# Location models for airline hubs behaving as M/D/c queues

• Daniel Serra

()

## Abstract

Models are presented for the optimal location of hubs in airline networks, that take into consideration the congestion effects. Hubs, which are the most congested airports, are modeled as M/D/c queuing systems, that is, Poisson arrivals, deterministic service time, and {\em c} servers. A formula is derived for the probability of a number of customers in the system, which is later used to propose a probabilistic constraint. This constraint limits the probability of {\em b} airplanes in queue, to be lesser than a value $\alpha$. Due to the computational complexity of the formulation. The model is solved using a meta-heuristic based on tabu search. Computational experience is presented.

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## Bibliographic Info

Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 453.

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Handle: RePEc:upf:upfgen:453

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Web page: http://www.econ.upf.edu/

## Related research

Keywords: Hub location; congestion; tabu-search;

Find related papers by JEL classification:

• C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
• R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
• R53 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Regional Government Analysis - - - Public Facility Location Analysis; Public Investment and Capital Stock

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## References

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1. Marianov, Vladimir & Serra, Daniel & ReVelle, Charles, 1999. "Location of hubs in a competitive environment," European Journal of Operational Research, Elsevier, vol. 114(2), pages 363-371, April.
2. Klincewicz, J. G., 1991. "Heuristics for the p-hub location problem," European Journal of Operational Research, Elsevier, vol. 53(1), pages 25-37, July.
3. O'kelly, Morton E., 1987. "A quadratic integer program for the location of interacting hub facilities," European Journal of Operational Research, Elsevier, vol. 32(3), pages 393-404, December.
4. Aykin, Turgut, 1995. "The hub location and routing problem," European Journal of Operational Research, Elsevier, vol. 83(1), pages 200-219, May.
5. Marianov, Vladimir & Revelle, Charles, 1994. "The queuing probabilistic location set covering problem and some extensions," Socio-Economic Planning Sciences, Elsevier, vol. 28(3), pages 167-178.
6. Campbell, James F., 1994. "Integer programming formulations of discrete hub location problems," European Journal of Operational Research, Elsevier, vol. 72(2), pages 387-405, January.
7. Skorin-Kapov, Darko & Skorin-Kapov, Jadranka, 1994. "On tabu search for the location of interacting hub facilities," European Journal of Operational Research, Elsevier, vol. 73(3), pages 502-509, March.
8. Marianov, Vladimir & ReVelle, Charles, 1996. "The Queueing Maximal availability location problem: A model for the siting of emergency vehicles," European Journal of Operational Research, Elsevier, vol. 93(1), pages 110-120, August.
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