Multiobjective routing in multiservice MPLS networks with traffic splitting — A network flow approach

Abstract

A multiobjective routing model for Multiprotocol Label Switching networks with multiple service types and traffic splitting is presented in this paper. The routing problem is formulated as a multiobjective mixed-integer program, where the considered objectives are the minimization of the bandwidth routing cost and the minimization of the load cost in the network links with a constraint on the maximal splitting of traffic trunks. Two different exact methods are developed for solving the formulated problem, one based on the classical constraint method and another based on a modified constraint method. A very extensive experimental study, with results on network performance measures in various reference test networks and in randomly generated networks, is also presented and its results are discussed.

This is a preview of subscription content, log in to check access.

References

  1. [1]

    Aarts, E. & Lenstra, J. K. (editors) (1997). Local Search in Combinatorial Optimization. John Wiley & Sons.

    Google Scholar 

  2. [2]

    Agdeppa, R. P., Yamashita, N. & Fukushima, M. (2007). The traffic equilibrium problem with nonadditive costs and its monotone mixed complementarity problem formulation. Transportation Research Part B — Methodological, 41(8):862–874.

    Article  Google Scholar 

  3. [3]

    Avallone, S., Manetti, V., Mariano, M. & Romano, S. P. (2007). A splitting infrastructure for load balancing and security in an MPLS network. Proceedings of the 3rd International Conference on Testbeds and Research Infrastructure for the Development of Networks and Communities (TridentCom 2007), Lake Buena Vista (FL), USA, May 21–23.

    Google Scholar 

  4. [4]

    Bekhor, S., Toledo, T. & Toledo, J. N. (2008). Effects of choice set size and route choice models on path-based traffic assignment. Transportmetrica, 4(2):117–133.

    Article  Google Scholar 

  5. [5]

    Bertsimas, D. & Tsitsiklis, J. (1993). Simulated annealing. Statistical Science, 8(1):10–15.

    Article  Google Scholar 

  6. [6]

    Bovy, P. H. L. (2009). On modelling route choice sets in transportation networks: A synthesis. Transport Reviews: A Transnational Transdisciplinary Journal, 29(1):43–68.

    Article  Google Scholar 

  7. [7]

    Brands, T. & van Eck, G. (2010). Multimodal network design and assessment — Proposal for a dynamic multi-objective approach. 11th TRAIL Congress, The Netherlands Research School on Transport, Infrastructure and Logistics, Nov.

    Google Scholar 

  8. [8]

    Branke, J., Deb, K., Miettinen, K. & Słowiński, R. (editors) (2008). Multiobjective Optimization — Interactive and Evolutionary Approaches. Lecture Notes in Computer Science, volume 5252, Springer.

    Google Scholar 

  9. [9]

    Chen, A., Zhou, Z., Chootinan, P., Ryu, S., Yang, C. & Wong, S. C. (2011). Transport network design problem under uncertainty: A review and new developments. Transport Reviews, 31(6):743–768.

    Article  Google Scholar 

  10. [10]

    Clímaco, J. C. N., Craveirinha, J. M. F. & Pascoal, M. M. B. (2006). An automated reference point-like approach for multicriteria shortest path problems. Journal of Systems Science and Systems Engineering, 15(3):314–329.

    Article  Google Scholar 

  11. [11]

    Clímaco, J. C. N., Craveirinha, J. M. F. & Pascoal, M. M. B. (2007). Multicriteria routing models in telecommunication networks — Overview and a case study. In Shi, Y., Olson, D. L. & Stam, A. (editors), Advances in Multiple Criteria Decision Making and Human Systems Management: Knowledge and Wisdom, pages 17–46, IOS Press.

    Google Scholar 

  12. [12]

    Clímaco, J. & Pascoal, M. (2009). Finding nondominated shortest pairs of disjoint simple paths. Computers & Operations Research, 36(11):2892–2898.

    Article  MathSciNet  MATH  Google Scholar 

  13. [13]

    Cohon, J. L. (1978). Multiobjective Programming and Planning. Mathematics in Science and Engineering, Academic Press.

    Google Scholar 

  14. [14]

    Craveirinha, J., Gomes, T., Pascoal, M. & Clímaco, J. (2011). A stochastic bicriteria approach for restorable QoS routing in MPLS. Proceedings of the 2011 International Conference on Telecommunication Systems — Modeling and Analysis (ICTSM2011), pages 1–15, Prague, Czech Republic, May 26–28.

