Transferability of collective transportation line networks from a topological and passenger demand perspective

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March 2015, 10(1): 1-16. doi: 10.3934/nhm.2015.10.1

Transferability of collective transportation line networks from a topological and passenger demand perspective

Eva Barrena ^1, , Alicia De-Los-Santos ^2, , Gilbert Laporte ^1, and Juan A. Mesa ^2,

1.	Interuniversity Research Center on Network Enterprise, Logistics and Transportation (CIRRELT), HEC Montréal, 3000 chemin de la Côte-Sainte-Catherine, Montréal, H3T 2A7, Canada, Canada
2.	Department of Applied Mathematics II, Higher Technical School of Engineering. University of Seville, Camino de los Descubrimientos s/n, Seville, 41092, Spain, Spain

Received July 2014 Revised December 2014 Published February 2015

Abstract
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We analyze the transferability of collective transportation line networks (CTLN) with the help of hypergraphs, their linearization, and connectivity measures from Complex Network Theory. In contrast to other existing works in the literature, where transferability is analyzed at a topological level, we are also concerned with passenger system level, introducing data on the travel patterns. This will allow us to have a more complete view of the functioning of the transfer system of a CTLN.

Keywords: Collective transportation line networks, transferability measures, passengers demand, complex networks, hypergraphs..

Mathematics Subject Classification: Primary: 05C82, 05C65, 05C40; Secondary: 90B10, 68M10, 90B0.

Citation: Eva Barrena, Alicia De-Los-Santos, Gilbert Laporte, Juan A. Mesa. Transferability of collective transportation line networks from a topological and passenger demand perspective. Networks and Heterogeneous Media, 2015, 10 (1) : 1-16. doi: 10.3934/nhm.2015.10.1

References:

[1]	A. Barabasi and R. Albert, Emergence of scaling in random networks, Science, 286 (1999), 509-512. doi: 10.1126/science.286.5439.509.
[2]	E. Barrena, A. De-Los-Santos, G. Laporte and J. A. Mesa, Passenger flow connectivity in collective transportation line networks, International Journal of Complex Systems in Science, 3 (2013), 1-10.
[3]	E. Barrena, A. De-Los-Santos, J. A. Mesa and F. Perea, Analyzing connectivity in collective transportation line networks by means of hypergraphs, European Physical Journal. Special Topics, 215 (2013), 93-108. doi: 10.1140/epjst/e2013-01717-3.
[4]	C. Berge, Graphes et Hypergraphes, Elsevier Science, Paris, 1973.
[5]	C. Berge, Hypergraphs: Combinatorics of Finite Sets, North-Holland Mathematical Library, North-Holland, Amsterdam, 1989. Available from: http://books.google.es/books?id=jEyfse-EKf8C.
[6]	R. Criado, B. Hernández-Bermejo and M. Romance, Efficiency, vulnerability and cost: An overview with applications to subway networks worldwide, International Journal of Bifurcation and Chaos, 17 (2007), 2289-2301. doi: 10.1142/S0218127407018397.
[7]	A. De-Los-Santos, G. Laporte, J. Mesa and F. Perea, Evaluating passenger robustness in a rail transit network, Transportation Research Part C: Emerging Technologies, 20 (2012), 34-46.
[8]	S. Derrible and C. Kennedy, The complexity and robustness of metro networks, Physica A: Statistical Mechanics and its Applications, 389 (2010), 3678-3691. doi: 10.1016/j.physa.2010.04.008.
[9]	G. Laporte, J. Mesa and F. Ortega, Assessing the efficiency of rapid transit configurations, TOP, 5 (1997), 95-104. doi: 10.1007/BF02568532.
[10]	G. Laporte, J. Mesa and F. Ortega, Optimization methods for the planning of rapid transit systems, European Journal of Operational Research, 122 (2000), 1-10. doi: 10.1016/S0377-2217(99)00016-8.
[11]	V. Latora and M. Marchiori, Efficient behavior of small-world networks, Physical Review Letters, 87 (2001), 198701-1-198701-4. doi: 10.1103/PhysRevLett.87.198701.
[12]	V. Latora and M. Marchiori, Is the Boston subway a small-world network?, Physica A, 314 (2002), 109-113. doi: 10.1016/S0378-4371(02)01089-0.
[13]	S. Milgram, The small world problem, Psychology Today, 1 (1967), 60-67. doi: 10.1037/e400002009-005.
[14]	C. Roth, S. Kang, M. Batty and M. Barthelemy, A long-time limit for world subway networks, Journal of The Royal Society Interface, 9 (2012), 2540-2550. doi: 10.1098/rsif.2012.0259.
[15]	K. Seaton and L. Hackett, Stations, trains and small-world networks, Physica A: Statistical Mechanics and its Applications, 339 (2004), 635-644. doi: 10.1016/j.physa.2004.03.019.
[16]	D. Watts and S. Strogatz, Collective dynamics of small-world networks, Nature, 393 (1998), 440-442.

