficiency Proof using Invariants We started t proving the necessity part of the theorem by describing the network of timed automata by primed formulas. We proved if ( C d ) k g ( C d) k 1 < min max holds, then is an Invariant. ( i, j )( WSN [ i]. SENDING csn [ i ] = csn [ j ]) 13

14 System Invariants 1. x[ i] max 2. clk[ i] k 3. csn [ i ] C 4. NODE [ i]. SENDING ( csn [ i ] = tsn [ i ] csn [ i] n ) ] 5. NODE[ i]. SENDING ( g clk[ i] k g) 14

15 System Invariants (cont.) t.k 1 g, t. k 1 If ( t;1 t ( C d ) ) then < min max ( i, j; i j)( NODE[ i]. WAITING clk[ i] = NODE[ j]. SENDING) Is an invariant: g+1 t.k -1 time units Sending the last synchronization point before the conflict g t.k -g time units 15

16 Proving Sufficiency We proved the sufficiency part of the theorem by induction on the length of the system execution. 16

17 A Fully-Connected Network vs. A non-fully-connected one A B A B C C C C n n k k g g min min max max ratio ratio

18 Theorem A chain-shape h wireless sensor network is synchronized, if and only if the formula below would be hold (C.k - g + N - (C.k -1) 2) min < max 4 2 n 1 3 n 1 n 2 18

19 Conclusion & Future Work We studied the fully-connected as well as chainshaped wireless sensor networks and obtained formulas showing what relation between network parameters should be to have a synchronized network. Our formulas don t describe the behavior of a wireless sensor network of a general topology. Our challenge is describing the synchronization process of a general wireless sensor network. 19

20 Thank You????