Evaluation of an Algorithm used in Routing and Service Discovery Protocols of Wireless Sensor Networks The Trickle Algorithm

Transcription

1 Evaluation of an Algorithm used in Routing and Service Discovery Protocols of Wireless Sensor Networks The Trickle Algorithm Markus Becker ComNets, TZI, University Bremen, Germany 19th of October 2012 Becker: FFV, TUHH, October / 29

2 Outline IETF Protocol Stack for Wireless Sensor Networks Routing Protocol for Low power and Lossy Networks Trickle Algorithm Simulation Analytical Model Evaluation Conclusions & Outlook Becker: FFV, TUHH, October / 29

3 The Internet Engineering Task Force protocol stack for Wireless Sensor Networks Becker: FFV, TUHH, October / 29

4 The Internet Engineering Task Force protocol stack for Wireless Sensor Networks USB WSN node Border Router Node Border Router Host Internet Host 6LoWPAN: IPv6 over Low power Wireless Personal Area Network AM: Active Messaging CoAP: Constrained Application Protocol IP: Internet Protocol MAC: Medium Access Control PHY: Physical Layer PPP: Point-to-Point Protocol RPL: Routing Protocol for Low power and Lossy Networks TCP: Transmission Control Protocol UDP: User Datagram Protocol WSN: Wireless Sensor Network Becker: FFV, TUHH, October / 29

5 The Internet Engineering Task Force protocol stack for Wireless Sensor Networks PPP Interface USB WSN node Border Router Node Border Router Host Internet Host 6LoWPAN: IPv6 over Low power Wireless Personal Area Network AM: Active Messaging CoAP: Constrained Application Protocol IP: Internet Protocol MAC: Medium Access Control PHY: Physical Layer PPP: Point-to-Point Protocol RPL: Routing Protocol for Low power and Lossy Networks TCP: Transmission Control Protocol UDP: User Datagram Protocol WSN: Wireless Sensor Network Becker: FFV, TUHH, October / 29

6 The Internet Engineering Task Force protocol stack for Wireless Sensor Networks PPP Interface USB WSN node Border Router Node Proxy Internet Host 6LoWPAN: IPv6 over Low power Wireless Personal Area Network AM: Active Messaging CoAP: Constrained Application Protocol IP: Internet Protocol MAC: Medium Access Control PHY: Physical Layer PPP: Point-to-Point Protocol RPL: Routing Protocol for Low power and Lossy Networks TCP: Transmission Control Protocol UDP: User Datagram Protocol WSN: Wireless Sensor Network Becker: FFV, TUHH, October / 29

7 Routing Protocol for Low power and Lossy Networks IETF RFC 6206 and RFC 6206: The Trickle Algorithm RFC 6550: Routing Protocol RPL RFC 6551: Routing Metrics RFC 6552: Objective Function RFC 6553: IPv6 Option for RPL RFC 6554: IPv6 Routing Header for RPL Low power and Lossy Networks (LLN) consist Border Router (BR), Router (R) and Host (H) nodes H choose only the default router RPL operates only within an LLN and terminates at BR Proactive distance-vector approach, uses graph structure Becker: FFV, TUHH, October / 29

8 RPL: Upward Routes DIO: Destination-Oriented Directed Acyclic Graph Information Object DIO announces upward routes (Routes to the BR) DIOs are sent using the Trickle algorithm (RFC 6206) Becker: FFV, TUHH, October / 29

9 Trickle Algorithm: Variables and Constants Variables τ Communication interval length T Timer value in range [τ/2, τ] C Communication counter Constants K Redundancy constant τ L Lowest τ τ H Highest τ Note: Notation according to the original Trickle paper: P. Levis, N. Patel, D. Culler, S. Shenker: Trickle: A Self-Regulating Algorithm for Code Propagation and Maintenance in Wireless Sensor Networks in NSDI 04 Proceedings. Becker: FFV, TUHH, October / 29

