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

## 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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 Length: Date of creation: Mar 2000 Date of revision: Handle: RePEc:upf:upfgen:453 Contact details of provider: Web page: http://www.econ.upf.edu/

## References

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1. 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.
2. 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.
3. Berman, Oded & Mandowsky, Ronald R., 1986. "Location-allocation on congested networks," European Journal of Operational Research, Elsevier, vol. 26(2), pages 238-250, August.
4. 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.
5. Klincewicz, J. G., 1991. "Heuristics for the p-hub location problem," European Journal of Operational Research, Elsevier, vol. 53(1), pages 25-37, July.
6. 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.
7. Aykin, Turgut, 1995. "The hub location and routing problem," European Journal of Operational Research, Elsevier, vol. 83(1), pages 200-219, May.
8. 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.
9. Vladimir Marianov & Daniel Serra, 1994. "Probabilistic maximal covering location models for congested systems," Economics Working Papers 70, Department of Economics and Business, Universitat Pompeu Fabra.
10. 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.
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