Journal of Global Optimization

, Volume 65, Issue 4, pp 745–776

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

  • Navneet Vidyarthi
  • Sachin Jayaswal
  • Vikranth Babu Tirumala Chetty
Article

DOI: 10.1007/s10898-015-0399-8

Cite this article as:
Vidyarthi, N., Jayaswal, S. & Tirumala Chetty, V.B. J Glob Optim (2016) 65: 745. doi:10.1007/s10898-015-0399-8

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.

Keywords

Bandwidth packing Telecommunications Call routing Integer programming Queuing delay Finite linearization Constraint generation 

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Navneet Vidyarthi
    • 1
  • Sachin Jayaswal
    • 2
  • Vikranth Babu Tirumala Chetty
    • 3
  1. 1.Department of Supply Chain and Business Technology Management, John Molson School of Business and Interuniversity Research Centre on Enterprise Networks, Logistics, and Transportation (CIRRELT)Concordia UniversityMontrealCanada
  2. 2.Production and Quantitative MethodsIndian Institute of ManagementVastrapur, AhmedabadIndia
  3. 3.Industrial and Systems Engineering College of EngineeringUniversity of WashingtonSeattleUSA

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