10 Trickle Algorithm: Rules τ expires Double τ, up to τ H, pick a new T from range [τ/2, τ] T expires If C < K, transmit Received consistent data Increment C Received inconsistent data Set τ to τ L. Reset C to 0, pick a new T from [τ/2, τ] Becker: FFV, TUHH, October / 29

11 Simulation Scenarios Line scenario with Closest Pattern Matching Propagation Model ( Line-CPM ) Grid scenario ( Grid ) Varying number of nodes Varying inter-node distances / scenario size Becker: FFV, TUHH, October / 29

12 Simulation Execution TinyOS application with 6LoWPAN implementation blip Simulation tool TOSSIM blip extended for simulations Monte-Carlo iterations for each scenario instance Becker: FFV, TUHH, October / 29

13 Analytical Models Number of Messages Consistency Time Becker: FFV, TUHH, October / 29

14 Analytical Models Number of Messages Consistency Time Becker: FFV, TUHH, October / 29

15 Trickle Algorithm Trickle algorithm in Line-Direct scenario: 0. Hop 1. Hop 2. Hop 3. Hop 0 τ L Becker: FFV, TUHH, October / 29

16 Analytical Model: Consistency Time Modelling consistency time for the Line scenario (1) 0. Hop: No Delay 1. Hop: Uniformly distributed delay 2. Hop: Addition of 2 uniformly distributed delays -> Triangle 3. Hop: Addition of 1 uniformly distributed delay and triangle τl 2τL 3τL τl 2τL 3τL τl 2τL 3τL τl 2τL 3τL Central limit theorem: mean of summation of i.i.d. random variables, each with finite mean and variance, will be approximately normally distributed Becker: FFV, TUHH, October / 29

17 Analytical Model: Consistency Time Modelling consistency time for the Line scenario (1) 0. Hop: No Delay 1. Hop: Uniformly distributed delay 2. Hop: Addition of 2 uniformly distributed delays -> Triangle 3. Hop: Addition of 1 uniformly distributed delay and triangle τl 2τL 3τL τl 2τL 3τL τl 2τL 3τL τl 2τL 3τL Central limit theorem: mean of summation of i.i.d. random variables, each with finite mean and variance, will be approximately normally distributed (1/4) 1/4 1/4 1/4 τl 2τL 3τL 1 τl 2τL 3τL Becker: FFV, TUHH, October / 29

18 Analytical Model: Consistency Time The probability density function (pdf) of the time to consistency scenario can be modeled in detail by p(t) = 1 N 1 C 1 N 1 N f h,c,a (t) p h,c,a (t), where h=0 c=0 a=1 h: hops c: Trickle cycle a: number of 1-hop ancestors closer to source N: total number of nodes C: maximum number of Trickle cycles to take into account Becker: FFV, TUHH, October / 29

19 Analytical Model: Consistency Time p(t) = 1 N N 1 C 1 N 1 h=0 c=0 a=1 f h,c,a (t) p h,c,a (t), where δ(t), h = 0, L 1 {L{Θ(t τ L 2 ) Θ(t τ L )} h }, h 1, c = 0 Θ(t τ L (2 c+1 1) τ L f h,c,a=1 (t) = 2 2 c ) Θ(t τ L (2 c+1 1)), h = 1, c 0 L 1 {L{Θ(t τ L 2 ) Θ(t τ L )} h c L{Θ(t 2τ L ) Θ(t 3τ L )} c }, h > 1, 0 < c < h. Θ( ) denotes the Heaviside step function. L denotes the Laplace transform and L 1 denotes the inverse Laplace transform. Becker: FFV, TUHH, October / 29

20 Analytical Model: Consistency Time f h,c,a (t) p(t) Distributions p h,c,a (t) h=1, a=0 c= p(t) Distributions p h,c,a (t) c=0, a=0 h= t [s] Time t [s] Becker: FFV, TUHH, October / 29

