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Bir Metro Hattında Yolcu Sayısına Bağlı Dinamiklerin Anahtarlamalı Sistem Olarak Modellenmesi ve Girişten Duruma Kararlılık Analizi

Yıl 2023, Sayı: 17, 133 - 144, 31.01.2023
https://doi.org/10.47072/demiryolu.1203693

Öz

Bir ulaşım sisteminde bulunan istasyon ve araçlardaki yolcu sayıları ile sefer aralığı (ardışık iki araç arasındaki süre) arasında doğrusal bir ilişki bulunmaktadır. Sefer aralıklarını azaltmak yolcu konforunu arttırsa da, işletme maliyetlerini arttırmaktadır. Bu nedenle iyi ayarlanmış bir sefer aralığı hem işletmeci hem de yolcular açısından önem kazanmaktadır. Sefer aralığının sağlıklı şekilde ayarlanması için iyi kurgulanmış bir modele ihtiyaç duyulmaktadır. Bir ulaşım sistemindeki yolcu dinamikleri bir aracın bir durağa yanaşıp yanaşmamasına göre değişkenlik gösterdiği için, bu sistemler anahtarlamalı sistem gibi davranırlar. Buna ek olarak, sefer aralığının güncellenmesi tüm istasyonları anında etkilemez. Güncelleme ilk istasyon dışındaki istasyonları bir zaman gecikmesi ile etkiler. Bu çalışmada, bir metro hattındaki yolcu sayıları anahtarlamalı sistem olarak modellenmiştir ve gerçek veriler ile MATLAB Simulink® yazılımında benzetimi yapılmıştır. Sistemin keyfi anahtarlama altındaki kararlılık analizi ortak Lyapunov fonksiyonları ve girişten duruma kararlılık yöntemleri kullanılarak yapılıp, benzetim sonuçları ile de doğrulanmıştır.