    Google Scholar 

  15. [15]

    Craveirinha, J., Clímaco, J., Martins, L., da Silva, C. G. & Ferreira, N. (2013). A bi-criteria minimum spanning tree routing model for MPLS/Overlay networks. Telecommunication Systems, 52(1):203–215.

    Article  Google Scholar 

  16. [16]

    Craveirinha, J. M. F., Clímaco, J. C. N., Pascoal, M. M. B. & Martins, L. M. R. A. (2007). Traffic splitting in MPLS networks — A hierarchical multicriteria approach. Journal of Telecommunications and Information Technology, (4):3–10.

    Google Scholar 

  17. [17]

    Craveirinha, J., Girão-Silva, R. & Clímaco, J. (2008). A meta-model for multiobjective routing in MPLS networks. Central European Journal of Operations Research, 16(1):79–105.

    Article  MATH  Google Scholar 

  18. [18]

    Dana, A., Zadeh, A. K., Kalantari, M. E. & Badie, K. (2003). A traffic splitting restoration scheme for MPLS network using case-based reasoning. Proceedings of the 9th Asia Pacific Conference on Communications (APCC 2003), volume 2, pages 763–766, Sep. 21–24.

    Google Scholar 

  19. [19]

    Dana, A., Khademzadeh, A., Kalantari, M. E. & Badie, K. (2004). Fault recovery in MPLS network using case-based reasoning. Modares Technical and Engineering, 16:127–138.

    Google Scholar 

  20. [20]

    Deb, K. (2001). Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons.

    Google Scholar 

  21. [21]

    Dial, R. B. (1996). Bicriterion traffic assignment: Basic theory and elementary algorithms. Transportation Science, 30(2):93–111.

    Article  MATH  Google Scholar 

  22. [22]

    Dial, R. B. (1997). Bicriterion traffic assignment: Efficient algorithms plus examples. Transportation Research Part B — Methodological, 31(5):357–379.

    Article  Google Scholar 

  23. [23]

    Dixit, A., Prakash, P. & Kompella, R. R. (2011). On the efficacy of fine-grained traffic splitting protocols in data center networks. Proceedings of SIGCOMM11, pages 430–431, Toronto (Ontario), Canada, Aug. 15–19.

    Google Scholar 

  24. [24]

    Doar, M. & Leslie, I. M. (1993). How bad is naive multicast routing? Proceedings of INFOCOM, volume 1, pages 82–89, San Francisco (CA), USA.

    Google Scholar 

  25. [25]

    Ehrgott, M. & Gandibleux, X. (2000). A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spektrum, 22(4):425–460.

    Article  MathSciNet  MATH  Google Scholar 

  26. [26]

    Elwalid, A., Jin, C., Low, S. & Widjaja, I. (2001). MATE: MPLS Adaptive Traffic Engineering. In Sengupta, B., Bauer, F. & Cavendish, D. (editors), Proceedings of the 20th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2001), volume 3, pages 1300–1309, Anchorage (AK), USA, IEEE Computer and Communications Societies.

    Article  Google Scholar 

  27. [27]

    Erbas, S. C. & Erbas, C. (2003). A multiobjective off-line routing model for MPLS networks. In Charzinski, J., Lehnert, R. & Tran-Gia, P. (editors), Proceedings of the 18th International Teletraffic Congress (ITC-18), pages 471–480, Berlin, Germany, Elsevier, Amsterdam.

    Google Scholar 

  28. [28]

    Ferng, H.-W. & Peng, C.-C. (2004). Traffic splitting in a network: Split traffic models and applications. Computer Communications, 27(12):1152–1165.

    Article  Google Scholar 

  29. [29]

    Fortz, B. & Thorup, M. (2000). Internet traffic engineering by optimizing OSPF weights. In Sidi, M., Katzela, I. & Shavitt, Y. (editors), Proceedings of the 19th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2000), volume 2, pages 519–528, Tel Aviv, Israel, Mar. 26–30, IEEE Computer and Communications Societies.

    Article  Google Scholar 

  30. [30]

    Fortz, B. & Thorup, M. (2002). Optimizing OSPF/IS-IS weights in a changing world. IEEE Journal on Selected Areas in Communications, 20(4):756–767.

