Skip to main content

Hierarchical Two Level Location Problems

  • Chapter
Telecommunications Network Planning

Part of the book series: Centre for Research on Transportation ((CRT))

Abstract

A telecommunication network is usually composed of a backbone network and of local access networks. The backbone network enables the transfer of large volumes of information between its nodes whereas each local access network connects a group of terminals to an access node of the backbone network. Communication channels between terminals are established through their access nodes via the backbone network. The design of a telecommunication network is so complex that the process is usually split into phases where each phase handles a subproblem and makes decisions that are fixed and used as input to the next phases (Gavish, 1991 and 1992). A standard approach involves the following phases (Minoux, 1989; Gavish, 1991):

  • â–  the choice of locations for backbone nodes,

  • â–  the assignment of terminals to backbone nodes,

  • â–  the design of local access networks,

  • â–  the design of the backbone network,

  • â–  the evaluation of the network in terms of performance and reliability.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Aardal K. Y. Pochet and L.A. Wolsey. 1995. Capacitated Facility Location Valid Inequalities and Facets. Mathematics of Operations Research 203562–582. Correction of printing errors in 211253-256

    Google Scholar 

  • Ahn, S., C. Cooper, G. Cornuéjols and A.M. Frieze. (1988). Probabilistic Analysis of a Relaxation for the k-Median Problem. Mathematics of Operations Research, 13:1–31.

    Article  Google Scholar 

  • Balakrishnan, A., T.L. Magnanti and P. Mirchandani. (1994a). A Dual-Based Algorithm for Multi-Level Network Design Problem. Management Science, 40:567–581.

    Article  Google Scholar 

  • Balakrishnan, A., T.L. Magnanti and P. Mirchandani. (1994b). Modeling and Worst-Case Performance Analysis of the Two-Level Network Design Problem. Management Science, 40:846–867.

    Article  Google Scholar 

  • Barcelo, J., E. Fernandez and K. Jörnten. (1991). Computational Results from a New Lagrangian Relaxation Algorithm for the Capacited Plant Location Problem. European Journal of Operational Research, 53:38–45.

    Article  Google Scholar 

  • Beasley, J.E. (1988). An Algorithm for Solving Large Capacitated Wharehouse Location Problems. European Journal of Operational Research, 33:314–325.

    Article  Google Scholar 

  • Beasley, J.E. (1993). Lagrangean Heuristics for Location Problems. European Journal of Operational Research, 65:383–399.

    Article  Google Scholar 

  • Chardaire, P., M.C. Costa and A. Sutter. (1996a). Solving the Dynamic Facility Location Problem. Networks, 28:117–124.

    Article  Google Scholar 

  • Chardaire, P. and M. Lesk. (1986). Grade of Service and Optimization of Distributed Packet-Switched Networks. Computer Networks and ISDN Systems, 11:139–146.

    Article  Google Scholar 

  • Chardaire, P. and J.-L. Lutton. (1990). L’optimisation des réseaux de données. L’écho des recherches, 141:19–30.

    Google Scholar 

  • Chardaire, P. and J.-L. Lutton. (1993). Using Simulated Annealing to Solve Concentrator Location Problems in Telecommunication Networks. In R. Valqui Vidal (ed), Applied Simulated Annealing, Lecture Notes Series, pages 175–199. Springer Verlag, Berlin.

    Chapter  Google Scholar 

  • Chardaire, P., J.-L. Lutton and A. Sutter. (1996b). Effective Formulation for the Two Level Simple Plant Location Problem. To appear in Annals of Operations Research.

    Google Scholar 

  • Christofides, N. and J.E. Beasley. (1983). Extension to a Lagrangian Relaxation Approach for the Capacitated Warehouse Location Problem. European Journal of Operational Research, 12(1):19–28.

    Article  Google Scholar 

  • Colbourn, C.J. (1987). The Combinatorics of Network Reliability. Oxford University Press, Oxford.

    Google Scholar 

  • Cornuéjols, G., M. Fisher and G.L. Nemhauser. (1977). Location of Banks Account to Optimise Float: An Analytic Study of Exact and Approximate Algorithm. Management Science, 23:789–810.

    Article  Google Scholar 

  • Cornuéjols, G., G.L. Nemhauser and L.A. Wolsey. (1990). The Uncapacited Facility Location Problem. In P. B. Mirchandani and R. L. Francis (eds), Discrete Location Theory, pages 119–172. John Wiley and Sons, New York, NY.

    Google Scholar 

  • Cornuéjols, G., R. Sridharan and J.M. Thizy. (1991). A Comparison of Heuristics and Relaxations for the Capacited Plant Location Problem. European Journal of Operational Research, 50:280–297.

    Article  Google Scholar 

  • Dionne, R. and M. Florian. (1979). Exact and Approximate Algorithm for Optimal Network Design. Networks, 9:39–59.

    Article  Google Scholar 

  • Erlenkotter, D. (1978). A Dual-Based Procedure for Uncapacited Facilities Location. Operations Research, 26:992–1009.

    Article  Google Scholar 

  • Francis, R, and P. Mirchandani, editors. (1990). Discrete Location Theory. John Wiley and Sons, New York, NY.

    Google Scholar 

  • Gavish, B. (1982). Topological Design of Centralized Computer Networks — Formulations and Algorithms. Networks, 12:355–377.

    Article  Google Scholar 

  • Gavish, B. (1983). Formulations and Algorithms for the Capacitated Minimal Directed Tree Problem. Journal of the ACM, 30(1):118–132.

    Article  Google Scholar 

  • Gavish, B. (1991). Topological Design of Telecommunication Networks — Survey of Local Access Network Design Methods. Annals of Operations Research, 33:17–71.

