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Bandwidth packing problem with queueing delays: modelling and exact solution approach

Author

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  • Navneet Vidyarthi

    (Concordia University)

  • Sachin Jayaswal

    (Indian Institute of Management)

  • Vikranth Babu Tirumala Chetty

    (University of Washington)

Abstract

We present a more generalized model for the bandwidth packing problem with queuing delays under congestion than available in the extant literature. The problem, under Poison call arrivals and general service times, is set up as a network of spatially distributed independent M/G/1 queues. We further present two exact solution approaches to solve the resulting nonlinear integer programming model. The first method, called finite linearization method, is a conventional Big-M based linearization, resulting in a finite number of constraints, and hence can be solved using an off-the-shelve MIP solver. The second method, called constraint generation method, is based on approximating the non-linear delay terms using supporting hyperplanes, which are generated as needed. Based on our computational study, the constraint generation method outperforms the finite linearization method. Further comparisons of results of our proposed constraint generation method with the Lagrangean relaxation based solution method reported in the literature for the special case of exponential service times clearly demonstrate that our approach outperforms the latter, both in terms of the quality of solution and computation times.

Suggested Citation

  • Navneet Vidyarthi & Sachin Jayaswal & Vikranth Babu Tirumala Chetty, 2016. "Bandwidth packing problem with queueing delays: modelling and exact solution approach," Journal of Global Optimization, Springer, vol. 65(4), pages 745-776, August.
  • Handle: RePEc:spr:jglopt:v:65:y:2016:i:4:d:10.1007_s10898-015-0399-8
    DOI: 10.1007/s10898-015-0399-8
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    References listed on IDEAS

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    1. Kyungchul Park & Seokhoon Kang & Sungsoo Park, 1996. "An Integer Programming Approach to the Bandwidth Packing Problem," Management Science, INFORMS, vol. 42(9), pages 1277-1291, September.
    2. Amiri, Ali, 2005. "The selection and scheduling of telecommunication calls with time windows," European Journal of Operational Research, Elsevier, vol. 167(1), pages 243-256, November.
    3. Bose, Indranil, 2009. "Bandwidth packing with priority classes," European Journal of Operational Research, Elsevier, vol. 192(1), pages 313-325, January.
    4. Jinil Han & Kyungsik Lee & Chungmok Lee & Sungsoo Park, 2013. "Exact Algorithms for a Bandwidth Packing Problem with Queueing Delay Guarantees," INFORMS Journal on Computing, INFORMS, vol. 25(3), pages 585-596, August.
    5. Manuel Laguna & Fred Glover, 1993. "Bandwidth Packing: A Tabu Search Approach," Management Science, INFORMS, vol. 39(4), pages 492-500, April.
    6. Amiri, Ali & Rolland, Erik & Barkhi, Reza, 1999. "Bandwidth packing with queuing delay costs: Bounding and heuristic solution procedures," European Journal of Operational Research, Elsevier, vol. 112(3), pages 635-645, February.
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    Cited by:

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    3. Tiwari, Richa & Jayaswal, Sachin & Sinha, Ankur, 2019. "Alternate Solution Approaches for Competitive Hub Location Problems," IIMA Working Papers WP 2019-12-01, Indian Institute of Management Ahmedabad, Research and Publication Department.

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