In this paper, we propose an enhanced information delivery scheme, FAMIDS, suitable for general applications of resource-restricted wireless sensor networks. Since FAMIDS adopts the concept of packet splitting schemes, and incorporate lightweight security mechanisms, it simultaneously gains the advantages of fault tolerance and information security. We also propose detailed analysis of the communication reliability achieved by FAMIDS. The communication reliability is first derived as an analytical form R(m, n) and is analyzed under four different network models: the simple model, the ideal model, the general model and the special model. For each network model, we derive fundamental theorems to help us understand the behavior of R(m, n) and propose an algorithm separately to determine the optimal (m, n) set with highest communication reliability. From the analysis results of each network model, we can draw some important conclusions:
1) For any kind of network, one achieves the maximum communication reliability only when total available paths are used for packet transmission.
2) Transmitting the original packet with the maximum information expansion ratio can not always achieve the best reliability. The reason is that packet splitting causes a drastic gain of link success probability when the BER of the sensing circumstance is relative high. The communication reliability is greatly benefited from packet splitting under such condition.
3) The optimal solution with the highest communication reliability for total N paths can only be (m, N) FAMIDS, 1≤ m≤η2, where η2 =
⎣ ⎦
n 2 . Under the circumstance of low link failure rate or high node failure rate, the advantages achieved by packet splitting are then diminished, and thus the candidate set canbe further reduced.
However, there is still no efficient way in the literature to estimate the node failure rate accurately, especially when the adversaries exist. Besides, the base station can make use of the incorrectly received sub-packets to detect the situation of node compromise, and provide a more secure network environment. We leave these challenges as our future work. In addition, although packet splitting mechanism achieves the advantage of fault tolerance, it increases the probability of network congestion simultaneously. Many schemes in the literature consider the problem of network congestion in various networks [4],[5],[16],[17]. We can further combine FAMIDS with some congestion control scheme to achieve better utilization of network bandwidth.
Appendix
A. Proof of Theorem 4.1
0 ) 1
( )
1 , 1 ( ) ,
(m m −R m+ m+ =Ps,1×Ps,2× ×Ps,m× −Ps,(m+1) >
R L
∴R(m,m)>R(m+1,m+1) for 1≤m≤N−1
B. Proof of Theorem 4.2
R(m ,n+1)-R(m ,n)=Ps(n+1)×Pr{any m-1 paths success among P1~Pn}>0
∴R(m,n)<R(m,n+1) for 1≤n≤ N−1, 1≤m≤n
C. Proof of Theorem 4.3
By the definition of R(m,n),
R(m, n)-R(m+1, n)= Pr {m paths success}>0 Î R(m,n)>R(m+1,n)
D. Proof of Theorem 4.4
∵ R(m, n) =
∑ ( )
=n ⋅ − −
m j
m m j
s F j
P, 1 1
R(m, n+1)=
∑
+( )
=1 , ⋅ −1 −1
n
m j
m m j
s F j
P
∴ R(m, n+1)-R(m, n)= mPs,n+1 ⋅Fm−1
( )
n >0 Æ R(m, n+1) > R(m, n)E. Proof of Theorem 4.5
( ) ( )
∴
( ) [ ( ) ]
Here we analyze two special cases of Pn as follows: (Corollary 3 & Corollary 4)
1) 1
P Î R(1,n) is the optimal solution.
2) 1
2 is the optimal solution.
H. Proof of Theorem 4.9
Let ).γ(Ps)≡R(m,n)−R(m+1,n
We use the same definition of γ(P) as Theorem 4.4.
For PnÆ0+, we have known that R(1,n) is the optimal solution when P
∴ nÆ 0+
63
References
[1] J. N. Al-Karaki and A. E. Kamal, "Routing techniques in wireless sensor networks: a survey," Wireless Communications, IEEE [see also IEEE Personal Communications], vol. 11, pp. 6-28, 2004.
[2] E. Ayanoglu, C.-L. I, R. D. Gitlin, and J. E. Mazo, "Diversity coding for transparent self-healing and fault-tolerant communication networks,"
Communications, IEEE Transactions on, vol. 41, pp. 1677-1686, 1993.
[3] S. Dulman, T. Nieberg, J. Wu, and P. Havinga, "Trade-off between traffic overhead and reliability in multipath routing for wireless sensor networks,"
presented at Wireless Communications and Networking, 2003. WCNC 2003.
