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README.md

USER-EQUILIBRIUM-SOLUTION

User equilibrium is a classical problem on the traffic flow assignment in the field of Transportation Engineering, its main idea is: Every driver cannot reduce his travel time by unilaterally change his travel route.

THEORY

Please read User-Equilibrium-Solution.pdf. (This part will be updated in few weeks)

INSTRUCTIONS

All the things are done within 3 main procedures, implement them in main.py:

1. Data input

There are two ways to introduce data into model: First one, invoke TrafficFlowModel.__init__. Second one, invoke TrafficFlowModel.create_template and TrafficFlowModel.read_data_from_excel to use a excel interface.

2. Solve

Invoke TrafficFlowModel.solve.

3. Output report

Invoke TrafficFlowModel.report and/or TrafficFlowModel.report_to_excel.

Then you can just run python main.py.

TIPS

  1. Parameters such as TrafficFlowModel._alpha, TrafficFlowModel._beta and TrafficFlowModel._conv_accuracy are directly exposed to users, one can revise them according to the requirements.
  2. Notice the mutual correspondence between each link and its parameters like capacity and free travel time, while using the first kind of input method, that is, writing down the data directly into data.py.
  3. If you want to extend this model according to your own demand, I strongly suggest that do NOT use the excel file as the data exchange interface, because it is not robust.
  4. When the program doesn't go well, please firstly use TrafficFlowModel.__str__ (which is already contained in TrafficFlowModel.report) to print all the current parameters for ensuring all the data having been introduced into model correctly.
  5. In the file main.py, all the common methods of TrafficFlowModel class are given in advance, which are guidelines for the user, and all functions in the repository are more or less with illustrations.
  6. If you have trouble with implementing of model, or you find some bugs, please contact me without hesitation.

EXAMPLE

This well-designed example was provided by Prof. F. Xiao within his lectures at Southwest Jiaotong University

Graph display

Parameters of links

LINK LENGTH NO. OF LANES FREE FLOW SPEED CAPACITY PER LANE
5 - 7 10.0 2 60 1800
5 - 9 10.0 2 60 1800
6 - 7 10.0 2 60 1800
6 - 8 14.1 2 60 1800
7 - 8 10.0 2 60 1800
7 - 10 10.0 2 60 1800
8 - 11 10.0 2 60 1800
8 - 12 14.1 2 60 1800
9 - 10 10.0 2 60 1800
9 - 16 22.4 2 60 1800
10 - 11 10.0 2 60 1800
10 - 13 10.0 2 60 1800
11 - 14 10.0 2 60 1800
12 - 15 10.0 2 60 1800
13 - 14 10.0 2 60 1800
13 - 16 10.0 2 60 1800
14 - 15 10.0 2 60 1800
14 - 17 10.0 2 60 1800
16 - 17 10.0 2 60 1800

Origin-destination pairs and demands

DEMAND 15 17
5 6000 7500
6 7500 5250

Report of solution (printed in console)

