1. EWSN 04 – Berlin, Jan. 20, 2004 Silence is Golden with High Probability: Maintaining a Connected Backbone in Wireless Sensor Networks Paolo Santi* Janos Simon † * Istituto di Informatica e Telematica del CNR, Pisa, Italy † Dept. of Computer Science, Univ. of Chicago, USA

2. EWSN 04 – Berlin, Jan. 20, 2004 Introduction Energy conservation is fundamental in WSNs Wireless transceiver major source of energy consumption in the node Considerable energy can be saved by turning the radio off Example: (Medusa II node [Raghunathan et al. 02]) sleep:idle:rx:tx ratios = 0.25:1:1.006:1.244 Silence is Golden: 1/15

3. EWSN 04 – Berlin, Jan. 20, 2004 Cooperative strategies Node transceivers’ sleeping times must be coordinated Why? To preserve connectivity Cooperative strategy: distributed protocol that coordinates nodes’ sleeping times GOAL: Saving as much energy as possible while preserving connectivity Silence is Golden: 2/15

4. EWSN 04 – Berlin, Jan. 20, 2004 Application scenario Connectivity: WHY? Silence is Golden: 3/15 Sleeping Active

5. EWSN 04 – Berlin, Jan. 20, 2004 Cell-based strategies Introduced by Xu et al. in [Xu et al. – Mobicom 01], analyzed by Blough and Santi in [BloughSanti – Mobicom 02] Idea (GAF protocol [Xu et al. 01]): – divide the deployment region into equal cells; – leave an active node for each cell Silence is Golden: 4/15 If the cell size is correctly chosen, connectivity is ensured

6. EWSN 04 – Berlin, Jan. 20, 2004 Our contribution Two simple cell-based coordination algorithms: deterministic and randomized The algorithms use: – location information (as in GAF) – loose synchronization (additional requirement) Good news: these features are likely to be available in WSNs The algorithms are asymptotically energy optimal: – in the worst case (deterministic algorithm) – on the average (randomized algorithm) Knowledge vs. performance tradeoff Silence is Golden: 5/15

7. EWSN 04 – Berlin, Jan. 20, 2004 The energy model A node can be: Energy for sensing and receiving GPS signal comparable to energy in the sleep state Our model: Silence is Golden: 6/15 sleeping0.25 idle1 receiving1.006 transmitting1.244 C units of energy per time unit when idle/rx/tx c << C units of energy per time unit when sleeping (and sensing). For simplicity, c=0

8. EWSN 04 – Berlin, Jan. 20, 2004 The system model n sensors are deployed in a square region of side l All sensors have the same transmitting range r << l Deployment region divided into N = 8 l 2 /r 2 square cells of r/2  2 With this setting, any two nodes in adjacent cells (horizontal, vertical, diagonal) can communicate directly Silence is Golden: 7/15

9. EWSN 04 – Berlin, Jan. 20, 2004 The FULL protocol Assumptions: Every node knows: – its cell ID; – the ID of every other node in its cell The leader election process starts at time T r. Every step lasts T s Protocol for node i: At time T r + (i-1)T s : – turn radio on and receive message M = (E max,m) from node i -1 – estimate available energy E i – E max = max {E max, E i } – if E max = E i then m  i At time T r + i T s : – send message (E max,m) – turn radio off Silence is Golden: 8/15

10. EWSN 04 – Berlin, Jan. 20, 2004 The FULL protocol (2) At time T r + n i T s : (n i is the number of nodes in the cell of node i ) – turn radio on and receive message M=(E max,m); m is the leader for the next sleep period – if i <> m turn the radio off The protocol is re-executed after a certain sleep period Why the sleep period? To balance energy consumption Silence is Golden: 9/15

11. EWSN 04 – Berlin, Jan. 20, 2004 Choosing the sleep period Time diagram of FULL execution with different sleep periods: E max /2C and E max /C E max /C : cell lifetime = 391 time units; average per node lifetime: 248.5 E max / 2C : cell lifetime = 324 time units; average per node lifetime: 321.75 Silence is Golden: 10/15

12. EWSN 04 – Berlin, Jan. 20, 2004 Analysis Assumptions: – initialization cost is disregarded – no “external factor” I.e., we estimate “The Cost of Silence” Theorem 1: Assume cell i contains n i nodes. Using the FULL protocol with sleep period set to E max /2C, the cell lifetime is  (n i T b ), where T b is the baseline cell lifetime (with no cooperative strategy). The FULL protocol is (worst-case) energy optimal Silence is Golden: 11/15

13. EWSN 04 – Berlin, Jan. 20, 2004 The RANDOM protocol Assumptions: Every node: – knows its cell ID; – can detect conflicts on the wireless channel The leader election process starts at time T r. Every iteration lasts T s Protocol for node i: At time T r : Repeat until TERMINATION – flip a coin with probability of success p – if SUCCESS send message (E i, i ) – if nobody sent a message or COLLISION, go to next iteration – TERMINATION=True; if not SUCCESS turn the radio off Silence is Golden: 12/15

14. EWSN 04 – Berlin, Jan. 20, 2004 Setting the value of p Ideally, we should set p=1/n i, where n i is the number of nodes in the cell WHY? Because with this setting the expected number of iterations #S is minimized: E [#S] = e (  2.718) (Optimal in expectation) What if n i is not known? If n is known, and nodes are distributed uniformly at random, we still have E [#S] = e Theorem 2: Assume n nodes are distributed uniformly in [0, l ] 2, and set p to the expected number of nodes in a cell. If r is appropriately chosen, then lim n, l  E [#S] = e. Silence is Golden: 13/15

15. EWSN 04 – Berlin, Jan. 20, 2004 Network-wide analysis How many iterations are needed to elect the leader in every cell? (Average-case analysis; N is the number of cells) Assume p = 1/n i - N/e cells elect the leader in the first iteration; - N(1-1/e)/e cells elect the leader in the second iteration; …. After k steps, N k = N (1-(1-1/e) k ) cells have elected the leader With k = 10 we have N 10 = 0.9898 N Silence is Golden: 14/15

16. EWSN 04 – Berlin, Jan. 20, 2004 Conclusion and future work We have presented two simple algorithms for cell-based node coordination in WSNs Our algorithms can be a starting point for real implementations of cell-based energy conservation Future work: – change p depending on the node’s energy level – change p depending on the duration of the previous election Silence is Golden: 15/15