    Article  Google Scholar 

  • Gavish, B. (1992). Topological Design of Computer Communication Networks — the Overall Design Problem. European Journal of Operational Research, 58:149–172.

    Article  Google Scholar 

  • Goffin, J.L. (1977). On Convergence Rates of Subgradient Optimization Methods. Mathematical Programming, 13:329–347.

    Article  Google Scholar 

  • Gouveia, L. and M.J. Lopes. (1997). Using Generalized Capacitated Trees for Designing the Topology of Local Access Networks. Telecommunication Systems, 7:315–337.

    Article  Google Scholar 

  • Gouveia, L, and J. Paixão. (1991). Dynamic Programming Based Heuristics for the Topological Design of Local Access Networks. Annals of Operations Research, 33:305–327.

    Article  Google Scholar 

  • Hu, T.C. (1974). Optimum Communication Spanning Trees. SIAM Journal On Computing, 3(3):188–195.

    Article  Google Scholar 

  • Jacobsen, S.K. (1983). Heuristics for the Capacitated Plant Location Model. European Journal of Operational Research, 12(3):253–261.

    Article  Google Scholar 

  • Kershenbaum, A. (1974). Computing Capacitated Minimal Spanning Trees Efficiently. Networks, 4:299–310.

    Article  Google Scholar 

  • Kershenbaum, A. and R.R. Boorstyn. (1983). Centralized Teleprocessing Network Design. Networks, 13:279–293.

    Article  Google Scholar 

  • Konangi, V.K., T. Aidja and C.R. Dhas. (1984). On the Multilevel Concentrator Location Problem for Local Access Networks. In Proceedings of IEEE Globecom, pages 912–915.

    Google Scholar 

  • Krarup, J. and P. Pruzan. (1983). The Simple Plant Location Problem: Survey and Synthesis. European Journal of Operational Research, 12:36–81.

    Article  Google Scholar 

  • Leung, J.M.Y. and T.L. Magnanti. (1989). Valid Inequalities and Facets of the Capacitated Plant Location Problem. Mathematical Programming, 44(3):271–291.

    Article  Google Scholar 

  • McGregor, P. and D. Shen. (1977). Network Design: An Algorithm for Access Facility Location Problems. IEEE Transactions on Communications, 25:61–73.

    Article  Google Scholar 

  • Minoux, M. (1986). Mathematical Programming: Theory and Algorithms. John Wiley and Sons, New York, NY.

    Google Scholar 

  • Minoux, M. (1989). Network Synthesis and Optimum Network Design Problems: Models, Solution Methods and Applications. Networks, 19:313–360.

    Article  Google Scholar 

  • Mirchandani, P. (1996). The Multi-Tier Tree Problem. INFORMS Journal on Computing, 8(3):202–218.

    Article  Google Scholar 

  • Myung, Y.S., C.H. Lee and D.W. Tcha. (1995). On the Generalized Minimum Spanning Tree Problem. Networks, 26(4):231–241.

    Article  Google Scholar 

  • Narasimhan, S. and H. Pirkul. (1992). Hierarchical Concentrator Location Problem. Computer Communications, 15(3):185–191.

    Article  Google Scholar 

  • Networks Special Issue. (1995). C.J. Colbourn and K. Sutner (eds), Special Issue on Computing Network Reliability and Performability. Networks, 25(3).

    Google Scholar 

  • Palmer, C.C. and A. Kershenbaum. (1995). An Approach to a Problem in Network Design Using Genetic Algorithms. Networks, 26(3):151–163.

    Article  Google Scholar 

  • Pirkul, H. and V. Nagarajan, (1992). Locating Concentrators in Centralized Computer Networks. Annals of Operations Research, 36:257–262.

    Article  Google Scholar 

  • Schneider, G.M. and M.N. Zastrow. (1982). An Algorithm for the Design of Multilevel Concentrator Networks. Computer Networks, 6:1–11.

    Google Scholar 

  • Sharaiha, Y., M. Gendreau, G. Laporte and I. Osman. (1997). A Tabu Search Algorithm for the Capacitated Shortest Spanning Tree Problem. Networks, 29:161–171.

    Article  Google Scholar 

  • Shetty, B. (1990). Approximate Solutions to Large-Scale Capacitated Facility Location-Problems. Applied Mathematics and Computation, 39(2):159–175.

    Article  Google Scholar 

  • Shier, D. (1991). Network Reliability and Algebraic Structures. Clarendon Press, Oxford.

    Google Scholar 

  • Shor, N.Z. (1968). On the Rate of Convergence of the Generalized Gradient Method. Kibernetika, 4(3):98–99.

    Google Scholar 

  • Tang, D.T., L.S. Woo and L.R. Bahl. (1978). Optimization of Teleprocessing Networks with Concentrators and Multiconnected Networks. IEEE Transactions on Computers, C-27. 594–604.

    Article  Google Scholar 

  • Van Roy, T.J. (1986). A Cross Decomposition Algorithm for Capacitated Facility Location. Operations Research, 34(1):145–163.

    Article  Google Scholar 

  • Xue, G, (1997). Linear Time Algorithm for Computing the Most Reliable Source on an Unreliable Tree Network. Networks, 30(1):37–45.

    Article  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media New York

About this chapter

Cite this chapter

Chardaire, P. (1999). Hierarchical Two Level Location Problems. In: Sansò, B., Soriano, P. (eds) Telecommunications Network Planning. Centre for Research on Transportation. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5087-7_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-5087-7_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7314-8

  • Online ISBN: 978-1-4615-5087-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics