Dynamic Node Activation in Networks of Rechargeable Sensors

1. Dynamic Node Activation in Networks of Rechargeable Sensors KoushikKar, Ananth Krishnamurthy and NeerajJaggi2006 – IEEE/ACM Transactions on Networking

2. Motivation • rechargeable sensors spend a lot of time recharging • not available for sensing • recharging usually take much longer than discharging • solution? redundant deployment • works like this: • while some sensors sleep… • …others are fully charged and ready for sensing. • reasoning: • if a large number of sensors are deployed • it is more likely that one will be available for sensing when needed • questions to answer… • where is the line of diminishing returns from adding more sensors? • when should charged and waiting sensors be switched on for sensing?

3. Given: • a stationary network of rechargeable sensors • fixed locations in fixed coverage area • sensors are offline during recharge

4. Find: • a sensor activation policy • when to become active • apply globally • configure locally • maximize the “utility” derived from the network • measure of the network’s benefit • in terms of utility per unit areaper unit time from N active sensors over area A • example: probability of detection • U(n) = 1 − (1 − pd)n

5. Contributions: • Demonstrate that utility, resulting from switching sensors on and off at the right times, can be modeled as a queuing network • This model can be solved using a steady-state Markov chain analysis if a threshold activation policy solution class is used • Show that the time-average utility of an optimal threshold activation policy is at least ¾ of the upper bound • Show that this solution holds both for completely redundant coverage and for partially overlapping sensor coverage • Show that correlation of charge/discharge cycles significantly degrades network utility

6. Activation as queuing network… • Sensor may be in one of 3 states • passive = switched off, charging • ready = charged & waiting • active = sensing and transmitting

7. Activation as queuing network… • Activation from passive state • passive (charged) sensors in region queue up to become active • active sensors deplete their energy and need replacement from the queue • Charging behavior affects model • correlated = charge/discharge cycles synchronized • independent = charge/discharge cycles randomized

8. Optimize network for “utility” • “Utility” = measure of effectiveness • utility under policy P is: U(P) = • for motivating example… • Use: probability of detection • U(n) = 1 − (1 − pd)n • where n is number of active sensors in area, A, at time, t, under policy P • Problem restated… • find the policy, P • such that the utility of the network is maximized

9. Simplify the problem… • Problem is intractable as stated… • Simplifying assumptions (for analysis): • sensor distribution is completely redundant • utility curve is concave down (asymptotic limit) • recharge rate << discharge rate • no energy is lost in passive (ready) state • activation will be based upon a threshold policy

10. Toeholds from the simplification… • Domain is reduced • from all activation policies • to onlythreshold activation policies • if number of sensors does not exceed m • activate ready sensor, s • Utility is simplified • was integral over Area and time • now, only integral over time • Analytical tools can be used • steady-state Markov decision problem • upper and lower bounds on utility may be calculated

11. Theoretical bounds on utility • Maximum utility for all policies • where • N is number of sensors • mu(1) is recharge time • mu(2) is discharge time • Minimum utility • ½ Maximum

12. Bounds on threshold policies • Lower bound for correlated charge cycles • UT,C ≥ ¾ of maximum bound • thus best threshold policy is at least ¾ of optimum • Lower bound for independent charge cycles • UT,I ≥ UT,C ≥ ¾ of optimal policy • independent charge cycles will be as good or better than correlated charge cycles

13. Finding a threshold • Given the utility function • probability of detection • U(n) = 1 − (1 − pd)n • Find utility vs. threshold for… • prob of detection, pd= {0.1, 0.9} • num of sensors, N = {16, 32, 48} • charge/ discharge ratio, rho = {3, 7, 15} • variable discharge rate, mu(2) • constant charge rate, mu(1)

14. Activation algorithm • Objective • maintain utility of U(m) • At each decision point, for each sensor • if local utility < U(m) then • activate • else • remain ready • Calculate local utility • know coverage area of neighbors (have map) • poll for neighbors’ activation state • calculate utility per …

15. Partial coverage overlap • Optimal time-average utility • where • N(A) = number of active sensors in area A

16. Results