# Rechargeable sensor activation under temporally correlated events

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## Abstract

Wireless sensor networks are often deployed to detect “interesting events” that are bound to show some degree of temporal correlation across their occurrences. Typically, sensors are heavily constrained in terms of energy, and thus energy usage at the sensors must be optimized for efficient operation of the sensor system. A key optimization question in such systems is—how the sensor (assumed to be rechargeable) should be activated in time so that the number of interesting events detected is maximized under the typical slow rate of recharge of the sensor. In this article, we consider the activation question for a single sensor, and pose it in a stochastic decision framework. The recharge-discharge dynamics of a rechargeable sensor node, along with temporal correlations in the event occurrences makes the optimal sensor activation question very challenging. Under complete state observability, we outline a deterministic, memoryless policy that is provably optimal. For the more practical scenario, where the inactive sensor may not have complete information about the state of event occurrences in the system, we comment on the structure of the deterministic, history-dependent optimal policy. We then develop a simple, deterministic, memoryless activation policy based upon energy balance and show that this policy achieves near-optimal performance under certain realistic assumptions. Finally, we show that an aggressive activation policy, in which the sensor activates itself at every possible opportunity, performs optimally only if events are uncorrelated.

### Keywords

Rechargeable sensors Temporal correlations Node activation Energy efficiency### References

- 1.Jaggi, N., Kar, K., & Krishnamurthy, A. (2007). Rechargeable sensor activation under temporally correlated events. In
*Proceedings of the fifth intl. symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks*(WiOpt’07), Cyprus, Apr.Google Scholar - 2.Kansal, A., & Srivastava, M. B. (2005). Energy harvesting aware power management (book chapter). In
*Wireless sensor networks: A systems perspective*. Norwood, MA: Artech House.Google Scholar - 3.Raghunathan, V., Kansal, A., Hsu, J., Friedman, J., & Srivastava, M. (2005). Design considerations for solar energy harvesting wireless embedded systems. In
*Proceedings of the 4th IEEE/ACM Intl. Conference on Information Processing in Sensor Networks (IPSN) – Special Track on Platform Tools and Design Methods for Network Embedded Sensors (SPOTS)*(pp. 457–462). Los Angeles, CA, Apr.Google Scholar - 4.Kar, K., Krishnamurthy, A., & Jaggi, N. (2006). Dynamic node activation in networks of rechargeable sensors.
*IEEE/ACM Transactions on Networking, 14*(1), 15–26.CrossRefGoogle Scholar - 5.Jaggi, N., Krishnamurthy, A., & Kar, K. (2005). Utility maximizing node activation policies in networks of partially rechargeable sensors. In
*Proceedings of the 39th Annual Conference on Information Sciences and Systems (CISS)*, Baltimore, March.Google Scholar - 6.Jaggi, N. (2006). Robust threshold based sensor activation policies under spatial correlation. In
*Proceedings of the Fourth Intl. Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt’06)*(pp. 1–8). Boston, Apr.Google Scholar - 7.Akyildiz, I. F., Vuran, M. C., & Akan, O. B. (2004). On exploiting spatial and temporal correlation in wireless sensor networks. In
*Proceedings of the Second Intl. Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt’04)*(pp. 71–80). Cambridge, UK, Mar.Google Scholar - 8.Vuran, M. C., Akan, O. B., & Akyildiz, I. F. (2004). Spatio-temporal correlation: Theory and applications for wireless sensor networks.
*Elsevier Computer Networks, 45*(3), 245–261.MATHCrossRefGoogle Scholar - 9.Gastpar, M., & Vitterli, M. (2003). Source-channel communication in sensor networks. In
*Proceedings of the Second Intl. Workshop on Information Processing in Sensor Networks (IPSN)*(pp. 162–177). New York: Springer, Apr.Google Scholar - 10.Pattem, S., Krishnamachari, B., & Govindan, R. (2004). The impact of spatial correlation on routing with compression in wireless sensor networks. In
*Proceedings of ACM/IEEE International Symposium on Information Processing in Sensor Networks (IPSN)*(pp. 28–35). Berkeley, CA, Apr.Google Scholar - 11.Jaggi, N. (2007). Node activation policies for energy-efficient coverage in rechargeable sensor systems. In PhD. thesis. Rensselaer Polytechnic Institute: http://www.ecse.rpi.edu/homepages/koushik/Thesis_Jaggi.pdf, May.
- 12.Puterman, M. L. (1994).
*Markov decision processes – discrete stochastic dynamic programming*. NJ: John Wiley and Sons.MATHGoogle Scholar - 13.Cassandra, A. R., Kaelbling, L. P., & Littman, M. L. (1994). Acting optimally in partially observable stochastic domains. In
*Proceedings of the 12th National Conference on Artificial Intelligence (AAAI-94)*, vol. 2 (pp. 1023–1028). Seattle, Washington: AAAI Press/MIT Press.Google Scholar - 14.Gaucherand, E. F., Arapostathis, A., & Marcus S. I. (1991). On the average cost optimality equation and the structure of optimal policies for partially observable markov decision processes.
*Annals of Operations Research, 29*(1–4), 439–470.MATHCrossRefMathSciNetGoogle Scholar - 15.Wolff, R. (1989).
*Stochastic modeling and the theory of queues*. NJ: Prentice Hall.MATHGoogle Scholar - 16.Bertsekas, D. P. (2000).
*Dynamic programming and optimal control, volume I*. Belmont, MA: Athena Scientific.Google Scholar - 17.Bhat, U. N. (1984).
*Elements of applied stochastic processes*, 2nd edn. New York: John Wiley.MATHGoogle Scholar - 18.Puterman, M. (2005).
*Markov decision processes: Discrete stochastic dynamic programming*. NY: Wiley.Google Scholar - 19.Littman, M. L. (1994). Memoryless policies: Theoretical limitations and practical results. In
*From Animals to Animats 3: Proceedings of the Third International Conference on Simulation of Adaptive Behavior*(pp. 238–245). Brighton, UK: MIT Press.Google Scholar - 20.Shaked, M., & Shanthikumar, J. (1994).
*Stochastic orders and their applications*. NY: Academic Press.MATHGoogle Scholar