show all references

References:

[1]	A. Barabasi and R. Albert, Emergence of scaling in random networks, Science, 286 (1999), 509-512. doi: 10.1126/science.286.5439.509.
[2]	E. Barrena, A. De-Los-Santos, G. Laporte and J. A. Mesa, Passenger flow connectivity in collective transportation line networks, International Journal of Complex Systems in Science, 3 (2013), 1-10.
[3]	E. Barrena, A. De-Los-Santos, J. A. Mesa and F. Perea, Analyzing connectivity in collective transportation line networks by means of hypergraphs, European Physical Journal. Special Topics, 215 (2013), 93-108. doi: 10.1140/epjst/e2013-01717-3.
[4]	C. Berge, Graphes et Hypergraphes, Elsevier Science, Paris, 1973.
[5]	C. Berge, Hypergraphs: Combinatorics of Finite Sets, North-Holland Mathematical Library, North-Holland, Amsterdam, 1989. Available from: http://books.google.es/books?id=jEyfse-EKf8C.
[6]	R. Criado, B. Hernández-Bermejo and M. Romance, Efficiency, vulnerability and cost: An overview with applications to subway networks worldwide, International Journal of Bifurcation and Chaos, 17 (2007), 2289-2301. doi: 10.1142/S0218127407018397.
[7]	A. De-Los-Santos, G. Laporte, J. Mesa and F. Perea, Evaluating passenger robustness in a rail transit network, Transportation Research Part C: Emerging Technologies, 20 (2012), 34-46.
[8]	S. Derrible and C. Kennedy, The complexity and robustness of metro networks, Physica A: Statistical Mechanics and its Applications, 389 (2010), 3678-3691. doi: 10.1016/j.physa.2010.04.008.
[9]	G. Laporte, J. Mesa and F. Ortega, Assessing the efficiency of rapid transit configurations, TOP, 5 (1997), 95-104. doi: 10.1007/BF02568532.
[10]	G. Laporte, J. Mesa and F. Ortega, Optimization methods for the planning of rapid transit systems, European Journal of Operational Research, 122 (2000), 1-10. doi: 10.1016/S0377-2217(99)00016-8.
[11]	V. Latora and M. Marchiori, Efficient behavior of small-world networks, Physical Review Letters, 87 (2001), 198701-1-198701-4. doi: 10.1103/PhysRevLett.87.198701.
[12]	V. Latora and M. Marchiori, Is the Boston subway a small-world network?, Physica A, 314 (2002), 109-113. doi: 10.1016/S0378-4371(02)01089-0.
[13]	S. Milgram, The small world problem, Psychology Today, 1 (1967), 60-67. doi: 10.1037/e400002009-005.
[14]	C. Roth, S. Kang, M. Batty and M. Barthelemy, A long-time limit for world subway networks, Journal of The Royal Society Interface, 9 (2012), 2540-2550. doi: 10.1098/rsif.2012.0259.
[15]	K. Seaton and L. Hackett, Stations, trains and small-world networks, Physica A: Statistical Mechanics and its Applications, 339 (2004), 635-644. doi: 10.1016/j.physa.2004.03.019.
[16]	D. Watts and S. Strogatz, Collective dynamics of small-world networks, Nature, 393 (1998), 440-442.

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