Test networks for the Asymmetric Network Equilibrium Problem

Here you can get 7 test networks for the asymmetric network equilibrium problem:

Network | nodes | arcs | O/D pairs | Topology | O/D demands | Arc costs |

Betsekas-Gafni | 25 | 40 | 5 | bergaf_net | bergaf_demands | bergaf_costs |

Nagurney 1 | 20 | 28 | 8 | nag1_net | nag1_demands | nag1_costs |

Nagurney 2 | 22 | 36 | 12 | nag2_net | nag2_demands | nag2_costs |

Nagurney 3 | 25 | 37 | 6 | nag3_net | nag3_demands | nag3_costs |

Nagurney 4 | 40 | 66 | 6 | nag4_net | nag4_demands | nag4_costs |

Asymmetric Sioux Falls | 24 | 76 | 528 | sf_net | sf_demands | sf_costs |

Asymmetric Barcelona | 1,020 | 2,522 | 7,922 | barcelona_net | barcelona_demands | barcelona_costs |

Asymmetric Winnipeg | 1,052 | 2,836 | 4,345 | winnipeg_net | winnipeg_demands | winnipeg_costs |

Arezzo | 213 | 598 | 2,423 | arezzo_net | arezzo_demands | arezzo_costs |

Lazio | 306 | 926 | 5,683 | lazio_net | lazio_demands | lazio_costs |

The networks

- topology contains one row per arc: tail node - head node
- O/D demands contains one row per O/D pair: origin - destination - demand
- arc costs is a MATLAB m-file defining the cost function

The networks *Asymmetric Sioux Falls, Asymmetric Bercelona, and Asymmetric Winnipeg* are modifications of well known networks
in literature [3, 4] in which the separable arc cost function is substituted with the following arc cost function with asymmetric jacobian:

c_{i,j} = t_{i,j}*{ 1 + B_{i,j}*[ (f_{i,j} + K_{i,j}*f_{j,i}) / (2*C_{i,j}) ]^p_{i,j} },
(1)

c_{i,j} = travel cost on arc (i,j)

t_{i,j} = free flow time on arc (i,j)

B_{i,j} = constant B on arc (i,j)

f_{i,j} = flow on arc (i,j)

K_{i,j} = asymmetry factor on arc (i,j)

f_{j,i} = flow on arc (j,i) opposite of (i,j)

C_{i,j} = capacity of arc (i,j)

p_{i,j} = power on arc (i,j)

These networks are described by 3 text files:

- topology contains one row per arc: tail node - head node
- O/D demands contains one row per O/D pair: origin - destination - demand
- arc costs contains one row per arc: free flow time - constant B - capacity - power - asymmetry factor

The networks *Arezzo and Lazio* are new real networks representing the extraurban area of the city of Arezzo (Italy)
and of the region Lazio (Italy). They have been provided by Prof. Antonio Pratelli at the Department of Civil
Engineering, University of Pisa.

These networks have arc cost functions defined as in (1) and they are described by 3 text files:

- topology contains one row per arc: tail node - head node
- O/D demands contains one row per O/D pair: origin - destination - demand
- arc costs contains one row per arc: free flow time - constant B - capacity - power - asymmetry factor

**References**

- Bertsekas D. P. and Gafni E. M., Projection methods for variational inequalities with application to the traffic assignment problem, Mathematical Programming Study, vol. 17 (1982), pp. 139?159.
- Nagurney A., Comparative test of multimodal traffic equilibrium methods, Transportation Research B, vol. 18 (1984), pp. 469?485.
- LeBlanc L. J., Morlok E. K. and Pierskalla W. P., An Efficient Approach to Solving the Road Network Equilibrium Traffic Assignment Problem, Transportation Research, vol. 9 (1975), pp. 309?318.
- http://www.bgu.ac.il/~bargera/tntp
- Panicucci B., Pappalardo M., Passacantando M. (2007), A path-based double projection method for solving the asymmetric traffic network equilibrium problem, Optimization Letters, vol. 1, pp. 171-185