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Routing algorithm of minimizing maximum link congestion on grid networks

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Abstract

As regular topology networks, grid networks are widely adopted in network deployment. Link congestion and routing path length are two critical factors that affect the delay and throughput of a network. In this paper, we study the routing problem in grid networks concerning these two factors. The main objective of our routing algorithms is to minimize the maximum link congestion. The shortest path minimum maximum (SPMM) link congestion and non-shortest path minimum maximum (NSPMM) link congestion routing problems are studied. The two problems are first formulated as integer optimization problems. Then, corresponding routing algorithms (SPMM and NSPMM routing algorithms) are proposed. For SPMM routing algorithm, the path length is optimal, while for NSPMM routing algorithm, the path is limited in a submesh. Thus, the path length can be bounded. At last, we compare the proposed routing algorithms under different scenarios with other popular routing algorithms (RowColumn, ZigZag, Greedy, Random routing algorithms). The performances are evaluated through different metrics including link congestion, path length, path congestion, path congestion to path length ratio, delay and throughput.

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References

  1. Awduche, D., Chiu, A., Elwalid, A., Widjaja, I., & Xiao, X. (2002). Overview and principles of internet traffic engineering. Tech. rep., RFC 3272.

  2. Siripongwutikorn, P., Banerjee, S. & Tipper, D. (2002). Traffic engineering in the internet: A survey of load balanced routing. White paper.

  3. Ravindra Kumar Singh, N. S. C., & Saxena, K. (2012). Load balancing in ip/mpls networks: A survey. Computer Science and Communications, 4(2), 151–156.

    Google Scholar 

  4. Askarian, C., & Beigy, H. (2012). A survey for load balancing in mobile wimax networks. Advanced Computing: An International Journal, 3(2), 119–137.

    Google Scholar 

  5. Wajgi, D., & Thakur, N. V. (2012). Load balancing algorithms in wireless sensor network: A survey. International Journal of Computer Networks and Wireless Communications (IJCNWC), 2, 456–460.

    Google Scholar 

  6. Yao, Y., Cao, Q., & Vasilakos, A. V. (2013). EDAL: An energy-efficient, delay-aware, and lifetime-balancing data collection protocol for wireless sensor networks. In: MASS (pp. 182–190).

  7. Shen, Zhijie, et al. (2011). Peer-to-peer media streaming: Insights and new developments. Proceedings of the IEEE, 99(12), 2089–2109.

    Article  Google Scholar 

  8. Suri, P. K., & Kaur, S. (2012). A survey of load balancing algorithms in manet. Engineering Science and Technology: An International Journal, 2(3), 495–504.

    Google Scholar 

  9. Maheshwari, D., & Nedunchezhian, R. (2012). Load balancing in mobile ad hoc networks: A survey. International Journal of Computer Applications, 59(16), 44–49.

    Article  Google Scholar 

  10. Kelly, F. P., Maulloo, A. K., & Tan, D. K. (1998). Rate control for communication networks: Shadow prices, proportional fairness and stability. Journal of the Operational Research Society, 49(3), 237–252.

    Article  MATH  Google Scholar 

  11. Firoiu, V. & Borden, M. (2000). A study of active queue management for congestion control. In INFOCOM 2000. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings. IEEE (Vol. 3, pp. 1435–1444).

  12. Li, Mo, et al. (2013). A survey on topology control in wireless sensor networks: Taxonomy, comparative study, and open issues. Proceedings of the IEEE, 101(12), 2538–2557.

    Article  Google Scholar 

  13. Chen, L., Low, S. H. & Doyle, J. C. (2005). Joint congestion control and media access control design for ad hoc wireless networks. In INFOCOM 2005. 24th Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings IEEE (Vol. 3, pp. 2212–2222).

  14. Kewei Sha, J. G., & Greve, J. G. (2013). Multipath routing techniques in wireless sensor networks: A survey. Wireless Personal Communications, 70(2), 807–829.

    Article  Google Scholar 

  15. Radi, M., Dezfouli, B., Bakar, K. A., & Lee, M. (2012). Multipath routing in wireless sensor networks: Survey and research challenges. Sensors, 12(1), 650–685.

    Article  Google Scholar 

  16. Piratla, N. M. & Jayasumana, A. P. (2006). Reordering of packets due to multipath forwarding-an analysis. In ICC’06 (Vol. 2, pp. 829–834).

  17. Robinson, J. & Knightly, E. W. (2007). A performance study of deployment factors in wireless mesh networks. In INFOCOM 2007. 26th IEEE International Conference on Computer Communications. IEEE (pp. 2054–2062).

  18. Busch, C., Kannan, R., & Samman, A. (2012). Bottleneck routing games on grids. In Game Theory for Networks (Vol. 75 LNICST, pp. 294–307).

  19. Leighton, F. T., Maggs, B. M., & Rao, S. B. (1994). Packet routing and job-shop scheduling in O (congestion + dilation) steps. Combinatorica, 14(2), 167–186.

    Article  MATH  MathSciNet  Google Scholar 

  20. Banner, R., & Orda, A. (2007). Bottleneck routing games in communication networks. IEEE Journal on Selected Areas in Communications, 25(6), 1173–1179.

    Article  Google Scholar 

  21. Busch, C., Kannan, R., & Vasilakos, A. V. (2008) Quality of routing congestion games in wireless sensor networks. In Proceedings of the 4th Annual International Conference on Wireless Internet. no. p. 71.

