7.16 Appendix 2: The Challenge of Fairness
151
Carvalho, Lubos Buzna and others,
20 I therefore investigated the problem of distributional fairness for the case of natural gas, which is transported through pipelines.
The proportion of a pipeline that is used to serve various different destinations can
be visualized in a pie chart (i.e. similar to cutting a cake). But in the case of natural
gas supply for various cities and countries, the problem of distributional fairness
requires one to cut several cakes at the same time. Given the multiple constraints set
by the capacities of the pipelines, it is usually impossible to achieve perfect fairness
everywhere. Therefore, it is often necessary to make a compromise, and it is actually
a difficult mathematical challenge to find a good one.
Surprisingly, the constraints implied by the pipeline capacities can be particularly
problematic if less gas is transported overall, as it might happen when one of the
source regions does not deliver for geopolitical or other reasons. Then it is necessary
to redistribute gas from other source regions, in order to maintain gas deliveries for
everyone. Despite the smaller volumes of gas delivery, this will often lead to pipeline
congestion problems, as the pipeline network was not designed to be used in this
way. However, our study could show that it is still possible to achieve a resilient gas
supply, if a fairness-oriented algorithm inspired by the Internet routing protocol is
applied.
References
1. D. Helbing et al. (2009) Theoretical vs. empirical classification and prediction of congested
traffic states. Eur. Phys. J. B 69, 583–598.
2. D. Helbing (2001) Traffic and related self-driven many-particle systems. Reviews of Modern
Physics 73, 1067–1141.
3. A. Kesting, M. Treiber, M. Schönhof, and D. Helbing (2008) Adaptive cruise control design
for active congestion avoidance. Transportation Research C 16(6), 668–683.
4. A. Kesting, M. Treiber, and D. Helbing (2010) Enhanced intelligent driver model to access the
impact of driving strategies on traffic capacity. Phil. Trans. R. Soc. A 368(1928), 4585–4605.
5. A. Kesting, M. Treiber, and D. Helbing (2010) Connectivity statistics of store-and-forward
intervehicle communication. IEEE Transactions on Intelligent Transportation Systems 11(1),
172–181.
6. D. Helbing and P. Molnár (1995) Social force model for pedestrian dynamics. Physical Review
E 51, 4282–4286.
7. D. Helbing, S. Lämmer, and J.-P. Lebacque (2005) Self-organized control of irregular or
perturbed network traffic. Pages 239–274 in: C. Deissenberg and R. F. Hartl (eds.) Optimal
Control and Dynamic Games (Springer, Dordrecht).
8. S. Lämmer (2007) Reglerentwurf zur dezentralen Online-Steuerung von Lichtsignalanlagen in
Straßennetzwerken (PhD thesis, TU Dresden).
9. S. Lämmer and D. Helbing (2008) Self-control of traffic lights and vehicle flows in urban road
networks. Journal of Statistical Mechanics: Theory and Experiment, P04019, see http://iopsci
ence.iop.org/1742-5468/2008/04/P04019.
10. S. Lämmer, R. Donner, and D. Helbing (2007) Anticipative control of switched queueing
systems, The European Physical Journal B 63(3) 341–347.
11. D. Helbing, J. Siegmeier, and S. Lämmer (2007) Self-organized network flows. Networks and
Heterogeneous Media 2(2), 193–210.
20 Carvalho et al. [25].
151
Carvalho, Lubos Buzna and others,
20 I therefore investigated the problem of distributional fairness for the case of natural gas, which is transported through pipelines.
The proportion of a pipeline that is used to serve various different destinations can
be visualized in a pie chart (i.e. similar to cutting a cake). But in the case of natural
gas supply for various cities and countries, the problem of distributional fairness
requires one to cut several cakes at the same time. Given the multiple constraints set
by the capacities of the pipelines, it is usually impossible to achieve perfect fairness
everywhere. Therefore, it is often necessary to make a compromise, and it is actually
a difficult mathematical challenge to find a good one.
Surprisingly, the constraints implied by the pipeline capacities can be particularly
problematic if less gas is transported overall, as it might happen when one of the
source regions does not deliver for geopolitical or other reasons. Then it is necessary
to redistribute gas from other source regions, in order to maintain gas deliveries for
everyone. Despite the smaller volumes of gas delivery, this will often lead to pipeline
congestion problems, as the pipeline network was not designed to be used in this
way. However, our study could show that it is still possible to achieve a resilient gas
supply, if a fairness-oriented algorithm inspired by the Internet routing protocol is
applied.
References
1. D. Helbing et al. (2009) Theoretical vs. empirical classification and prediction of congested
traffic states. Eur. Phys. J. B 69, 583–598.
2. D. Helbing (2001) Traffic and related self-driven many-particle systems. Reviews of Modern
Physics 73, 1067–1141.
3. A. Kesting, M. Treiber, M. Schönhof, and D. Helbing (2008) Adaptive cruise control design
for active congestion avoidance. Transportation Research C 16(6), 668–683.
4. A. Kesting, M. Treiber, and D. Helbing (2010) Enhanced intelligent driver model to access the
impact of driving strategies on traffic capacity. Phil. Trans. R. Soc. A 368(1928), 4585–4605.
5. A. Kesting, M. Treiber, and D. Helbing (2010) Connectivity statistics of store-and-forward
intervehicle communication. IEEE Transactions on Intelligent Transportation Systems 11(1),
172–181.
6. D. Helbing and P. Molnár (1995) Social force model for pedestrian dynamics. Physical Review
E 51, 4282–4286.
7. D. Helbing, S. Lämmer, and J.-P. Lebacque (2005) Self-organized control of irregular or
perturbed network traffic. Pages 239–274 in: C. Deissenberg and R. F. Hartl (eds.) Optimal
Control and Dynamic Games (Springer, Dordrecht).
8. S. Lämmer (2007) Reglerentwurf zur dezentralen Online-Steuerung von Lichtsignalanlagen in
Straßennetzwerken (PhD thesis, TU Dresden).
9. S. Lämmer and D. Helbing (2008) Self-control of traffic lights and vehicle flows in urban road
networks. Journal of Statistical Mechanics: Theory and Experiment, P04019, see http://iopsci
ence.iop.org/1742-5468/2008/04/P04019.
10. S. Lämmer, R. Donner, and D. Helbing (2007) Anticipative control of switched queueing
systems, The European Physical Journal B 63(3) 341–347.
11. D. Helbing, J. Siegmeier, and S. Lämmer (2007) Self-organized network flows. Networks and
Heterogeneous Media 2(2), 193–210.
20 Carvalho et al. [25].