A cutting plane approach to combinatorial bandwidth packing problem with queuing delays
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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.
KeywordsOR in telecommunications Bandwidth packing Integer programming Queueing Cutting plane algorithm
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.
- 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)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
- 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