8 Design of Integrated Transit Service with Stochastic Demand
8.2 Future Research
The limitations of this research require additional research in the future, especially in the topics given below.
130
1. The waiting times: it should be included in the design model for the DAR service to consider the waiting time costs before picking up the passengers. Also, in the case of transferring between different integrated services.
2. Transfers between DAR vehicles: one possible future extension is to consider the transferring between the DAR vehicles to reduce the operating costs of the DAR service and improve the service quality for the users. However, one issue will rise in selecting the transfer mechanism.
3. Passengers’ choice behavior: the design models presented in this study does not consider any passenger choice and only consider the passengers’ interests in the design objectives.
4. Solution methods: to overcome the complexity of the design models and be able to solve bigger-sized networks new solution methods should be considered such as Branch-and-Price, Genetic Algorithm, Simulated Annealing, and Artificial Bee Colony.
131
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Appendix
I present here the detailed calculations for the Gini index using Equation 5.41 for different optimal solutions presented in Chapter 5 using the absolute difference and the relative increase for the travel time of travelers.
140
Table A.1. Detailed Calculations of Gini Index for the Multimodal Service Using the Travel Time Absolute Differences OD Pair OD Demand Mode Travel Time Proportions Cumulative
Subtract X Summation Y Product Direct Actual Difference X Y X Y
6-9 37 Bus 4 4 0 0.041 0.000 0.041 0.000 0.041 0.000 0.000
6-9 8 DAR 4 4 0 0.009 0.000 0.049 0.000 0.009 0.000 0.000
7-11 32 DAR 11 11 0 0.035 0.000 0.084 0.000 0.035 0.000 0.000
11-1 50 Bus 10 10 0 0.055 0.000 0.139 0.000 0.055 0.000 0.000
4-8 90 Bus 12 12 0 0.099 0.000 0.238 0.000 0.099 0.000 0.000
4-8 1 DAR 12 12 0 0.001 0.000 0.239 0.000 0.001 0.000 0.000
5-7 110 Bus 13 13 0 0.121 0.000 0.360 0.000 0.121 0.000 0.000
9-2 117 Bus 12 12 0 0.129 0.000 0.489 0.000 0.129 0.000 0.000
1-5 119 Bus 13 14 1 0.131 0.026 0.620 0.026 0.131 0.026 0.003
1-5 2 DAR 13 14 1 0.002 0.026 0.622 0.051 0.002 0.077 0.000
8-6 40 Bus 7 9 2 0.044 0.051 0.666 0.103 0.044 0.154 0.007
2-4 90 Bus 12 14 2 0.099 0.051 0.765 0.154 0.099 0.256 0.025
9-2 3 DAR 12 14 2 0.003 0.051 0.768 0.205 0.003 0.359 0.001
7-11 165 Bus 11 16 5 0.181 0.128 0.949 0.333 0.181 0.538 0.098
7-11 3 DAR 11 16 5 0.003 0.128 0.953 0.462 0.003 0.795 0.003
1-5 29 Bus 13 19 6 0.032 0.154 0.984 0.615 0.032 1.077 0.034
4-8 9 Bus 12 19 7 0.010 0.179 0.994 0.795 0.010 1.410 0.014
6-9 5 DAR 4 12 8 0.005 0.205 1.000 1.000 0.005 1.795 0.010
910 39.000 1.000 1.000 0.195
Gini Index 0.805
141
Table A.2. Detailed Calculations of Gini Index for the Bus Only Service Using the Travel Time Absolute Differences OD Pair OD Demand Mode Travel Time Proportions Cumulative
Subtract X Summation Y Product Direct Actual Difference X Y X Y
6-9 50 Bus 4 4 0 0.055 0.000 0.055 0.000 0.055 0.000 0.000
8-6 40 Bus 7 7 0 0.044 0.000 0.099 0.000 0.044 0.000 0.000
11-1 50 Bus 10 10 0 0.055 0.000 0.154 0.000 0.055 0.000 0.000
4-8 10 Bus 12 12 0 0.011 0.000 0.165 0.000 0.011 0.000 0.000
9-2 120 Bus 12 14 2 0.132 0.033 0.297 0.033 0.132 0.033 0.004
1-5 40 Bus 13 17 4 0.044 0.066 0.341 0.098 0.044 0.131 0.006
2-4 90 Bus 12 16 4 0.099 0.066 0.440 0.164 0.099 0.262 0.026
7-11 90 Bus 11 16 5 0.099 0.082 0.538 0.246 0.099 0.410 0.041
4-8 90 Bus 12 18 6 0.099 0.098 0.637 0.344 0.099 0.590 0.058
1-5 20 Bus 13 20 7 0.022 0.115 0.659 0.459 0.022 0.803 0.018
5-7 110 Bus 13 23 10 0.121 0.164 0.780 0.623 0.121 1.082 0.131
7-11 110 Bus 11 21 10 0.121 0.164 0.901 0.787 0.121 1.410 0.170
1-5 90 Bus 13 26 13 0.099 0.213 1.000 1.000 0.099 1.787 0.177
