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Zhichao Cao,Ting Xu,Silin Zhang,Avishai (Avi) Ceder,Yuyao Sun 대한토목학회 2022 KSCE Journal of Civil Engineering Vol.26 No.7
Even-headway timetables with easy to memorize departure times are commonly in use in public transport (PT) service. In addition, some PT services are using timetables where their departure times are based on even-passenger-load at the max-load stop along the route. In practice, these two types of timetables are implemented in daily operation plans, allowing for their merits, with the former maintaining the initial, even-interval departure rules and conventions, especially when a new PT line is planned without available demand information, while the latter is demand-oriented, exhibiting fluctuation in time and space. The principles of creating the aforementioned timetables have been presented in the literature, but very few evaluations feasibly attest to performance by means of mathematical analysis. Concentrating on building a modelling framework for PT timetabling problems during the planning stage, this work is taking into account 1) passengers’ service-frequency satisfaction, in terms of waiting times, 2) passengers’ perception of riding comfort, in terms of seat availability, and 3) planned passengers’ load ratio (concerning vehicle’s capacity) linked with operation efficiency. Yielding to the models developed in a theoretical manner, the comparative evaluation is conducted through multiple timetable schemes that include four different dimensions: (A) even-headway departures with same headway throughout the time horizon, (B) even-load departures with same load throughout the time horizon, (C) even-headway departures for each demand-dependent period, and (D) even-load departures for each demand-dependent period. Finally, a case study in Nantong, China examines the comparison performances produced and the best plans for operational timetables. The results indicate that travelers attributed great importance to higher satisfaction preferences on frequency or headway-related experience linked with their waiting time.
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An Integral Function Approach to the Exponential Stability of Linear Time-Varying Systems
Yu Yao,Kai Liu,Jian Guo,Dengfeng Sun,Venkataramanan Balakrishnan 제어·로봇·시스템학회 2012 International Journal of Control, Automation, and Vol.10 No.6
This paper studies the exponential stability of linear time-varying (LTV) systems using the recent pro-posed integral function. By showing the properties of the integral function and applying the Bellman-Gronwall Lemma, a sufficient and necessary condition for the exponential stability of LTV systems is derived. Furthermore, the exponential decay rate of the system trajectories can be obtained by computing the radii of convergence of integral function. The algorithm for computing the integral function is also developed and two classical examples are given to illustrate the proposed approach.
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