    Article  Google Scholar 

  31. [31]

    Gandibleux, X., Sevaux, M., Sőrensen, K. & T’Kindt, V. (editors) (2004). Metaheuristics for Multiobjective Optimisation. Lecture Notes in Economics and Mathematical Systems, volume 535, Springer.

    Google Scholar 

  32. [32]

    Gendreau, M. & Potvin, J.-Y. (2010). Tabu search. In Gendreau, M. & Potvin, J.-Y. (editors), Handbook of Metaheuristics, International Series in Operations Research & Management Science, volume 146, pages 41–59, Springer.

    Article  Google Scholar 

  33. [33]

    Ghosh, A. & Dehuri, S. (2004). Evolutionary algorithms for multi-criterion optimization: A survey. International Journal of Computing & Information Sciences, 2(1):38–57.

    Google Scholar 

  34. [34]

    Girão-Silva, R., Craveirinha, J. & Clímaco, J. (2009). Hierarchical multiobjective routing in Multiprotocol Label Switching networks with two service classes — A heuristic solution. International Transactions in Operational Research, 16(3):275–305.

    Article  MATH  Google Scholar 

  35. [35]

    Girão-Silva, R., Craveirinha, J., Clímaco, J. & Captivo, M. E. (2013). Multiobjective Routing in Multiservice MPLS Networks with Traffic Splitting — Report on a Network Flow Approach. Research Report 2/2013, INESC-Coimbra.

    Google Scholar 

  36. [36]

    Gomes, T., Martins, L. & Craveirinha, J. (2001). An algorithm for calculating k shortest paths with a maximum number of arcs. Investigação Operacional, 21:235–244.

    Google Scholar 

  37. [37]

    Guihaire, V. & Hao, J.-K. (2008). Transit network design and scheduling: a global review. Transportation Research Part A: Policy and Practice, 42(10):1251–1273.

    Google Scholar 

  38. [38]

    He, J. & Rexford, J. (2008). Towards Internet-wide multipath routing. IEEE Network, 22(2):16–21.

    Article  Google Scholar 

  39. [39]

    Huang, H.-J. & Li, Z.-C. (2007). A multiclass, multicriteria logit-based traffic equilibrium assignment model under ATIS. European Journal of Operational Research, 176(3):1464–1477.

    Article  MATH  Google Scholar 

  40. [40]

    Knowles, J., Oates, M. & Corne, D. (2000). Advanced multi-objective evolutionary algorithms applied to two problems in telecommunications. BT Technology Journal, 18(4):51–65.

    Article  Google Scholar 

  41. [41]

    Krishnadas, C. S. & Roy, R. (2009). Quality of Experience (QoE) assurance by a multipath balanced traffic splitting algorithm in MPLS networks. Annales UMCS Informatica AI, 9(1):165–177.

    Google Scholar 

  42. [42]

    Lee, G. M. & Choi, J. S. (2002). A survey of multipath routing for traffic engineering. [Online]

    Google Scholar 

  43. [43]

    Lee, Y., Seok, Y., Choi, Y. & Kim, C. (2002). A constrained multipath traffic engineering scheme for MPLS networks. Proceedings of the IEEE International Conference on Communications (ICC 2002), New York, USA, Apr.28–May2.

    Google Scholar 

  44. [44]

    Lee, K., Toguyeni, A., Noce, A. & Rahmani, A. (2005). Comparison of multipath algorithms for load balancing in a MPLS network. In Kim, C. (editor), Proceedings of the International Conference on Information Networking, Convergence in Broadband and Mobile Networking (ICOIN2005), Lecture Notes in Computer Science, volume 3391, pages 463–470, Jeju Island, Korea, Jan.31–Feb.2, Springer.

    Google Scholar 

  45. [45]

    Lee, K., Toguyeni, A. & Rahmani, A. (2006). Hybrid multipath routing algorithms for load balancing in MPLS based IP network. Proceedings of the 20th International Conference on Advanced Information Networking and Applications (AINA 2006), Apr.18–20.

    Google Scholar 

  46. [46]

    Liu, Y., Bunker, J. & Ferreira, L. (2010). Transit users’ route-choice modelling in transit assignment: A review. Transport Reviews: A Transnational Transdisciplinary Journal, 30(6):753–769.

    Article  Google Scholar 

  47. [47]

    Lo, H. K. & Chen, A. (2000a). Reformulating the traffic equilibrium problem via a smooth gap function. Mathematical and Computer Modelling, 31(2–3):179–195.