910 61 1.000 1.000 0.631
Gini Index 0.369
142
Table A.3. Detailed Calculations of Gini Index for An and Lo Model Using the Travel Time Absolute Differences OD Pair OD Demand Mode Travel Time Proportions Cumulative
Subtract X Summation Y Product Direct Actual Difference X Y X Y
6-9 50 DAR 4 4 0 0.055 0.000 0.055 0.000 0.055 0.000 0.000
8-6 40 DAR 7 7 0 0.044 0.000 0.099 0.000 0.044 0.000 0.000
7-11 152 Bus 11 11 0 0.167 0.000 0.266 0.000 0.167 0.000 0.000
7-11 48 DAR 11 11 0 0.053 0.000 0.319 0.000 0.053 0.000 0.000
1-5 1 DAR 13 13 0 0.001 0.000 0.320 0.000 0.001 0.000 0.000
4-8 90 Bus 12 12 0 0.099 0.000 0.419 0.000 0.099 0.000 0.000
4-8 10 DAR 12 12 0 0.011 0.000 0.430 0.000 0.011 0.000 0.000
9-2 54 Bus 12 12 0 0.059 0.000 0.489 0.000 0.059 0.000 0.000
2-4 90 Bus 12 13 1 0.099 0.048 0.588 0.048 0.099 0.048 0.005
1-5 54 Bus 13 14 1 0.059 0.048 0.647 0.095 0.059 0.143 0.008
11-1 50 Bus 10 11 1 0.055 0.048 0.702 0.143 0.055 0.238 0.013
5-7 110 Bus 13 14 1 0.121 0.048 0.823 0.190 0.121 0.333 0.040
9-2 32 DAR 12 14 2 0.035 0.095 0.858 0.286 0.035 0.476 0.017
1-5 95 Bus 13 20 7 0.104 0.333 0.963 0.619 0.104 0.905 0.094
9-2 34 Bus 12 20 8 0.037 0.381 1.000 1.000 0.037 1.619 0.060
910 21.000 1.000 1.000 0.238
Gini Index 0.762
143
Table A.4. Detailed Calculations of Gini Index for the Multimodal Service Using the Travel Time Relative Increase OD Pair OD Demand Mode Travel Time Proportions Cumulative
Subtract X Summation Y Product Direct Actual Relative X Y X Y
6-9 37 Bus 4 4 0.000 0.041 0.000 0.041 0.000 0.041 0.000 0.000
6-9 8 DAR 4 4 0.000 0.009 0.000 0.049 0.000 0.009 0.000 0.000
7-11 32 DAR 11 11 0.000 0.035 0.000 0.085 0.000 0.035 0.000 0.000
11-1 50 Bus 10 10 0.000 0.055 0.000 0.140 0.000 0.055 0.000 0.000
4-8 90 Bus 12 12 0.000 0.099 0.000 0.238 0.000 0.099 0.000 0.000
4-8 1 DAR 12 12 0.000 0.001 0.000 0.240 0.000 0.001 0.000 0.000
5-7 110 Bus 13 13 0.000 0.121 0.000 0.360 0.000 0.121 0.000 0.000
9-2 117 Bus 12 12 0.000 0.129 0.000 0.489 0.000 0.129 0.000 0.000
1-5 119 Bus 13 14 0.077 0.131 0.016 0.620 0.016 0.131 0.016 0.002
1-5 2 DAR 13 14 0.077 0.002 0.016 0.622 0.033 0.002 0.049 0.000
8-6 40 Bus 7 9 0.286 0.044 0.060 0.666 0.093 0.044 0.126 0.006
2-4 90 Bus 12 14 0.167 0.099 0.035 0.765 0.128 0.099 0.221 0.022
9-2 3 DAR 12 14 0.167 0.003 0.035 0.768 0.164 0.003 0.292 0.001
7-11 165 Bus 11 16 0.455 0.181 0.096 0.949 0.260 0.181 0.423 0.077
7-11 3 DAR 11 16 0.455 0.003 0.096 0.953 0.356 0.003 0.616 0.002
1-5 29 Bus 13 19 0.462 0.032 0.098 0.985 0.453 0.032 0.809 0.026
4-8 9 Bus 12 19 0.583 0.010 0.123 0.995 0.577 0.010 1.030 0.010
6-9 5 DAR 4 12 2.000 0.005 0.423 1.000 1.000 0.005 1.577 0.009
910 4.727 1.000 1.000 0.154
Gini Index 0.846
144
Table A.5. Detailed Calculations of Gini Index for the Bus Only Service Using the Travel Time Relative Increase OD Pair OD Demand Mode Travel Time Proportions Cumulative
Subtract X Summation Y Product
Direct Actual Relative X Y X Y
6-9 50 Bus 4 4 0.000 0.055 0.000 0.055 0.000 0.055 0.000 0.000
8-6 40 Bus 7 7 0.000 0.044 0.000 0.099 0.000 0.044 0.000 0.000
11-1 50 Bus 10 10 0.000 0.055 0.000 0.154 0.000 0.055 0.000 0.000
4-8 10 Bus 12 12 0.000 0.011 0.000 0.165 0.000 0.011 0.000 0.000
9-2 120 Bus 12 14 0.167 0.132 0.033 0.297 0.033 0.132 0.033 0.004
1-5 40 Bus 13 17 0.308 0.044 0.062 0.341 0.095 0.044 0.129 0.006
2-4 90 Bus 12 16 0.333 0.099 0.067 0.440 0.162 0.099 0.257 0.025
7-11 90 Bus 11 16 0.455 0.099 0.091 0.538 0.254 0.099 0.416 0.041
4-8 90 Bus 12 18 0.500 0.099 0.100 0.637 0.354 0.099 0.607 0.060
1-5 20 Bus 13 20 0.538 0.022 0.108 0.659 0.462 0.022 0.816 0.018
5-7 110 Bus 13 23 0.769 0.121 0.154 0.780 0.617 0.121 1.079 0.130
7-11 110 Bus 11 21 0.909 0.121 0.183 0.901 0.799 0.121 1.416 0.171
1-5 90 Bus 13 26 1.000 0.099 0.201 1.000 1.000 0.099 1.799 0.178
910 4.979 1.000 1.000 0.634
Gini Index 0.366