Optimal Routing and Call Scheduling in Wireless Mesh Networks with Localized Informations

  • Christelle Molle
  • Fabrice Peix
  • Stéphane Pérennes
  • Hervé Rivano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5474)


Wireless mesh network performance issues have been modeled by the Joint Routing and Scheduling Problem (JRSP) in which a maximum per-flow throughput is computed.

A classical relaxation of JRSP, denoted as the Round Weighting Problem (RWP), consists in assigning enough weight to sets of compatible simultaneous transmissions (rounds), while minimizing the sum of them, thus maximizing the relative weight of each round, which model the throughput.

In this work, we present a new linear formulation of RWP focused on the transport capacity over the network cuts, thus eliminating the routing. We prove its equivalence with existing formulations with flows and formalize a primal-dual algorithm that quickly solves this problem using a cross line and column generations process.

An asset of this formulation is to point out a bounded region, a ”bottleneck” of the network, that is enough to optimize in order to get the optimal RWP of the whole network. The size and location of this area is experimentally made through simulations, highlighting a few hop distant neighborhood of the mesh gateways. One would then apply approximated methods outside this zone to route the traffic without degrading the achieved capacity.


Column Generation Optimal Routing Wireless Mesh Network Mesh Router Link Schedule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Akyildiz, I., Wang, X., Wang, W.: Wireless mesh networks: a survey. Computer Networks 47(4), 445–487 (2005)CrossRefzbMATHGoogle Scholar
  2. 2.
    Jain, K., Padhye, J., Padhamanabhan, V., Qiu, L.: Impact of interference on multi-hop wireless network performance. In: ACM MobiCom, pp. 66–80 (2003)Google Scholar
  3. 3.
    Kodialam, M., Nandagopal, T.: On the capacity region of multi-radio multi-channel wireless mesh networks. In: First IEEE WiMesh (2005)Google Scholar
  4. 4.
    Gupta, P., Kumar, P.: The capacity of wireless networks. IEEE Transactions on Information Theory 46(2), 388–404 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Dousse, O., Franceschetti, M., Tse, D., Thiran, P.: Closing the gap in the capacity of random wireless networks. In: IEEE International Symposium on Information Theory (ISIT) (2004)Google Scholar
  6. 6.
    Jun, J., Sichitiu, M.: The nominal capacity of wireless mesh networks. IEEE Wireless Communications 10(5), 8–14 (2003)CrossRefGoogle Scholar
  7. 7.
    Rivano, H., Theoleyre, F., Valois, F.: Capacity evaluation framework and validation of self-organized routing schemes. In: IEEE International Workshop on Wireless Ad-hoc and Sensor Networks (IWWAN) (2006)Google Scholar
  8. 8.
    Liu, H., Zhao, B.: Optimal scheduling for link assignment in traffic-sensitive STDMA wireless ad-hoc networks. In: Lu, X., Zhao, W. (eds.) ICCNMC 2005. LNCS, vol. 3619, pp. 218–228. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Carello, G., Filippini, I., Gualandi, S., Malucelli, F.: Scheduling and routing in wireless multi-hop networks by column generation. In: INOC (2007)Google Scholar
  10. 10.
    Gomes, C., Molle, C., Reyes, P.: Optimal design of wireless mesh networks. In: JDIR, Villeneuve d’Ascq, France (January 2008)Google Scholar
  11. 11.
    Molle, C., Peix, F., Rivano, H.: An optimization framework for the joint routing and scheduling in wireless mesh networks. In: IEEE PIMRC (2008)Google Scholar
  12. 12.
    Bermond, J.C., Galtier, J., Klasing, R., Morales, N., Pérennes, S.: Hardness and approximation of gathering in static radio networks. Parallel Processing Letters 16(2), 165–183 (2006)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Bonifaci, V., Korteweg, P., Marchetti-Spaccamela, A., Stougie, L.: An approximation algorithm for the wireless gathering problem. In: Arge, L., Freivalds, R. (eds.) SWAT 2006. LNCS, vol. 4059, pp. 328–338. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Klasing, R., Morales, N., Perennes, S.: On the complexity of bandwidth allocation in radio networks with steady traffic demands. Theoretical Computer Science (to appear) (2008)Google Scholar
  15. 15.
    Cook, W.J., Cunningham, W.H., Pulleyblank, W.R., Schrijver, A.: Combinatorial optimization. John Wiley & Sons, Inc., New York (1998)zbMATHGoogle Scholar
  16. 16.
    Lubbecke, M.E., Desrosiers, J.: Selected topics in column generation. Operations Research 53(6), 1007–1023 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Goldberg, A., Tarjan, R.: A new approach to the maximum flow problem. In: STOC 1986: Proceedings of the eighteenth annual ACM symposium on Theory of computing, pp. 136–146. ACM, New York (1986)CrossRefGoogle Scholar
  18. 18.
    Zhang, J., Wu, H., Zhang, Q., Li, B.: Joint routing and scheduling in multi-radio multi-channel multi-hop wireless networks. In: IEEE BROADNETS, pp. 678–687 (2005)Google Scholar
  19. 19.
    Lalande, J.F., Syska, M., Verhoeven, Y.: Mascopt - a network optimization library: Graph manipulation. Research Report 0293, INRIA (2004),
  20. 20.
    Gomes, C., Pérennes, S., Reyes, P., Rivano, H.: Bandwidth allocation in radio grid networks. In: 10èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel) (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Christelle Molle
    • 1
  • Fabrice Peix
    • 1
  • Stéphane Pérennes
    • 1
  • Hervé Rivano
    • 1
  1. 1.MASCOTTE ProjectI3S(CNRS-UNSA)/INRIA, Sophia AntipolisFrance

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