# --------------------------------------------------------------------------------
# TRAFFIC FLOW ASSIGN MODEL (USER EQUILIBRIUM)
# FRANK-WOLFE ALGORITHM - PARAMS OF MODEL
# --------------------------------------------------------------------------------
# --------------------------------------------------------------------------------
# LINK Information:
# --------------------------------------------------------------------------------
#  0 : link= ['5', '7'], free time= 10.00, capacity= 3600
#  1 : link= ['5', '9'], free time= 10.00, capacity= 3600
#  2 : link= ['6', '7'], free time= 10.00, capacity= 3600
#  3 : link= ['6', '8'], free time= 14.10, capacity= 3600
#  4 : link= ['7', '8'], free time= 10.00, capacity= 3600
#  5 : link= ['7', '10'], free time= 10.00, capacity= 3600
#  6 : link= ['8', '11'], free time= 10.00, capacity= 3600
#  7 : link= ['8', '12'], free time= 14.10, capacity= 3600
#  8 : link= ['9', '10'], free time= 10.00, capacity= 3600
#  9 : link= ['9', '16'], free time= 22.40, capacity= 3600
# 10 : link= ['10', '11'], free time= 10.00, capacity= 3600
# 11 : link= ['10', '13'], free time= 10.00, capacity= 3600
# 12 : link= ['11', '14'], free time= 10.00, capacity= 3600
# 13 : link= ['12', '15'], free time= 10.00, capacity= 3600
# 14 : link= ['13', '14'], free time= 10.00, capacity= 3600
# 15 : link= ['13', '16'], free time= 10.00, capacity= 3600
# 16 : link= ['14', '15'], free time= 10.00, capacity= 3600
# 17 : link= ['14', '17'], free time= 10.00, capacity= 3600
# 18 : link= ['16', '17'], free time= 10.00, capacity= 3600
# --------------------------------------------------------------------------------
# OD Pairs Information:
# --------------------------------------------------------------------------------
#  0 : OD pair= ['5', '15'], demand= 6000
#  1 : OD pair= ['5', '17'], demand= 6750
#  2 : OD pair= ['6', '15'], demand= 7500
#  3 : OD pair= ['6', '17'], demand= 5250
# --------------------------------------------------------------------------------
# Path Information:
# --------------------------------------------------------------------------------
#  0 : Conjugated OD pair= 0, Path= ['5', '7', '8', '11', '14', '15']
#  1 : Conjugated OD pair= 0, Path= ['5', '7', '8', '12', '15']
#  2 : Conjugated OD pair= 0, Path= ['5', '7', '10', '11', '14', '15']
#  3 : Conjugated OD pair= 0, Path= ['5', '7', '10', '13', '14', '15']
#  4 : Conjugated OD pair= 0, Path= ['5', '9', '10', '11', '14', '15']
#  5 : Conjugated OD pair= 0, Path= ['5', '9', '10', '13', '14', '15']
#  6 : Conjugated OD pair= 1, Path= ['5', '7', '8', '11', '14', '17']
#  7 : Conjugated OD pair= 1, Path= ['5', '7', '10', '11', '14', '17']
#  8 : Conjugated OD pair= 1, Path= ['5', '7', '10', '13', '14', '17']
#  9 : Conjugated OD pair= 1, Path= ['5', '7', '10', '13', '16', '17']
# 10 : Conjugated OD pair= 1, Path= ['5', '9', '10', '11', '14', '17']
# 11 : Conjugated OD pair= 1, Path= ['5', '9', '10', '13', '14', '17']
# 12 : Conjugated OD pair= 1, Path= ['5', '9', '10', '13', '16', '17']
# 13 : Conjugated OD pair= 1, Path= ['5', '9', '16', '17']
# 14 : Conjugated OD pair= 2, Path= ['6', '7', '8', '11', '14', '15']
# 15 : Conjugated OD pair= 2, Path= ['6', '7', '8', '12', '15']
# 16 : Conjugated OD pair= 2, Path= ['6', '7', '10', '11', '14', '15']
# 17 : Conjugated OD pair= 2, Path= ['6', '7', '10', '13', '14', '15']
# 18 : Conjugated OD pair= 2, Path= ['6', '8', '11', '14', '15']
# 19 : Conjugated OD pair= 2, Path= ['6', '8', '12', '15']
# 20 : Conjugated OD pair= 3, Path= ['6', '7', '8', '11', '14', '17']
# 21 : Conjugated OD pair= 3, Path= ['6', '7', '10', '11', '14', '17']
# 22 : Conjugated OD pair= 3, Path= ['6', '7', '10', '13', '14', '17']
# 23 : Conjugated OD pair= 3, Path= ['6', '7', '10', '13', '16', '17']
# 24 : Conjugated OD pair= 3, Path= ['6', '8', '11', '14', '17']
# --------------------------------------------------------------------------------
# Link - Path Incidence Matrix:
# --------------------------------------------------------------------------------
# [[1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
#  [0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0]
#  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0]
#  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1]
#  [1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0]
#  [0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0]
#  [1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1]
#  [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0]
#  [0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0]