Kaynakça

  • [1] S. I. J. Chien, “Optimization of headway, vehicle size and route choice for minimum cost feeder service,” Transp. Plan. Technol., 2005, doi: 10.1080/03081060500322565.
  • [2] B. Birol and A. F. Ergenç, “A modelling and simulation study of a metro line as a time-delayed switched system,” J. Rail Transp. Plan. Manag., vol. 22, p. 100318, 2022, doi: https://doi.org/10.1016/j.jrtpm.2022.100318.
  • [3] J. Fang, T. Fujiyama, and H. Wong, “Modelling passenger distribution on metro platforms based on passengers’ choices for boarding cars,” Transp. Plan. Technol., 2019, doi: 10.1080/03081060.2019.1609218.
  • [4] G. F. Newell, “Dispatching policies for a transportation route,” Transp. Sci., vol. 5, no. 1, pp. 91–105, Mar. 1971, [Online]. Available: http://www.jstor.org/stable/25767595.
  • [5] E. E. Osuna, and G. F. Newell, “Control strategies for an idealized public transportation system,” Transp. Sci., vol. 6, no. 1, pp. 52–72, Mar. 1972, [Online]. Available: http://www.jstor.org/stable/25767635.
  • [6] V. F. Hurdle, “Minimum cost schedules for a public transportation route: II. examples,” Transp. Sci., vol. 7, no. 2, pp. 138–157, Mar. 1973, [Online]. Available: http://www.jstor.org/stable/25767694.
  • [7] V. F. Hurdle, “Minimum cost schedules for a public transportation route: I. theory,” Transp. Sci., vol. 7, no. 2, pp. 109–137, Mar. 1973, [Online]. Available: http://www.jstor.org/stable/25767693.
  • [8] S. Yıldırım, “Yüksek Hızlı Tren Hatlarında Sinyalizasyon Blok Mesafelerinin Hesaplanması” Demiryolu Mühendisliği, Sayı 14, Sayfa 14-25, Temmuz 2021.
  • [9] L. Sun, J. G. Jin, D. H. Lee, K. W. Axhausen, and A. Erath, “Demand-driven timetable design for metro services,” Transp. Res. Part C Emerg. Technol., 2014, doi: 10.1016/j.trc.2014.06.003.
  • [10] I. Sahin, “Markov chain model for delay distribution in train schedules: Assessing the effectiveness of time allowances,” J. Rail Transp. Plan. Manag., vol. 7, Sep. 2017, doi: 10.1016/j.jrtpm.2017.08.006.
  • [11] J. Xie, J. Zhang, K. Sun, S. Ni, and D. Chen, “Passenger and energy-saving oriented train timetable and stop plan synchronization optimization model,” Transp. Res. Part D Transp. Environ., vol. 98, p. 102975, Sep. 2021, doi: 10.1016/j.trd.2021.102975.
  • [12] S. Van Aken, N. Bešinović, and R. Goverde, “Solving large-scale train timetable adjustment problems under infrastructure maintenance possessions,” J. Rail Transp. Plan. Manag., vol. 7, Jul. 2017, doi: 10.1016/j.jrtpm.2017.06.003.
  • [13] Y. Zhu and R. Goverde, “Railway timetable rescheduling with flexible stopping and flexible short-turning during disruptions,” Transp. Res. Part B Methodol., vol. 123, pp. 149–181, Apr. 2019, doi: 10.1016/j.trb.2019.02.015.
  • [14] Y. Zhu and R. Goverde, “Dynamic and robust timetable rescheduling for uncertain railway disruptions,” J. Rail Transp. Plan. Manag., Apr. 2020, doi: 10.1016/j.jrtpm.2020.100196.
  • [15] B. F. Nielsen, L. Frølich, O. Nielsen, and D. Filges, “Estimating passenger numbers in trains using existing weighing capabilities,” Transp. A Transp. Sci., vol. 10, Jul. 2014, doi: 10.1080/23249935.2013.795199.
  • [16] W. Li and W. Zhu, “A dynamic simulation model of passenger flow distribution on schedule-based rail transit networks with train delays,” J. Traffic Transp. Eng. (English Ed., vol. 3, no. 4, pp. 364–373, 2016, doi: https://doi.org/10.1016/j.jtte.2015.09.009.
  • [17] D. Liberzon and A. S. Morse, “Basic problems in stability and design of switched systems,” IEEE Control Syst. Mag., vol. 19, no. 5, pp. 59–70, 1999, doi: 10.1109/37.793443.
  • [18] A. S. Morse, Control using logic-based switching. Springer, London, 1997.
  • [19] M. Mahmoud, Switched time-delay systems: Stability and control. Springer, New York, 2010.
  • [20] D. Liberzon, Switching in system and control. Boston, Birkhäuser, 2003.
  • [21] S. Chen, L. Jiang, W. Yao and Q. H. Wu, "Application of switched system theory in power system stability," 2014 49th International Universities Power Engineering Conference (UPEC), 2014, pp. 1-6, doi: 10.1109/UPEC.2014.6934651.
  • [22]W. Xu, L. Yu, G. Lin and Z. G. Feng, “Optimal switching signal design with a cost on switching action”, Journal of Industrial and Management Optimization, vol. 16, no. 5, pp. 2531-2549, 2020, doi: https://doi.org/10.3934/jimo.2019068
  • [23] Z. Sun and S. Ge, Switched linear systems: Control and design. London, Springer, 2005.
  • [24] E. Sontag, “Smooth stabilization implies coprime factorization,” Autom. Control. IEEE Trans., vol. 34, pp. 435–443, May 1989, doi: 10.1109/9.28018.
  • [25] L. Vu, D. Chatterjee, and D. Liberzon, “Input-to-state stability of switched systems and switching adaptive control,” Automatica, vol. 43, no. 4, pp. 639–646, 2007, doi: https://doi.org/10.1016/j.automatica.2006.10.007.