    Article  MathSciNet  MATH  Google Scholar 

  48. [48]

    Lo, H. K. & Chen, A. (2000b). Traffic equilibrium problems with route-specific costs: formulation and algorithms. Transportation Research Part B — Methodological, 34(6):493–513.

    Article  Google Scholar 

  49. [49]

    Lu, C.-C., Mahmassani, H. S. & Zhou, X. (2008). A bi-criterion dynamic user equilibrium traffic assignment model and solution algorithm for evaluating dynamic road pricing strategies. Transportation Research Part C, 16:371–389.

    Article  Google Scholar 

  50. [50]

    Marcotte, P. & Patriksson, M. (2007). Traffic equilibrium. In Barnhart, C. & Laporte, G. (editors), Transportation, Handbooks in Operations Research and Management Science, volume 14, pages 623–713, North-Holland, Amsterdam.

    Article  Google Scholar 

  51. [51]

    Mavrotas, G. (2009). Effective implementation of the ɛ-constraint method in Multi-Objective Mathematical Programming problems. Applied Mathematics and Computation, 213(2):455–465.

    Article  MathSciNet  MATH  Google Scholar 

  52. [52]

    Medhi, D. & Tipper, D. (2000). Some approaches to solving a multi-hour broadband network capacity design problem with single-path routing. Telecommunication Systems, 13(2):269–291.

    Article  MATH  Google Scholar 

  53. [53]

    Messac, A., Ismail-Yahaya, A. & Mattson, C. A. (2003). The normalized normal constraint method for generating the Pareto frontier. Structural and Multidisciplinary Optimization, 25(2):86–98.

    Article  MathSciNet  MATH  Google Scholar 

  54. [54]

    Mitra, D. & Ramakrishnan, K. G. (2001). Techniques for traffic engineering of multiservice, multipriority networks. Bell Labs Technical Journal, 6(1):139–151.

    Article  Google Scholar 

  55. [55]

    Murugesan, G., Natarajan, A. M. & Venkatesh, C. (2008). Enhanced variable splitting ratio algorithm for effective load balancing in MPLS networks. Journal of Computer Science, 4(3):232–238.

    Article  Google Scholar 

  56. [56]

    Nagurney, A., Dong, J. & Mokhtarian, P. L. (2002). Traffic network equilibrium and the environment: A multicriteria decision-making perspective. In Kontoghiorghes, E., Rustem, B. & Siokos, S. (editors), Computational Methods in Decision-Making, Economics and Finance, pages 501–523, Kluwer.

    Google Scholar 

  57. [57]

    Nelakuditi, S. & Zhang, Z.-L. (2001). On selection of paths for multipath routing. In Wolf, L., Hutchison, D. & Steinmetz, R. (editors), Proceedings of IWQoS 2001, Lecture Notes in Computer Science, volume 2092, pages 170–184, Karlsruhe, Germany, Springer.

    Google Scholar 

  58. [58]

    Patriksson, M. (1994). The Traffic Assignment Problem — Models and Methods. Topics in Transportation, VSP.

    Google Scholar 

  59. [59]

    Pióro, M., Szentesi, Á., Harmatos, J., Jüttner, A., Gajowniczek, P. & Kozdrowski, S. (2002). On open shortest path first related network optimization problems. Performance Evaluation, 48:201–223.

    Article  MATH  Google Scholar 

  60. [60]

    Prashker, J. N. & Bekhor, S. (2004). A review on route choice models used in the stochastic user equilibrium problem. Transport Reviews, 24(4):437–463.

    Article  Google Scholar 

  61. [61]

    Prato, C. G. (2009). Route choice modeling: past, present and future research directions. Journal of Choice Modelling, 2(1):65–100.

    Article  MathSciNet  Google Scholar 

  62. [62]

    Raith, A., Wang, J. Y. T., Ehrgott, M. & Mitchell, S. A. (2011). Solving multi-objective traffic assignment. In ORP3 Meeting, Cádiz, Spain, Sep.13–17.

    Google Scholar 

  63. [63]

    Ran, B. & Boyce, D. (1996). Modeling Dynamic Transportation Networks — An Intelligent Transportation System Oriented Approach. Lecture Notes in Economics and Mathematical Systems, volume 417, Springer, 2nd ed.