#  [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
#  [0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0]
#  [0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0]
#  [1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 0 0 1]
#  [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0]
#  [0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0]
#  [0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0]
#  [1 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0]
#  [0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 1]
#  [0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0]]
# --------------------------------------------------------------------------------
# TRAFFIC FLOW ASSIGN MODEL (USER EQUILIBRIUM)
# FRANK-WOLFE ALGORITHM - REPORT OF SOLUTION
# --------------------------------------------------------------------------------
# --------------------------------------------------------------------------------
# TIMES OF ITERATION : 1199
# --------------------------------------------------------------------------------
# --------------------------------------------------------------------------------
# PERFORMANCE OF LINKS
# --------------------------------------------------------------------------------
#  0 : link=   ['5', '7'], flow=  5632.68, time=  18.99, v/c= 1.565
#  1 : link=   ['5', '9'], flow=  7117.32, time=  32.92, v/c= 1.977
#  2 : link=   ['6', '7'], flow=  6048.31, time=  21.95, v/c= 1.680
#  3 : link=   ['6', '8'], flow=  6701.69, time=  39.50, v/c= 1.862
#  4 : link=   ['7', '8'], flow=  5392.05, time=  17.55, v/c= 1.498
#  5 : link=  ['7', '10'], flow=  6288.95, time=  23.97, v/c= 1.747
#  6 : link=  ['8', '11'], flow=  5191.43, time=  16.49, v/c= 1.442
#  7 : link=  ['8', '12'], flow=  6902.30, time=  42.68, v/c= 1.917
#  8 : link=  ['9', '10'], flow=  1481.14, time=  10.04, v/c= 0.411
#  9 : link=  ['9', '16'], flow=  5636.18, time=  42.59, v/c= 1.566
# 10 : link= ['10', '11'], flow=  1648.04, time=  10.07, v/c= 0.458
# 11 : link= ['10', '13'], flow=  6122.05, time=  22.54, v/c= 1.701
# 12 : link= ['11', '14'], flow=  6839.47, time=  29.54, v/c= 1.900
# 13 : link= ['12', '15'], flow=  6902.30, time=  30.27, v/c= 1.917
# 14 : link= ['13', '14'], flow=  5303.10, time=  17.06, v/c= 1.473
# 15 : link= ['13', '16'], flow=   818.95, time=  10.00, v/c= 0.227
# 16 : link= ['14', '15'], flow=  6597.70, time=  26.92, v/c= 1.833
# 17 : link= ['14', '17'], flow=  5544.87, time=  18.44, v/c= 1.540
# 18 : link= ['16', '17'], flow=  6455.13, time=  25.51, v/c= 1.793
# --------------------------------------------------------------------------------
# PERFORMANCE OF PATHS (GROUP BY ORIGIN-DESTINATION PAIR)
# --------------------------------------------------------------------------------
#  0 : group=  0, time= 109.49, path= ['5', '7', '8', '11', '14', '15']
#  1 : group=  0, time= 109.49, path= ['5', '7', '8', '12', '15']
#  2 : group=  0, time= 109.49, path= ['5', '7', '10', '11', '14', '15']
#  3 : group=  0, time= 109.49, path= ['5', '7', '10', '13', '14', '15']
#  4 : group=  0, time= 109.49, path= ['5', '9', '10', '11', '14', '15']
#  5 : group=  0, time= 109.49, path= ['5', '9', '10', '13', '14', '15']
#  6 : group=  1, time= 101.01, path= ['5', '7', '8', '11', '14', '17']
#  7 : group=  1, time= 101.01, path= ['5', '7', '10', '11', '14', '17']
#  8 : group=  1, time= 101.01, path= ['5', '7', '10', '13', '14', '17']
#  9 : group=  1, time= 101.01, path= ['5', '7', '10', '13', '16', '17']
# 10 : group=  1, time= 101.01, path= ['5', '9', '10', '11', '14', '17']
# 11 : group=  1, time= 101.01, path= ['5', '9', '10', '13', '14', '17']
# 12 : group=  1, time= 101.01, path= ['5', '9', '10', '13', '16', '17']
# 13 : group=  1, time= 101.01, path= ['5', '9', '16', '17']
# 14 : group=  2, time= 112.45, path= ['6', '7', '8', '11', '14', '15']
# 15 : group=  2, time= 112.45, path= ['6', '7', '8', '12', '15']
# 16 : group=  2, time= 112.45, path= ['6', '7', '10', '11', '14', '15']
# 17 : group=  2, time= 112.45, path= ['6', '7', '10', '13', '14', '15']
# 18 : group=  2, time= 112.45, path= ['6', '8', '11', '14', '15']
# 19 : group=  2, time= 112.45, path= ['6', '8', '12', '15']
# 20 : group=  3, time= 103.97, path= ['6', '7', '8', '11', '14', '17']
# 21 : group=  3, time= 103.97, path= ['6', '7', '10', '11', '14', '17']
# 22 : group=  3, time= 103.97, path= ['6', '7', '10', '13', '14', '17']
# 23 : group=  3, time= 103.98, path= ['6', '7', '10', '13', '16', '17']
# 24 : group=  3, time= 103.97, path= ['6', '8', '11', '14', '17']