  22. Busch, C., & Magdon-Ismail, M. (2009). Atomic routing games on maximum congestion. Theoretical Computer Science, 410(36), 3337–3347.

    Article  MATH  MathSciNet  Google Scholar 

  23. Rajgopal Kannan,et al. “Optimal Price of Anarchy of Polynomial and Super-Polynomial Bottleneck Congestion Games.” GAMENETS. pp. 308-320, 2011.

  24. Busch, Costas, et al. (2012). Approximating congestion + dilation in networks via ‘quality of routing’ games. IEEE Transactions on Computers, 61(9), 1270–1283.

    Article  MathSciNet  Google Scholar 

  25. Spyropoulos, T., et al. (2010). Routing for disruption tolerant networks: Taxonomy and design. Wireless Networks, 16(8), 2349–2370.

    Article  Google Scholar 

  26. Zeng, Y., et al. (2013). Directional routing and scheduling for green vehicular delay tolerant networks. Wireless Networks, 19(2), 161–173.

    Article  Google Scholar 

  27. Youssef, M., et al. (2014). Routing metrics of cognitive radio networks: A survey. IEEE Communications Surveys and Tutorials, 16(1), 92–109.

    Article  Google Scholar 

  28. Liu, Y., et al. (2010). Multi-layer clustering routing algorithm for wireless vehicular sensor networks. IET Communications, 4(7), 810–816.

    Article  Google Scholar 

  29. Chen, Kai, et al. (2011). Survey on routing in data centers: Insights and future directions. IEEE Network, 25(4), 6–10.

    Article  Google Scholar 

  30. Li, P., Guo, S., Yu, S., & Vasilakos, A. V. (2012). CodePipe: An opportunistic feeding and routing protocol for reliable multicast with pipelined network coding. In INFOCOM (pp. 100–108).

  31. Demestichas, Panagiotis, et al. (2004). Service configuration and traffic distribution in composite radio environments. IEEE Transactions on Systems, Man, and Cybernetics, Part C, 34(1), 69–81.

    Article  Google Scholar 

  32. Britta, P., Martin, S., & Andreas, W. (2010). Packet routing on the grid. In Theoretical Informatics—9th Latin American Symposium, Proceedings (Vol. 6034 LNCS, pp. 120–130).

  33. Badr, H. G., & Podar, S. (1989). An optimal shortest-path routing policy for network computers with regular mesh-connected topologies. IEEE Transactions on Computers, 38(10), 1362–1371.

    Article  MathSciNet  Google Scholar 

  34. Weller, T., & Hajek, B. (1994). Comments on”an optimal shortest-path routing policy for network computers with regular mesh-connected topologies. IEEE Transactions on Computers, 43(7), 862–863.

    Article  Google Scholar 

  35. Wu, J. (1999). Maximum-shortest-path (msp): An optimal routing policy for mesh-connected multicomputers. IEEE Transactions on Reliability, 48(3), 247–255.

    Article  Google Scholar 

  36. Takatsu, S., Ooshita, F., Kakugawa, H., & Masuzawa, T. (2013). Zigzag: Local-information-based self-optimizing routing in virtual grid networks. In International Conference on Distributed Computing Systems, 33rd IEEE (pp. 357–368).

  37. Liu, J. W. (2000). Real-time systems (pp.115–189). Upper Saddle River, NJ: Prentice Hall PTR.

  38. Dhanapala, D. C., Jayasumana, A. P., & Han, Q. (2009). Performance of random routing on grid-based sensor networks. CCNC, 2009, 1–5.

    Google Scholar 

  39. Rajasekaran, S. (1991). Randomized algorithms for packet routing on the mesh. Technical Reports (CIS). Paper 328. http://repository.upenn.edu/cis_reports/328.

  40. Busch, C., Magdon-lsmail, M., & Xi, J. (2008). Optimal oblivious path selection on the mesh. IEEE Transactions on Computers, 57(5), 660–671.

    Article  Google Scholar 

  41. Ahuja, R. K., Magnanti, T. L., & Orlin, J. B. (1993). Network flows: Theory, algorithms, and applications (pp. 649–684). Upper Saddle River, NJ: Prentice Hall PTR.

  42. Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2001). Introduction to algorithms (Vol. 2). Cambridge: MIT press.

    MATH  Google Scholar 

  43. Kaibel, V., & Peinhardt, M. (2006). On the bottleneck shortest path problem. Technical Reports.

  44. Fredman, M. L., & Tarjan, R. E. (1987). Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM (JACM), 34(3), 596–615.

    Article  MathSciNet  Google Scholar 

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Acknowledgments

This work was supported by the National High-tech R&D Program of China (863 Program) (Grant No. 2012AA010904), and the Scientific Research Fund of Sichuan Province, China (Grant Nos. 2013GZ0016, 13ZA0296). And our thanks to the China Scholarship Council (CSC) for the support for the Joint Ph.D. Program.

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Authors and Affiliations

  1. School of Electronic Information, Wuhan University, Wuhan, Hubei, China

    Jun Xu, Jianfeng Yang & Chengcheng Guo

  2. Computer Science Department, Arizona State University, Tempe, AZ, USA

    Yann-Hang Lee & Duo Lu

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  1. Jun Xu
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Correspondence to Jianfeng Yang.

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Xu, J., Yang, J., Guo, C. et al. Routing algorithm of minimizing maximum link congestion on grid networks. Wireless Netw 21, 1713–1732 (2015). https://doi.org/10.1007/s11276-014-0878-8

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