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Packets travelling in non-homogeneous networks

Published: 31 October 2011 Publication History

Abstract

This paper considers a probability model for travel of a packet from a source node to a destination node in a large non-homogeneous multiple hop network with unreliable routing tables. Use of a random model is justified by the lack of precise information that can be used in each step of the packet's travel, and randomness can also be useful in exploring alternate paths when a long sequence of hops has not resulted in the packet's arrival to the destination. The packet's travel may also be impeded if certain routers on its path prove to be unreliable, or the packet may be dropped from a buffer or destroyed due to packet loss. The packet also has a limited time-out that allows the source to retransmit a dropped or lost packet. Because the network itself may be extremely large, we consider packet travel in an infinite random non-homogeneous medium, with events that may interrupt, destroy or stop the packet from moving towards its destination. We derive a numerical-analytical solution allowing us to compute the average travel time of the packet from source to destination, as well as to estimate its energy consumption. Two interesting applications are then presented. In the first one a wireless network where areas which are remote from the source and destination nodes may have poor wireless coverage so that the packet losses become more frequent as the packet "unknowingly" (due to poor routing tables for instance) meanders away from the source and destination node. The second application is related to defending a destination node against attacks that take the form of packets that carry a virus or a worm that can be detected via deep packet inspection at intermediate nodes, and as the packet approaches the destination node it is more frequently inspected and dropped if it is a threat.

References

[1]
R. Beraldi. Biased random walks in uniform wireless networks. IEEE Transactions on Mobile Computing, 8(4):500--513, April 2009.
[2]
R. Beraldi, Q. Leonardo, and B. Roberto. Low hitting time random walks in wireless networks. Wireless Communications and Mobile Computing, 9:719--732, May 2009.
[3]
T. Czachórski, K. Grochla, and F. Pekergin. Diffusion approximation model for the distribution of packet travel time at sensor networks. In Wireless Systems and Mobility in Next Generation Internet, volume 5122 of LNCS, pages 10--25. Springer Berlin / Heidelberg, 2008.
[4]
D. Dhanapala, A. Jayasumana, and Q. Han. Performance of random routing on grid-based sensor networks. In Proceedings of 6th IEEE Consumer Communications and Networking Conference (CCNC'09), Las Vegas, NV, USA, January 2009.
[5]
A. Einstein. Investigations on the Theory of Brownian Motion. Dutton & Dover, New York, 1926.
[6]
E. Gelenbe. On approximate computer system models. Journal of the ACM, 22:261--269, April 1975.
[7]
E. Gelenbe. Probabilistic models of computer systems. part II: Diffusion approximations, waiting times and batch arrivals. Acta Informatica, 12:285--303, 1979. 10.1007/BF00268317.
[8]
E. Gelenbe. Travel delay in a large wireless ad hoc network. In Proceedings of 2nd Workshop on Spatial Stochastic Models for Wireless Networks (SpaSWiN'06), Boston, MA, USA, April 2006.
[9]
E. Gelenbe. A diffusion model for packet travel time in a random multihop medium. ACM Transactions on Sensor Networks, 3(2):1--19, June 2007.
[10]
E. Gelenbe. Steps towards self-aware networks. Communications of the ACM, 52(7):66--75, July 2009.
[11]
E. Gelenbe. Search in unknown random environments. Physical Review E, 82(6):061112, December 2010.
[12]
E. Gelenbe and Y. Cao. Autonomous search for mines. European Journal of Operational Research, 108(2):319--333, July 1998.
[13]
E. Gelenbe, X. Mang, and R. Onvural. Diffusion based call admission control in A™. Performance Evaluation, 27 & 28:411--436, 1996.
[14]
Y.-B. Ko and N. H. Vaidya. Location-aided routing (LAR) in mobile ad hoc networks. Wireless Networks, 6:307--321, July 2000.
[15]
I. Mabrouki, G. Froc, and X. Lagrange. On the data delivery delay taken by random walks in wireless sensor networks. In Proceedings of 5th International Conference on Quantitative Evaluation of Systems (QEST'08), pages 17--26, St Malo, France, September 2008.
[16]
J. Medhi. Stochastic Models in Queueing Theory. Academic Press, New York, 1991.
[17]
G. F. Newell. Applications of Queueing Theory. Monographs on Applied Probability and Statistics, Chapman and Hall Ltd., London, 1971.
[18]
G. Oshanin, O. Vasilyev, P. L. Krapivsky, and J. Klafter. Suvival of an evasive prey. Proceedings of the National Academy of Sciences, 106(33):13696--13701, 2009.
[19]
F. Rojo, J. Revelli, C. E. Budd, H. S. Wio, G. Oshanin, and K. Lindenberg. Intermittent search strategies revisited: effect of the jump length and biased motion. Journal of Physics A: Mathematical and General, 43(34):345001, 2010.
[20]
S. Shakkottai. Asymptotics of search strategies over a sensor network. IEEE Transactions on Automatic Control, 50(5):594--606, May 2005.
[21]
B. Tilch, F. Schweitzer, and W. Ebeling. Active brownian particles with internal energy depots modelling animal mobility. BioSystems, 49:17--92, 1999.
[22]
B. Tilch, F. Schweitzer, and W. Ebeling. Directed motion of brownian particles with internal energy depot. Physica A: Statistical Mechanics and its Applications, 273:294--314, 1999.
[23]
S.-P. Wang and W.-J. Pei. First passage time of multiple brownian particles on networks with applications. Physica A: Statistical Mechanics and its Applications, 387(18):4699--4708, 2008.

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cover image ACM Conferences
MSWiM '11: Proceedings of the 14th ACM international conference on Modeling, analysis and simulation of wireless and mobile systems
October 2011
462 pages
ISBN:9781450308984
DOI:10.1145/2068897
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 31 October 2011

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Author Tags

  1. brownian motion
  2. diffusion process
  3. multi-hop networks

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