    Google Scholar 

  64. [64]

    Sheffi, Y. (1985). Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods. Prentice-Hall, Inc.

    Google Scholar 

  65. [65]

    Singh, R. K., Chaudhari, N. S. & Saxena, K. (2012). Load balancing in IP/MPLS networks: A survey. Communications and Network, 4:151–156.

    Article  Google Scholar 

  66. [66]

    Song, J., Kim, S. & Lee, M. (2003). Dynamic load distribution in MPLS networks. In Kahng, H.-K. (editor), Proceedings of the International Conference on Information Networking, Convergence in Broadband and Mobile Networking (ICOIN2003), Lecture Notes in Computer Science, volume 2662, pages 989–999, Jeju Island, Korea, Feb.12–14, Springer.

    Google Scholar 

  67. [67]

    Srivastava, S., Krithikaivasan, B., Medhi, D. & Pióro, M. (2003). Traffic engineering in the presence of tunneling and diversity constraints: Formulation and Lagrangean decomposition approach. In Charzinski, J., Lehnert, R. & Tran-Gia, P. (editors), Proceedings of the 18th International Teletraffic Congress (ITC-18), pages 461–470, Berlin, Germany, Elsevier, Amsterdam.

    Google Scholar 

  68. [68]

    Srivastava, S., Agrawal, G., Pióro, M. & Medhi, D. (2005). Determining link weight system under various objectives for OSPF networks using a Lagrangian relaxation-based approach. IEEE Transactions on Network and Service Management, 2(1):9–18.

    Article  Google Scholar 

  69. [69]

    Steuer, R. E. (1986). Multiple Criteria Optimization: Theory, Computation and Application. Probability and Mathematical Statistics. John Wiley & Sons.

    Google Scholar 

  70. [70]

    Talbi, E.-G., Basseur, M., Nebro, A. J. & Alba, E. (2012). Multi-objective optimization using metaheuristics: non-standard algorithms. International Transactions in Operational Research, 19(1–2):283–305.

    Article  MathSciNet  MATH  Google Scholar 

  71. [71]

    Wang, J., Patek, S., Wang, H. & Liebeherr, J. (2002). Traffic engineering with AIMD in MPLS networks. In Carle, G. & Zitterbart, M. (editors), Proceedings of the 7th IFIP/IEEE International Workshop on Protocols for High Speed Networks (PfHSN 2002), Lecture Notes in Computer Science, volume 2334, pages 192–210, Berlin, Germany, Apr.22–24, Springer.

    Google Scholar 

  72. [72]

    Wang, J. Y. T. & Ehrgott, M. (2011). Modelling stochastic route choice with bi-objective traffic assignment. In Proceedings of International Choice Modelling Conference 2011, Leeds, UK, Jul.4–6.

    Google Scholar 

  73. [73]

    Wang, J. Y. T. & Ehrgott, M. (2013). Modelling route choice behavior in a tolled road network with a time surplus maximisation bi-objective user equilibrium. Procedia — Social and Behavioral Sciences, 80:266–288.

    Article  Google Scholar 

  74. [74]

    Wierzbicki, A. P. & Burakowski, W. (2011). A conceptual framework for multiple-criteria routing in QoS IP networks. International Transactions in Operational Research, 18(3):377–399.

    Article  MathSciNet  Google Scholar 

  75. [75]

    Yang, H. & Huang, H.-J. (2004). The multiclass, multi-criteria traffic network equilibrium and systems optimum problem. Transportation Research Part B — Methodological, 38:1–15.

    Article  Google Scholar 

  76. [76]

    Zhang, Q. & Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 11(6):712–731.

    Article  Google Scholar 

  77. [77]

    Zitzler, E. (2012). Evolutionary multiobjective optimization. In Rozenberg, G., Bäck, T. & Kok, J. N. (editors), Handbook of Natural Computing, pages 871–904, Springer.

    Google Scholar 

  78. [78]

    gt-itm (2000). Modeling Topology of Large Internetworks. http://www.cc.gatech.edu/projects/gtitm/

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Rita Girão-Silva.

