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Analysis of routing protocols and interference-limited communication in large wireless networks via continuum modeling

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Abstract

The evaluation and assessment of the design of large wireless networks is an important problem in numerous applications. Direct simulation is a traditional approach for studying such networks but is severely limited in its utility as the size of the network increases. This necessitates other means for studying large networks, one of which is the modeling of large networks with continuum models. In this paper, we introduce nonlinear partial differential equations whose solutions approximate the expected behavior of large networks governed by probabilistic communication rules. The relative speed at which solutions can be obtained from the continuum models allows for the investigation of routing protocols and communication limitations due to interference—a feat that is not feasible via simulation methods. Specifically, we investigate the effects of a directed diffusion routing protocol and explore communication limitations in an interference-sensitive network. Network design studies using the approximating continuum models are then presented.

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References

  1. Chiasserini CF, Gaeta R, Garetto M, Gribaudo M, Manini D, Sereno M (2007) Fluid models for large-scale wireless sensor networks. Perform Eval 64(7–8): 715–736

    Article  Google Scholar 

  2. Chong EKP, Estep D, Hannig J (2007) Continuum modeling of large networks. Int J Numer Model Electron Netw Devices Fields 21(3): 169–186

    Article  Google Scholar 

  3. Hart JK, Martinez K (2006) Environmental sensor networks: a revolution in the earth system science?. Earth-Sci Rev 78(3–4): 177–191

    Article  ADS  Google Scholar 

  4. Estrin D, Govindan R, Heidemann J, Kumar S (1999) Next century challenges: scalable coordination in sensor networks. In: Proceedings of the 5th annual ACM/IEEE international conference on mobile computing and networking. ACM, New York, pp 263–270

  5. Lees JM, Johnson JB, Ruiz M, Troncoso L, Welsh M (2008) Reventador volcano 2005: eruptive activity inferred from seismo-acoustic observation. J Volcanol Geotherm Res 176(1): 179–190

    Article  ADS  Google Scholar 

  6. Werner-Allen G, Dawson-Haggerty S, Welsh M (2008) Lance: optimizing high-resolution signal collection in wireless sensor networks. In: Proceedings of the 6th ACM conference on embedded network sensor systems. ACM, New York, pp 169–182

  7. Tolle G, Polastre J, Szewczyk R, Turner N, Tu K, Buonadonna P, Burgess S, Gay D, Hong W, Dawson T, Culler D (2005) A macroscope in the redwoods. In: Proceedings of the 3rd international conference on embedded networked sensor systems. ACM, New York, p 63

  8. Akyildiz IF, Su W, Sankarasubramaniam Y, Cayirci E (2002) Wireless sensor networks: a survey. Comput Netw 38(4): 393–422

    Article  Google Scholar 

  9. Martinez K, Hart JK, Ong R (2004) Environmental sensor networks. Computer 37(8): 50–56

    Article  Google Scholar 

  10. Gamal HE (2005) On the scaling laws of dense wireless sensor networks: the data gathering channel. IEEE Trans Inf Theory 51(3): 1229–1234

    Article  Google Scholar 

  11. Toumpis S, Tassiulas L (2005) Packetostatics: deployment of massively dense sensor networks as an electrostatics problem. In: INFOCOM 2005. 24th Annual joint conference of the IEEE computer and communications societies. Proceedings IEEE, vol 4. IEEE, pp 2290–2301

  12. Toumpis S, Tassiulas L (2006) Optimal deployment of large wireless sensor networks. IEEE Trans Inf Theory 52(7): 2935–2953

    Article  MathSciNet  Google Scholar 

  13. Ganesan D, Krishnamachari B, Woo A, Culler D, Estrin D, Wicker S (2002) Complex behavior at scale: an experimental study of low-power wireless sensor networks. Technical report, Citeseer

    Google Scholar 

  14. Gupta P, Kumar PR (2000) The capacity of wireless networks. IEEE Trans Inf Theory 46(2): 388–404

    Article  MathSciNet  MATH  Google Scholar 

  15. Herdtner JD, Chong EKP (2005) Throughput-storage tradeoff in ad hoc networks. In: Proceedings IEEE INFOCOM 2005. 24th Annual joint conference of the IEEE computer and communications societies, vol 4

  16. Li J, Blake C, De Couto DSJ, Lee HI, Morris R (2001) Capacity of ad hoc wireless networks. In: Proceedings of the 7th annual international conference on mobile computing and networking. ACM, New York, p 69

  17. Xie LL, Kumar PR (2004) A network information theory for wireless communication: scaling laws and optimal operation. IEEE Trans Inf Theory 50(5): 748–767

    Article  MathSciNet  Google Scholar 

  18. Jain K, Padhye J, Padmanabhan VN, Qiu L (2005) Impact of interference on multi-hop wireless network performance. Wirel Netw 11(4): 471–487

    Article  Google Scholar 

  19. Klein DJ, Hespanha J, Madhow U (2010) A reaction-diffusion model for epidemic routing in sparsely connected MANETs. In: INFOCOM, 2010 proceedings IEEE. IEEE, pp 1–9

  20. Kalantari M, Shayman M (2004) Energy efficient routing in wireless sensor networks. In: Proceedings of conference on information sciences and systems, Citeseer

  21. Kalantari M, Shayman M (2004) Routing in wireless ad hoc networks by analogy to electrostatic theory. In: 2004 IEEE international conference on communications, vol 7. IEEE, pp 4028–4033

  22. Kalantari M, Haghpanahi M, Shayman M (2008) A p-norm flow optimization problem in dense wireless sensor networks. In: INFOCOM 2008. The 27th conference on computer communications. IEEE, pp 341–345

  23. Zhang Y, Chong EKP, Hannig J, Estep D (2010) On continuum limits of Markov chains and network modeling. In: 2010 49th IEEE conference on decision and control (CDC), pp 6779–6784. IEEE

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Authors and Affiliations

  1. Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, NC, 27709, USA

    Nathanial Burch

  2. Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO, 80523, USA

    Edwin K. P. Chong

  3. Department of Statistics, Colorado State University, Fort Collins, CO, 80523, USA

    Don Estep

  4. Department of Mathematics, Colorado State University, Fort Collins, CO, 80523, USA

    Edwin K. P. Chong & Don Estep

  5. Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599, USA

    Jan Hannig

Authors
  1. Nathanial Burch
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  2. Edwin K. P. Chong
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  3. Don Estep
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  4. Jan Hannig
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Correspondence to Nathanial Burch.

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Burch, N., Chong, E.K.P., Estep, D. et al. Analysis of routing protocols and interference-limited communication in large wireless networks via continuum modeling. J Eng Math 79, 183–199 (2013). https://doi.org/10.1007/s10665-012-9566-9

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  • DOI: https://doi.org/10.1007/s10665-012-9566-9

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