Modelling a Metro Line as a Switched System and Performing Input-to-State Stability Analysis

Yıl 2023, Sayı: 17, 133 - 144, 31.01.2023
https://doi.org/10.47072/demiryolu.1203693

Öz

There is a linear relationship between the headway (the time distance between two consecutive vehicles) of the vehicles and the passenger quantities in stations in a public transportation system. Reducing the headway increases passenger satisfaction but increases operational costs. Therefore, an optimized headway is beneficial for both passengers and the operator. The passenger quantities in the line should be well-modelled to tune the headway efficiently. The passenger dynamics in a public transportation system behave like a switched system since the passenger dynamics differ if a vehicle is berthed to a station or not. Furthermore, updating the headway does not affect all stations instantaneously. The update in the headway affects stations other than the first station with a time delay. In this study, passenger quantities in a metro line have been modelled as a switched system and simulated in MATLAB Simulink®. The stability of the system under arbitrary switching has been analysed by using the common Lyapunov and input-to-state stability methods and verified by the simulation results.

Kaynakça

  • [1] S. I. J. Chien, “Optimization of headway, vehicle size and route choice for minimum cost feeder service,” Transp. Plan. Technol., 2005, doi: 10.1080/03081060500322565.
  • [2] B. Birol and A. F. Ergenç, “A modelling and simulation study of a metro line as a time-delayed switched system,” J. Rail Transp. Plan. Manag., vol. 22, p. 100318, 2022, doi: https://doi.org/10.1016/j.jrtpm.2022.100318.
  • [3] J. Fang, T. Fujiyama, and H. Wong, “Modelling passenger distribution on metro platforms based on passengers’ choices for boarding cars,” Transp. Plan. Technol., 2019, doi: 10.1080/03081060.2019.1609218.
  • [4] G. F. Newell, “Dispatching policies for a transportation route,” Transp. Sci., vol. 5, no. 1, pp. 91–105, Mar. 1971, [Online]. Available: http://www.jstor.org/stable/25767595.
  • [5] E. E. Osuna, and G. F. Newell, “Control strategies for an idealized public transportation system,” Transp. Sci., vol. 6, no. 1, pp. 52–72, Mar. 1972, [Online]. Available: http://www.jstor.org/stable/25767635.
  • [6] V. F. Hurdle, “Minimum cost schedules for a public transportation route: II. examples,” Transp. Sci., vol. 7, no. 2, pp. 138–157, Mar. 1973, [Online]. Available: http://www.jstor.org/stable/25767694.
  • [7] V. F. Hurdle, “Minimum cost schedules for a public transportation route: I. theory,” Transp. Sci., vol. 7, no. 2, pp. 109–137, Mar. 1973, [Online]. Available: http://www.jstor.org/stable/25767693.
  • [8] S. Yıldırım, “Yüksek Hızlı Tren Hatlarında Sinyalizasyon Blok Mesafelerinin Hesaplanması” Demiryolu Mühendisliği, Sayı 14, Sayfa 14-25, Temmuz 2021.
  • [9] L. Sun, J. G. Jin, D. H. Lee, K. W. Axhausen, and A. Erath, “Demand-driven timetable design for metro services,” Transp. Res. Part C Emerg. Technol., 2014, doi: 10.1016/j.trc.2014.06.003.
  • [10] I. Sahin, “Markov chain model for delay distribution in train schedules: Assessing the effectiveness of time allowances,” J. Rail Transp. Plan. Manag., vol. 7, Sep. 2017, doi: 10.1016/j.jrtpm.2017.08.006.
