1 Rendezvous Design Algorithms for Wireless Sensor Networks with a Mobile Station Guoliang Xing; Tian Wang; Weijia Jia; Minming Li Department of Computer Science City University of Hong Kong

2 Outline Motivation Problem formulation Rendezvous design algorithms –Free mobility model –Limited mobility model Simulations Conclusion

3 Challenges for Data-intensive Sensing Applications Many applications are data-intensive –Structural health monitoring 30 min/day, 80Gb/year –Micro-climate and habitat monitoring Acoustic & video, 10 min/day, 1Gb/year Most sensor nodes are powered by batteries A tension exists between the sheer amount of data generated and the limited power supply

4 Mobility-assisted Data Collection Mobile nodes collect data via short-range communications Mobile nodes are less power-constrained –Can move to wired power sources Base Station 500K bytes 100K bytes 150K bytes 5 mins 10 mins 5 mins

5 Mobile Sensor Platforms Low movement speed (0.1~2 m/s) –Increased latency of data collection –Reduced network capacity Networked Infomechanical Systems CENS, UCLA USC [Dantu05robomote] Yale enalab/XYZ/

6 Static vs. Mobile All-static networks Mobility-assisted Networks DelayLowHigh Energy Consumption High nonreplenishable High replenishable BandwidthMediumMedium to high

7 Rendezvous-based Data Collection Some nodes serve as “rendezvous points” (RPs) –Other nodes send their data to the closest RP –Mobiles visit RPs and transport data to base station Advantages –In-network caching + controlled mobility –Mobiles can collect a large volume of data at a time –Minimize disruptions due to mobility Mobiles contact static nodes at RPs at scheduled time

8 mobile node rendezvous point Rendezvous-based Data Collection source node Some nodes serve as “rendezvous points” (RPs) –Others nodes send data to the closest RP –Mobiles visit RPs and carry data to base station Advantages –In-network caching + controlled mobility –Minimize disruptions due to mobility

9 Outline Motivation Problem formulation Rendezvous design algorithms –Free mobility model –Limited mobility model Simulations Conclusion

10 The Rendezvous Design Problem Choose RPs s.t. mobile nodes can visit all RPs within data collection deadline Total network energy of transmitting data from sources to RPs is minimized Joint optimization of positions of RPs, mobile motion paths, and data routes

11 Assumptions Only one mobile, moves at speed v Mobile picks up data at locations of nodes Data from two sources can be aggregated Data collection deadline is D –User requirement: “report every 10 minutes and the data is sampled every 10 seconds” –Recharging period: e.g., Robomotes powered by 2 AA batteries recharge every ~30 minutes

12 Geometric Network Model Transmission energy is proportional to distance Base station, source nodes and RPs are connected by straight lines a multi-hop route is approximated by a straight line source nodes Source nodes approximated data route real data route Non-source nodes Rendezvous points

13 The Rendezvous Design Problem Given a base station B, and sources { s i }, find trees T i ( V i, E i ), and a tour visiting the roots of T i such that 1) the tour is no longer than L; 2) the total edge length of T i is minimized R1R1 s1s1 s5s5 s4s4 B s2s2 s3s3 R2R2 R3R3 R4R4 s6s6 Hardness General case is NP-Hard When L=0, the opt solution is Steiner Min Tree that connects {B} U { s i }

14 Outline Motivation Problem formulation Rendezvous design algorithms –Free mobility model –Limited mobility model Simulations Conclusion

15 An Approx. Algorithm Find an approx. Steiner Min Tree for { B } U { s i } Depth-first traverses the tree until covers L/2 edge length

16 An Improved Algorithm 1. Find T -- an approx. SMT for { B } U { s i } 2. Y=L/2; 3. Depth-first traverses T from B until cover Y length, denote I as the set of current RPs 4. if X = L − TSP(I) > δ Y=Y+X/2; goto 3; else exit; TSP(I) – the length of tour visiting points in set I, computed by a Traveling Salesman Problem solver

17 Illustration 1. Find T - an approx. Steiner min tree of {B} U {s i } 2. Y=L/2; 3. Depth-first traverse T from B until cover Y length, denote I as the set of border points 4. if X = L − TSP(I) > δ Y=Y+X/2; goto 3; else exit;

18 Approx. Ratio The approximation ratio of the algorithm is α+β(2α-1)/2(1-β) –α is the best approximation ratio of the Steiner Minimum Tree problem –β = L / SMT(BS + Sources) –Assume L << SMT(BS + Sources)

19 Outline Motivation Problem formulation Rendezvous design algorithms –Free mobility model –Limited mobility model Simulations Conclusion

20 Illustration The mobile only moves along a fixed track Track of Mobile XYZ Yale source node rendezvous point

21 Theoretical Results An MST-based approximation algorithm Approximation ratio is 2(1+3 β)/sqrt(3) –β = ∆L/c(MST opt ) –∆L is a user-specified constant –c(MST opt ) is cost of the optimal Min Spanning Tree connecting sources to the track

22 Simulation Results 100 sources are randomly distributed in a 300m X 300m field, base station is on the left corner Each source generates 2 bytes/s, deadline is 20 mins

23 Conclusions Rendezvous-based data collection for WSNs w/ a mobile base station –In-network caching + controlled mobility –Problem formulations under both free/limited mobility models Two graph-theoretical rendezvous algos –Provable performance bounds –Simulation-based evaluation

24 Geometric Network Model Transmission energy is proportional to distance Base station, source nodes and branch nodes are connected with straight lines a multi-hop route is approximated by a straight line Source nodes approximated data route real data route Non-source nodes Branch nodes Rendezvous points a branch node lies on two or more source- to-root routes

25 Problem Formulation Given a tree T(V,E) rooted at B and sources {s i }, find RPs, {R i }, and a tour no longer than L=vD that visits {B}U{R i }, and The problem is NP-hard (reduction from the Traveling Salesman Problem) d T (s i,R i ) – the on-tree distance between s i and R i

26 Illustration of Problem Formulation Objective –Minimize edge length of routing tree Constraint –Tour length ≤ L Source nodes Rendezvous pointsdata route branch nodes

27 Proof Sketch I A* is opt solution R={B} U {R i } S={B} U {S i } T is the tree used in input SMT(X) - SMT connecting points in set X TSP*(X) - length of the shortest tour visiting points in R R1R1 R2R2 R3R3 B

28 Proof Sketch II R1R1 R2R2 R3R3 B A* U SMT(R) is a Steiner tree connecting S: c(A*) + c(SMT(R)) ≥ c(SMT(S)) SMT is a lower bound of TSP problem: c(SMT(R)) < c(TSP*(R)) ≤ L  c(A*) > c(SMT(S)) – L > c(T)/ α - L Our solution = c(T)-L/2 S1S1 S2S2 S3S3 S4S4 S5S5