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

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## 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.

## Suggested Citation

• Vladimir Marianov & Daniel Serra, 2000. "Location models for airline hubs behaving as M/D/c queues," Economics Working Papers 453, Department of Economics and Business, Universitat Pompeu Fabra.
• Handle: RePEc:upf:upfgen:453
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File URL: https://econ-papers.upf.edu/papers/453.pdf
File Function: Whole Paper

## References listed on IDEAS

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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. 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. 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.
4. 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.
5. 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.
6. Klincewicz, J. G., 1991. "Heuristics for the p-hub location problem," European Journal of Operational Research, Elsevier, vol. 53(1), pages 25-37, July.
7. 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.
8. Aykin, Turgut, 1995. "The hub location and routing problem," European Journal of Operational Research, Elsevier, vol. 83(1), pages 200-219, May.
9. 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.
10. Berman, Oded & Mandowsky, Ronald R., 1986. "Location-allocation on congested networks," European Journal of Operational Research, Elsevier, vol. 26(2), pages 238-250, August.
Full references (including those not matched with items on IDEAS)

## Citations

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Cited by:

1. Jayaswal, Sachin & Vidyarthi, Navneet, 2013. "Capacitated Multiple Allocation Hub Location with Service Level Constraints for Multiple Consignment Classes," IIMA Working Papers WP2013-11-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
2. Ishfaq, Rafay & Sox, Charles R., 2012. "Design of intermodal logistics networks with hub delays," European Journal of Operational Research, Elsevier, vol. 220(3), pages 629-641.
3. repec:pal:jorsoc:v:60:y:2009:i:5:d:10.1057_palgrave.jors.2602606 is not listed on IDEAS
4. repec:spr:compst:v:73:y:2011:i:1:p:1-18 is not listed on IDEAS
5. Caccavale, Maria Virginia & Iovanella, Antonio & Lancia, Carlo & Lulli, Guglielmo & Scoppola, Benedetto, 2014. "A model of inbound air traffic: The application to Heathrow airport," Journal of Air Transport Management, Elsevier, vol. 34(C), pages 116-122.
6. Edward Hult & Houyuan Jiang & Daniel Ralph, 2014. "Exact computational approaches to a stochastic uncapacitated single allocation p-hub center problem," Computational Optimization and Applications, Springer, vol. 59(1), pages 185-200, October.
7. Vahdani, Behnam & Tavakkoli-Moghaddam, Reza & Modarres, Mohammad & Baboli, Armand, 2012. "Reliable design of a forward/reverse logistics network under uncertainty: A robust-M/M/c queuing model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(6), pages 1152-1168.
8. G. Guadagni & S. Ndreca & B. Scoppola, 2011. "Queueing systems with pre-scheduled random arrivals," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(1), pages 1-18, February.
9. Alumur, Sibel A. & Nickel, Stefan & Saldanha-da-Gama, Francisco, 2012. "Hub location under uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 46(4), pages 529-543.
10. Zhongfeng Qin & Yuan Gao, 2017. "Uncapacitated $$p$$ p -hub location problem with fixed costs and uncertain flows," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 705-716, March.
11. repec:pal:jorsoc:v:61:y:2010:i:6:d:10.1057_jors.2009.12 is not listed on IDEAS
12. Contreras, Ivan & Cordeau, Jean-François & Laporte, Gilbert, 2011. "Stochastic uncapacitated hub location," European Journal of Operational Research, Elsevier, vol. 212(3), pages 518-528, August.

### Keywords

Hub location; congestion; tabu-search;

### 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

### NEP fields

This paper has been announced in the following NEP Reports:

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