  • [11] J. Xie, J. Zhang, K. Sun, S. Ni, and D. Chen, “Passenger and energy-saving oriented train timetable and stop plan synchronization optimization model,” Transp. Res. Part D Transp. Environ., vol. 98, p. 102975, Sep. 2021, doi: 10.1016/j.trd.2021.102975.
  • [12] S. Van Aken, N. Bešinović, and R. Goverde, “Solving large-scale train timetable adjustment problems under infrastructure maintenance possessions,” J. Rail Transp. Plan. Manag., vol. 7, Jul. 2017, doi: 10.1016/j.jrtpm.2017.06.003.
  • [13] Y. Zhu and R. Goverde, “Railway timetable rescheduling with flexible stopping and flexible short-turning during disruptions,” Transp. Res. Part B Methodol., vol. 123, pp. 149–181, Apr. 2019, doi: 10.1016/j.trb.2019.02.015.
  • [14] Y. Zhu and R. Goverde, “Dynamic and robust timetable rescheduling for uncertain railway disruptions,” J. Rail Transp. Plan. Manag., Apr. 2020, doi: 10.1016/j.jrtpm.2020.100196.
  • [15] B. F. Nielsen, L. Frølich, O. Nielsen, and D. Filges, “Estimating passenger numbers in trains using existing weighing capabilities,” Transp. A Transp. Sci., vol. 10, Jul. 2014, doi: 10.1080/23249935.2013.795199.
  • [16] W. Li and W. Zhu, “A dynamic simulation model of passenger flow distribution on schedule-based rail transit networks with train delays,” J. Traffic Transp. Eng. (English Ed., vol. 3, no. 4, pp. 364–373, 2016, doi: https://doi.org/10.1016/j.jtte.2015.09.009.
  • [17] D. Liberzon and A. S. Morse, “Basic problems in stability and design of switched systems,” IEEE Control Syst. Mag., vol. 19, no. 5, pp. 59–70, 1999, doi: 10.1109/37.793443.
  • [18] A. S. Morse, Control using logic-based switching. Springer, London, 1997.
  • [19] M. Mahmoud, Switched time-delay systems: Stability and control. Springer, New York, 2010.
  • [20] D. Liberzon, Switching in system and control. Boston, Birkhäuser, 2003.
  • [21] S. Chen, L. Jiang, W. Yao and Q. H. Wu, "Application of switched system theory in power system stability," 2014 49th International Universities Power Engineering Conference (UPEC), 2014, pp. 1-6, doi: 10.1109/UPEC.2014.6934651.
  • [22]W. Xu, L. Yu, G. Lin and Z. G. Feng, “Optimal switching signal design with a cost on switching action”, Journal of Industrial and Management Optimization, vol. 16, no. 5, pp. 2531-2549, 2020, doi: https://doi.org/10.3934/jimo.2019068
  • [23] Z. Sun and S. Ge, Switched linear systems: Control and design. London, Springer, 2005.
  • [24] E. Sontag, “Smooth stabilization implies coprime factorization,” Autom. Control. IEEE Trans., vol. 34, pp. 435–443, May 1989, doi: 10.1109/9.28018.
  • [25] L. Vu, D. Chatterjee, and D. Liberzon, “Input-to-state stability of switched systems and switching adaptive control,” Automatica, vol. 43, no. 4, pp. 639–646, 2007, doi: https://doi.org/10.1016/j.automatica.2006.10.007.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Bilimsel Yayınlar (Hakemli Araştırma ve Derleme Makaleler)
Yazarlar

Berkin Birol 0000-0003-4194-6065

Ali Fuat Ergenc 0000-0003-2782-5566

Yayımlanma Tarihi 31 Ocak 2023
Gönderilme Tarihi 14 Kasım 2022
Yayımlandığı Sayı Yıl 2023 Sayı: 17

Kaynak Göster

IEEE B. Birol ve A. F. Ergenc, “Bir Metro Hattında Yolcu Sayısına Bağlı Dinamiklerin Anahtarlamalı Sistem Olarak Modellenmesi ve Girişten Duruma Kararlılık Analizi”, Demiryolu Mühendisliği, sy. 17, ss. 133–144, Ocak 2023, doi: 10.47072/demiryolu.1203693.