21 Analytical Model: Consistency Time f h,c,a (t) Distributions p h,c,a (t) c=0 p(t) h=0, a=0 h=0, a=1 h=0, a=2 h=1, a=0 h=1, a=1 h=1, a=2 h=2, a=0 h=2, a=1 h=2, a=2 h=3, a=0 h=3, a=1 h=3, a=2 h=4, a=0 h=4, a=1 h=4, a=2 h=5, a=0 h=5, a=1 h=5, a=2 h=6, a=0 h=6, a=1 h=6, a=2 h=7, a=0 h=7, a=1 h=7, a=2 h=8, a=0 h=8, a=1 h=8, a=2 The distribution for a 1 can be calculated from the cdf given by 1 (1 P(X x)) a of the cdf for a = Time t [s] Becker: FFV, TUHH, October / 29

22 Analytical Model: Consistency Time f h,c,a (t) Distributions p h,c,a (t) h=2, a=0 c= Distributions p h,c,a (t) h=3, a=0 c= p(t) p(t) Time t [s] Time t [s] Figure: Probability Density Function for h = 2, a = 0, c varied Figure: Probability Density Function for h = 3, a = 0, c varied Becker: FFV, TUHH, October / 29

23 Analytical Model: Consistency Time p h,c,a (t) Packet Receive Ratio 0.80 PRR1 PRR1 PRR PRR2 PRR3 PRR2 PRR Distance [m] Becker: FFV, TUHH, October / 29

24 Algorithm for Analytical Model calc_base_dists() calc_prr() calc_neigh(prr) calc_tx_outcomes(neighbors, prr) calc_hopcounts(prr, inject_node, trickle_k, neighbors, scenario) calc_hopcounts_next_cycles(hopcounts) calc_neighbors_hop_closer(hopcounts, prr, trickle_k) calc_prob_mix_from_hopcount(hopcounts) calc_timeseries(prob_mix, distributions) plot_graphs(timeseries) Becker: FFV, TUHH, October / 29

25 Simulation & Analytical Model: Parameters The Trickle settings for the following results are: τ L = 2 s τ H = 32 s K = 1, 3, or 9 Becker: FFV, TUHH, October / 29

26 Simulation & Analytical Model: Line 9, K = 1 Nodes consistent P(T t) Model Time to Consistency (cdf) (#Nodes: 9, K: 1) Model Time t [s] Distance [m] analytical simulated Becker: FFV, TUHH, October / 29

28 Nodes consistent P(T t) Simulation & Analytical Model: Line 9, K = 9 Model Time to Consistency (cdf) (#Nodes: 9, K: 9) Model Time t [s] Distance [m] analytical simulated Becker: FFV, TUHH, October / 29

31 Simulation & Analytical Model: Grid 9, K = 3 Nodes consistent P(T t) Model Time to Consistency (cdf) (#Nodes: 9, K: 3) Model Time t [s] Distance [m] analytical simulated Becker: FFV, TUHH, October / 29

32 Simulation results and 95% confidence intervals Nodes consistent P(T t) Model Time to Consistency (cdf) (#Nodes: 9, K: 3) 95 % Confidence Interval Distance [m] Model Time t [s] Becker: FFV, TUHH, October / 29

33 Trickle/Push Comparison Trickle Push t push = 3 s t push = 5 s t push = 39 s t 95% 29.4 s 27.9 s 36.4 s s t max 34.9 s 33.0 s 47.0 s s Packets until consistent Packets in steady state s s 20 1 s s Trickle Settings: τ L = 2s, τ H = 32s, K =3 Scenario: Grid with 100 nodes Becker: FFV, TUHH, October / 29

34 Conclusions & Outlook Conclusions Implemented and studied the Trickle algorithm Important algorithm for RPL and distribution of other information Distributes faster and more-efficient than fixed-interval pushing First analytical model of Trickle algorithm Model for delay distribution was shown here Model for number of sent packets exists as well Analytical delay model fits simulation results Outlook Execute measurements and compare against simulation and analytical model Becker: FFV, TUHH, October / 29