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 Bertsekas-Gafni, Nagurney 1, 2, 3, and 4 are well known in literature [1, 2] and here described by 3 files:

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:

ci,j = ti,j*{ 1 + Bi,j*[ (fi,j + Ki,j*fj,i) / (2*Ci,j) ]^pi,j },                        (1)


ci,j = travel cost on arc (i,j)
ti,j = free flow time on arc (i,j)
Bi,j = constant B on arc (i,j)
fi,j = flow on arc (i,j)
Ki,j = asymmetry factor on arc (i,j)
fj,i = flow on arc (j,i) opposite of (i,j)
Ci,j = capacity of arc (i,j)
pi,j = power on arc (i,j)

These networks are described by 3 text files:

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:



  1. 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.
  2. Nagurney A., Comparative test of multimodal traffic equilibrium methods, Transportation Research B, vol. 18 (1984), pp. 469?485.
  3. 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.
  4. http://www.bgu.ac.il/~bargera/tntp
  5. 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