2003 IEEE, 2003.
[4] C. T. Ee and R. Bajcsy, "Congestion control and fairness for many-to-one routing in sensor networks," in Proceedings of the 2nd international conference on Embedded networked sensor systems Baltimore, MD, USA ACM Press, 2004 pp. 148-161
[5] R. Jain, S. Kalyanaraman, S. Fahmy, R. Goyal, and S.-C. Kim, "Source behavior for ATM ABR traffic management: an explanation," Communications Magazine, IEEE, vol. 34, pp. 50-56, 1996.
[6] M. Y. Kemal Akkaya, "A survey on routing protocols for wireless sensor networks," Ad Hoc Networks, Elsevier, pp. 325-349, 2003.
[7] M. K. Marina and S. R. Das, "On-demand multipath distance vector routing in ad hoc networks," presented at Network Protocols, 2001. Ninth International Conference on, 2001.
[8] Z. J. H. Panagiotis Papadimitratos, "Secure message transmission in mobile ad hoc networks," Ad Hoc Networks, Elsevier, pp. 193-209, 2003.
[9] M. O. Rabin, "Efficient dispersal of information for security, load balancing, and fault tolerance," J. ACM vol. 36 pp. 335-348 1989
[10] S.-P. Shieh, Y.-C. Tsai, and Y.-L. Huang, "Optimal information-dispersal for fault-tolerant communication over a burst-error channel," Reliability, IEEE Transactions on, vol. 52, pp. 354-366, 2003.
[11] J. A. Stankovic, T. E. Abdelzaher, C. Lu, L. Sha, and J. C. Hou, "Real-time communication and coordination in embedded sensor networks," Proceedings of the IEEE, vol. 91, pp. 1002-1022, 2003.
[12] H.-M. Sun and S.-P. Shieh, "Optimal information-dispersal for increasing the reliability of a distributed service," Reliability, IEEE Transactions on, vol. 46, pp.
462-472, 1997.
[13] A. Tsirigos and Z. J. Haas, "Analysis of multipath routing, part 2: mitigation of the effects of frequently changing network topologies," Wireless Communications, IEEE Transactions on, vol. 3, pp. 500-511, 2004.
[14] A. Tsirigos and Z. J. Haas, "Analysis of multipath Routing-Part I: the effect on the packet delivery ratio," Wireless Communications, IEEE Transactions on, vol.
3, pp. 138-146, 2004.
[15] M. A. M. Vieira, C. N. Coelho, Jr., D. C. da Silva, Jr., and J. M. da Mata,
"Survey on wireless sensor network devices," presented at Emerging Technologies and Factory Automation, 2003. Proceedings. ETFA '03. IEEE Conference, 2003.
[16] C.-Y. Wan, S. B. Eisenman, and A. T. Campbell, "CODA: congestion detection and avoidance in sensor networks," in Proceedings of the 1st international conference on Embedded networked sensor systems Los Angeles, California, USA ACM Press, 2003 pp. 266-279
[17] A. Woo and D. E. Culler, "A transmission control scheme for media access in
sensor networks ," in Proceedings of the 7th annual international conference on Mobile computing and networking Rome, Italy ACM Press, 2001 pp. 221-235 [18] S. Zhu, S. Setia, and S. Jajodia, "LEAP: efficient security mechanisms for
large-scale distributed sensor networks," in Proceedings of the 10th ACM conference on Computer and communications security Washington D.C., USA ACM Press, 2003 pp. 62-72
[19] L. Gargono, A. A. Rescigno, and U. Vaccaro, "Fault-tolerant hypercube broadcasting via information dispersal," Networks, vol. 23, pp. 271-282, 1993.
[20] Y. D. Lyuu, "Fast fault-tolerant parallel communication for de Bruijn and digit-exchange networks using information dispersal," Networks, vol. 23, pp.
365-378, 1993.
[21] D. Ganesan, R. Govindan, S. Shenker, D. Estrin, "Highly-Resilient, Energy-Efficient Multipath Routing in Wireless Sensor Networks," Networks, vol. 23, pp. 271-282, 1993.
[22] D. Ganesan, R. Govindan, S. Shenker, and D. Estrin, "Highly-resilient, energy-efficient multipath routing in wireless sensor networks," SIGMOBILE Mob. Comput. Commun. Rev. , vol. 5, pp. 11-25, 2001.