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A cutting plane approach to combinatorial bandwidth packing problem with queuing delays

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Abstract

The combinatorial bandwidth packing problem (CBPP), arising in a telecommunication network with limited bandwidth, is defined as follows. Given a set of requests, each with its potential revenue, and each consisting of calls with their bandwidth requirements, decide: (1) a subset of the requests to accept/reject; and (2) a route for each call in accepted requests, so as to maximize the total revenue earned in a telecommunication network with limited bandwidth. However, telecommunication networks are generally characterized by variability in the call (bits) arrival rates and service times, resulting in queuing delays in the network. In this paper, we present a non-linear integer programming model to account for such delays in CBPP. Using simple transformation and piecewise outer-approximation, we reformulate the model as a linear mixed integer program (MIP), but with a large number of constraints. We present an efficient cutting plane approach to solve the resulting linear MIP to \(\epsilon \)-optimality.

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References

  1. Amiri, A.: The multi-hour bandwidth packing problem with response time guarantees. Inform. Technol. Manag. 4, 113–127 (2003)

    Article  Google Scholar 

  2. Amiri, A.: The selection and scheduling of telecommunication calls with time windows. Eur. J. Oper. Res. 167(1), 243–256 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Amiri, A., Barkhi, R.: The multi-hour bandwidth packing problem. Comput. Oper. Res. 27, 1–14 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Amiri, A., Barkhi, R.: The combinatorial bandwidth packing problem. Eur. J. Oper. Res. 208, 37–45 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Amiri, A., Rolland, E., Barkhi, R.: Bandwidth packing with queuing delay costs: bounding and heuristic procedures. Eur. J. Oper. Res. 112, 635–645 (1999)

    Article  MATH  Google Scholar 

  6. Anderson, C., Fraughnaugh, K., Parkner, M., Ryan, J.: Path assignment for call routing: an application of tabu search. Ann. Oper. Res. 41, 301–312 (1993)

    Article  MATH  Google Scholar 

  7. Bose, I.: Bandwidth packing with priority classes. Eur. J. Oper. Res. 192, 313–325 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cox, L., Davis, L., Qui, Y.: Dynamic anticipatory routing in circuit-switched telecommunications networks. In: Davis, L. (ed.). Handbook of Genetic Algorithms, vol. 11, pp 229–340. Van Norstrand/Reinhold, New York (1991)

  9. Elhedhli, S.: Exact solution of a class of nonlinear knapsack problems. Oper. Res. Lett. 33(6), 615–624 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Gavish, B., Hantler, S.: An algorithm for optimal route selection in SNA networks. IEEE Trans. Commun. 31(10), 1154–1161 (1983)

    Article  Google Scholar 

  11. Han, J., Lee, K., Lee, C., Park, S.: Exact algorithms for a bandwidth packing problem with queueing delay guarantees. INFORMS J. Comput. (2012). doi:10.1287/ijoc.1120.0523

  12. Laguna, M., Glover, F.: Bandwidth packing: a tabu search approach. Manag. Sci. 39, 492–500 (1993)

    Article  MATH  Google Scholar 

  13. Park, K., Kang, S., Park, S.: An integer programming approach to the bandwidth packing problem. Manag. Sci. 42, 1277–1291 (1996)

    Article  MATH  Google Scholar 

  14. Parker, M., Ryan, J.: A column generation algorithm for bandwidth packing. Telecommun. Syst. 2(1), 185–195 (1993)

    Article  Google Scholar 

  15. Rolland, E., Amiri, A., Barkhi, R.: Queueing delay guarantees in bandwidth packing. Comput. Oper. Res. 26, 921–935 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  16. Vidyarthi, N., Jayaswal, S., Tirumala Chetty, V.B.: Exact solution to bandwidth packing problem with queuing delays. J. Glob. Optim. (2016). doi:10.1007/s10898-015-0399-8

  17. Villa, C., Hoffman, K.: A column-generation and branch-and-cut approach to the bandwidth-packing problem. J. Res. Natl. Instit. Stand. Technol. 111, 161–185 (2006)

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by the Research and Publication Grant, Indian Institute of Management Ahmedabad, provided to the first author, and by the Canadian Natural Science and Engineering Research Council Discovery Grant 386501-2010 provided to the second author. This support is gratefully acknowledged. The authors also acknowledge Vikranth B. T. Chetty for his assistance in computational experiments. The authors would like to thank the editor-in-chief as well as the referees for the constructive comments on the earlier version of the paper.

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Authors and Affiliations

  1. Production and Quantitative Methods, Indian Institute of Management Ahmedabad, Ahmedabad, India

    Sachin Jayaswal

  2. Department of Supply Chain and Business Technology Management, John Molson School of Business, Concordia University, Montreal, Canada

    Navneet Vidyarthi

  3. Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Sagnik Das

Authors
  1. Sachin Jayaswal
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  2. Navneet Vidyarthi
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  3. Sagnik Das
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Correspondence to Sachin Jayaswal.

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Jayaswal, S., Vidyarthi, N. & Das, S. A cutting plane approach to combinatorial bandwidth packing problem with queuing delays. Optim Lett 11, 225–239 (2017). https://doi.org/10.1007/s11590-016-1005-9

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  • DOI: https://doi.org/10.1007/s11590-016-1005-9

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