Silence is Golden with High Probability: Maintaining a Connected Backbone in Wireless Sensor Networks Paolo Santi* - PowerPoint PPT Presentation

* Istituto di Informatica e Telematica del CNR, Pisa, Italy

† Dept. of Computer Science, Univ. of Chicago, USA

• 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

• 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

Connectivity: WHY?

Active

Sleeping

Silence is Golden: 3/15

• 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

If the cell size is correctly chosen, connectivity is ensured

Silence is Golden: 4/15

• 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

A node can be:

• Energy for sensing and receiving GPS signal comparable to energy in the sleep state
• Our model:

sleeping 0.25

idle 1

receiving 1.006

transmitting 1.244

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

Silence is Golden: 6/15

• 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 l2/r2 square cells of r/22

With this setting, any two nodes in adjacentcells (horizontal, vertical,

diagonal) can communicate directly

Silence is Golden: 7/15

Assumptions: Every node knows:

• its cell ID;
• the ID of every other node in its cell

The leader election process starts at time Tr . Every step lasts Ts

Protocol for node i:

At time Tr + (i-1)Ts:

• turn radio on and receive message M = (Emax,m) from node i -1
• estimate available energy Ei
• Emax = max {Emax, Ei}
• if Emax = Ei then m i

At time Tr + iTs:

• send message (Emax ,m)
• turn radio off

Silence is Golden: 8/15

At time Tr + niTs: (niis the number of nodes in the cell of node i )

• turn radio on and receive message M=(Emax,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

Time diagram of FULL execution with different sleep periods: Emax/2C and Emax/C

Emax/C : cell lifetime = 391 time units; average per node lifetime: 248.5

Emax/ 2C : cell lifetime = 324 time units; average per node lifetime: 321.75

Silence is Golden: 10/15

Assumptions:

• initialization cost is disregarded
• no “external factor”

I.e., we estimate “The Cost of Silence”

Theorem 1:

Assume cell i contains ni nodes. Using the FULL protocol with sleep period set to Emax/2C, the cell lifetime is (ni Tb), where Tb is the baseline cell lifetime (with no cooperative strategy).

The FULL protocol is (worst-case) energy optimal

Silence is Golden: 11/15

Assumptions: Every node:

• knows its cell ID;
• can detect conflicts on the wireless channel

The leader election process starts at time Tr . Every iteration lasts Ts

Protocol for node i:

At time Tr :

Repeat until TERMINATION

• flip a coin with probability of success p
• if SUCCESS send message (Ei , 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

Ideally, we should set p=1/ni, where ni 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 ni 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 limn, l E [#S] = e .

Silence is Golden: 13/15

How many iterations are needed to elect the leader in every cell?

(Average-case analysis; N is the number of cells)

Assume p = 1/ni

• 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, Nk = N (1-(1-1/e)k) cells have elected the leader

With k = 10 we have N10 = 0.9898 N

Silence is Golden: 14/15

• 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