Additional information

Rita Girão-Silva graduated in electrical engineering (telecommunications) in 1999 and received her Ph.D. diploma in electrical engineering (telecommunications and electronics) in 2009, both at the University of Coimbra. She is an Assistant Professor at the Department of Electrical and Computer Engineering, University of Coimbra, and a researcher at INESC Coimbra. Her research areas include routing models in telecommunications networks and multiobjective optimization. She has participated in different research and development projects financed by FCT and the EC, and has also participated in projects of cooperation between university and industry (being the leader of one of them).

José Craveirinha is a retired Full Professor in Telecommunications at the Department of Electrical Engineering and Computers of the Faculty of Sciences and Technology of the University of Coimbra, Portugal. Academic degrees: diploma in Electrical Engineering Science (EES) — Telecommunications & Electronics, IST Lisbon Technical University, 1975; M.Sc. (1981) and Ph.D. in EES, University of Essex (UK) (1984), Doctor of Science (“Agregação”) in EES at the University of Coimbra (1996). Previous positions: Associate Professor at FCTUC, Coimbra Univ; Telecom R&D Engineer (CET-Portugal Telecom). Coordinator of a research group in Teletraffic Engineering and Network Design, INESC-Coimbra R&D institute, since 1986, Director of this institute 1994–99 and President of its Scientific Council. He is author of scientific publications in teletraffic modelling, reliability analysis, planning and optimisation of telecommunication networks. His main present interests are in multicriteria routing and resilient routing models and optimisation algorithms for optical and IP/MPLS networks.

João Clímaco is a retired Full Professor at the Faculty of Economics of the University of Coimbra. He is currently a researcher and Member of Conselho Geral of INESC-Coimbra, and co-coordinator of the PhD program on “Science Applied to Decision” at the Faculty of Economics of the University of Coimbra. He is Special Invited Researcher (PVE) of the Brazilian Scientific Program — Science Without Borders (Ciência sem Fronteiras), at the Federal University of Rio de Janeiro, two months per year till 2016. He obtained a Master of Science Degree in “Control Systems” at the Imperial College of Science and Technology, University of London (1978); the “Diploma of Membership of the Imperial College of Science and Technology” (1978); the Ph.D. in Optimization and Systems Theory, Electrical Engineering Department, University of Coimbra (1982); and the title of “Agregação” at the University of Coimbra (1989). He was awarded with: “Conference Chairman Award”, International Society on Multiple Criteria Decision Making (1995) and Grande Oficial da Ordem do Rio Branco, Brazil (1996). In 2013 he was awarded with the “Georg Cantor Award” by the International Society on Multiple Criteria Decision Making. He is Past Vice-President of ALIO — Latin Ibero American OR Association, Past Vice-President of the Portuguese OR Society, and Past Member of the International Executive Committee of the International Society on Multiple Criteria Decision Making. He is member of the IFIP-WG 8.3-Decision Support Systems. He belongs to the Editorial Board of the following Scientific Journals: “Group Decision and Negotiation”, “International Transactions in Operational Research”, “International Journal of Decision Support Systems” and Scientific World Journal — Operations Research Stream. He is also member of the Editorial Board of the University of Coimbra Press. He is author of about 160 works of Scientific Journal Papers (about 120) and Book Chapters (about 40) using the “peers refereeing selection”.

Maria Eugénia Captivo is an Associate Professor of Operations Research at Faculdade de Ciências da Universidade de Lisboa, and a researcher at the Operations Research Center. She obtained a graduation in Mathematics (1976), a Ph.D. in Operations Research (1988) and the title of “Agregação” (2005), all at Universidade de Lisboa. Her current research interests are in multicriteria combinatorial optimization, location problems, network optimization, surgery scheduling, decision support systems, production planning, cutting and packing. She coordinates the Master course in Statistics and Operational Research at Faculdade de Ciências da Universidade de Lisboa. She has supervised 11 Ph.D. and 20 M.Sc. students and participated in several research and development projects financed by different R&D agencies, such as the INIC, JNICT, FCT and AID (was the leader of two such projects) and in different projects of cooperation between university and industry. She is a member of INFORMS, EURO, MCDM, APDIO and SPM.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Girão-Silva, R., Craveirinha, J., Clímaco, J. et al. Multiobjective routing in multiservice MPLS networks with traffic splitting — A network flow approach. J. Syst. Sci. Syst. Eng. 24, 389–432 (2015). https://doi.org/10.1007/s11518-015-5262-4

Download citation

Keywords

  • Routing models
  • multiobjective optimization
  • telecommunication networks
  • network flow approach
  • traffic splitting