Parseh Designers Transportation Research Institute Quarterly Journal of Transportation Engineering 2008-6598 17 1 2025 09 23 Modeling the First Holding and All Holding Control Strategy of Buses under Uncertainty Modeling the First Holding and All Holding Control Strategy of Buses under Uncertainty 4995 5010 159620 10.22119/jte.2022.360498.2618 FA Masoud Mohammad Hosein Mirzaei M.Sc., Department of Road and Transportation Engineering, School of Civil Engineering, Iran University of Science and Technology, Tehran, Iran Abdolreza Sheikholeslami Assistant Professor, Department of Road and Transportation Engineering, School of Civil Engineering, Iran University of Science and Technology, Tehran, Iran Journal Article 2022 09 04 <span style="mso-ascii-font-family: 'Times New Roman'; mso-ascii-theme-font: major-bidi; mso-fareast-font-family: 'Times New Roman'; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: 'Times New Roman'; mso-hansi-theme-font: major-bidi;">In recent decades, due to the importance of keeping transportation system performance in the condition of disturbance at the desired level, a new definition has been provided to evaluate the performance of transportation system, which expresses the reliability of the system in conditions of uncertainty. <span style="mso-ascii-font-family: 'Times New Roman'; mso-ascii-theme-font: major-bidi; mso-fareast-font-family: 'Times New Roman'; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: 'Times New Roman'; mso-hansi-theme-font: major-bidi;">Therefore, assessment the reliability of the performance of transportation system in their design or upgrading and reconstruction has become very important. To increase reliability, control strategies are used that reduce the waiting time of passengers at the station. The scenario of the absence of overtaking conditions of buses and the scenario of the presence of overtaking conditions of buses are introduced and a separate mathematical model is presented for each<span style="mso-ascii-font-family: 'Times New Roman'; mso-ascii-theme-font: major-bidi; mso-fareast-font-family: 'Times New Roman'; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: 'Times New Roman'; mso-hansi-theme-font: major-bidi;"> to determine the optimal holding time of buses at the stop so that the waiting time of passengers is minimized. Then, the constraint of the maximum holding time of buses in the condition of uncertainty (soft limit) and its effect on the objective function are evaluated. <span style="mso-ascii-font-family: 'Times New Roman'; mso-ascii-theme-font: major-bidi; mso-fareast-font-family: 'Times New Roman'; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: 'Times New Roman'; mso-hansi-theme-font: major-bidi;">An assumed example has been used to investigate the impact of uncertainty on control strategies. <span style="mso-ascii-font-family: 'Times New Roman'; mso-ascii-theme-font: major-bidi; mso-fareast-font-family: 'Times New Roman'; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: 'Times New Roman'; mso-hansi-theme-font: major-bidi;">Passenger waiting time results for different confidence levels for each strategy are given. <span style="mso-ascii-font-family: 'Times New Roman'; mso-ascii-theme-font: major-bidi; mso-fareast-font-family: 'Times New Roman'; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: 'Times New Roman'; mso-hansi-theme-font: major-bidi;">In the first holding control strategy and all holding (first scenario), the waiting time of passengers increases with the increase of the confidence level, but in the all holding control strategy (second scenario), changes in the confidence level do not affect the objective function and the objective function is almost constant. <span style="mso-ascii-font-family: 'Times New Roman'; mso-ascii-theme-font: major-bidi; mso-fareast-font-family: 'Times New Roman'; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: 'Times New Roman'; mso-hansi-theme-font: major-bidi;">In recent decades, due to the importance of keeping transportation system performance in the condition of disturbance at the desired level, a new definition has been provided to evaluate the performance of transportation system, which expresses the reliability of the system in conditions of uncertainty. <span style="mso-ascii-font-family: 'Times New Roman'; mso-ascii-theme-font: major-bidi; mso-fareast-font-family: 'Times New Roman'; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: 'Times New Roman'; mso-hansi-theme-font: major-bidi;">Therefore, assessment the reliability of the performance of transportation system in their design or upgrading and reconstruction has become very important. To increase reliability, control strategies are used that reduce the waiting time of passengers at the station. The scenario of the absence of overtaking conditions of buses and the scenario of the presence of overtaking conditions of buses are introduced and a separate mathematical model is presented for each<span style="mso-ascii-font-family: 'Times New Roman'; mso-ascii-theme-font: major-bidi; mso-fareast-font-family: 'Times New Roman'; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: 'Times New Roman'; mso-hansi-theme-font: major-bidi;"> to determine the optimal holding time of buses at the stop so that the waiting time of passengers is minimized. Then, the constraint of the maximum holding time of buses in the condition of uncertainty (soft limit) and its effect on the objective function are evaluated. <span style="mso-ascii-font-family: 'Times New Roman'; mso-ascii-theme-font: major-bidi; mso-fareast-font-family: 'Times New Roman'; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: 'Times New Roman'; mso-hansi-theme-font: major-bidi;">An assumed example has been used to investigate the impact of uncertainty on control strategies. <span style="mso-ascii-font-family: 'Times New Roman'; mso-ascii-theme-font: major-bidi; mso-fareast-font-family: 'Times New Roman'; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: 'Times New Roman'; mso-hansi-theme-font: major-bidi;">Passenger waiting time results for different confidence levels for each strategy are given. <span style="mso-ascii-font-family: 'Times New Roman'; mso-ascii-theme-font: major-bidi; mso-fareast-font-family: 'Times New Roman'; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: 'Times New Roman'; mso-hansi-theme-font: major-bidi;">In the first holding control strategy and all holding (first scenario), the waiting time of passengers increases with the increase of the confidence level, but in the all holding control strategy (second scenario), changes in the confidence level do not affect the objective function and the objective function is almost constant.

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