نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی عمران، دانشکده مهندسی، دانشگاه بیرجند، بیرجند، ایران.

2 گروه مهندسی عمران، دانشکده مهندسی شهید نیکبخت، دانشگاه سیستان و بلوچستان، زاهدان، ایران.

10.22105/dmor.2021.271141.1313

چکیده

هدف: در این مقاله یک روش عددی جدید، با استفاده از تکنیک حجم محدود نوع گودونو، نسخه موج شار الگوریتم پخش‌موج اصلاح‌شده با دقت بالا برای حل یک‌بعدی مدل کلان‌نگر مرتبه‌دوم جریان ترافیک ارائه شده‌است.
روش‌شناسی پژوهش: از مدل متداول پین-ویتهام و مدل پین-ویتهام مبتنی بر پاسخ فیزیولوژیکی راننده به ‌منظور صحت‌سنجی حل عددی استفاده شده‌است. معادلات مشتق‌های پاره‌ای غیرخطی هذلولوی جریان ترافیک که پاسخ تحلیلی ندارند، با درنظرگرفتن یک سرعت نوین برای امواج ریمن، براساس حل‌کننده ریمن تقویت‌شده، حل‌شده‌اند. در این روش ابتدا معادلات غیرخطی به یک مسئله شبه‌خطی قطری با منحنیهای مشخصه خطی تبدیل شده و مولفه‌های منبع مربوطه در تفاضل شار سلول‌های محاسباتی حجم‌محدود شرکت داده می‌شوند. راه‌حل‌های موج مرتبه‌دوم و شرایط پرش اولیه آن‌ها درنظرگرفته شده و نتایج عددی به‌دست‌آمده برای دو مدل پین-ویتهام قبل و بعد از لحاظ‌کردن پاسخ فیزیولوژیکی راننده، با تکنیک تجزیه رو به‌عنوان روش متداول در گسسته‌سازی مدل‌های کلان‌نگر مرتبه‌دوم جریان ترافیک مقایسه می‌شوند.
یافته ها: مسئله انتشار صف در حالت جریان یکنواخت با دو ناپیوستگی شامل امواج شوک و متعاقبا امواج انبساطی، با شرایط مرزی تناوبی به‌عنوان مثال عددی انتخاب شده‌است. پروفیل‌های سرعت و چگالی در زمان‌های مختلف به همراه تغییرات مکانی-زمانی آن‌ها و نرخ تردد جریان ترافیک کلان‌نگر ارایه‌گردیده‌است.
اصالت/ارزش افزوده علمی: نتایج عددی حاصل نشان‌می‌دهد که روش پیشنهادی رفتار واقع‌بینانه‌تری را برای دو مدل ذکرشده درخصوص متغیرهای اساسی جریان ترافیک فراهم می‌کند.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Numerical modelling of macroscopic traffic flow based on driver physiological response using a modified wave propagation algorithm

نویسندگان [English]

  • Morteza Araghi 1
  • Hossein Mahdizadeh 1
  • Sadegh Moodi 2

1 Department of Civil Engineering, Faculty of Engineering, University of Birjand, Birjand, Iran.

2 Department of Civil Engineering, Shahid Nikbakht Faculty of Engineering, University of Sistan and Baluhestan, Zahedan, Iran.

چکیده [English]

Purpose: In this paper, a novel numerical method, using the Godunov-type finite volume technique, the flux wave version of Modified Wave Propagation Algorithm (MWPA) with high-resolution is presented to solve one-dimensional second-order macroscopic model of traffic flow.
Methodology: To demonstrate the effectiveness of the proposed approach, the commonly employed Payne–Whitham model and PW based on driver physiological response have been used. The hyperbolic nonlinear Partial Derivatives Equations (PDEs) of traffic flow which do not have analytical solution are solved considering a new Riemann wave speeds, based on an augmented Riemann solver. In this method, nonlinear equations are first transformed into a diagonal quasi-linear problem with linear characteristic curves, the corresponding source terms are involved in the flux difference of finite volume computational cells. The second-order wave solutions and their initial jump conditions are considered and the obtained numerical results are compared with Roe Decomposition Technique (RDT) as a common method in macroscopic traffic flow models discretization for the PW model before and after considering driver physiological response.
Findings: The problem of queue propagation in uniform traffic flow condition with two discontinuities including shock waves and subsequent rarefaction waves with periodic boundary conditions was selected as a numerical example. Velocity and density profiles at different times, the spatio-temporal changes of the two mentioned variables and traffic flow rates were presented.
Originality/Value: The numerical results indicate that the proposed method provides a more realistic behavior for the two mentioned models regarding the basic variables of traffic flow.

کلیدواژه‌ها [English]

  • Numerical modelling
  • Macroscopic Traffic Flow
  • Wave propagation algorithm
  • Flux wave method
  • Rieman solver
Bale, D. S., LeVeque, R. J., Mitran, S., & Rossmanith, J. A. (2003). A wave propagation method for conservation laws and balance laws with spatially varying flux functions. SIAM journal on scientific computing, 24(3), 955–978.
Borges, R., Carmona, M., Costa, B., & Don, W. S. (2008). An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws. Journal of computational physics, 227(6), 3191–3211.
Chen, J., Shi, Z., & Hu, Y. (2012). Numerical solutions of a multi-class traffic flow model on an inhomogeneous highway using a high-resolution relaxed scheme. Journal of zhejiang university SCIENCE C, 13(1), 29–36.
Davoodi, N. (2014). Adaptive numerical methods for macroscopic traffic flow problems (PhD thsis, Ferdowsi university of mashhad). (In Persian). Retrieved from https://ganj.irandoc.ac.ir//#/articles/2e6dec8a5984967fac6fbc0b3c2c2e85
Del Castillo, J. M., Pintado, P., & Benitez, F. G. (1994). The reaction time of drivers and the stability of traffic flow. Transportation research part B: methodological, 28(1), 35–60.
Delis, A. I., Nikolos, I. K., & Papageorgiou, M. (2014). High-resolution numerical relaxation approximations to second-order macroscopic traffic flow models. Transportation research part C: emerging technologies, 44, 318–349.
Greenshields, B. D. (1935). A study in highway capacity. Highway research board.
Mahdizadeh, H. (2018). A modified flux-wave formula for the solution of one-dimensional Euler equations with gravitational source term. Iranian journal of numerical analysis and optimization, 8(2), 25–37. (In Persian). DOI: 10.22067/IJNAO.V8I2.59531
Khan, Z. H., Gulliver, T. A., Nasir, H., Rehman, A., & Shahzada, K. (2019). A macroscopic traffic model based on driver physiological response. Journal of engineering mathematics, 115(1), 21–41.
Khan, Z. H., & Gulliver, T. A. (2020). A macroscopic traffic model based on transition velocities. Journal of computational science, 43, 101131.
Khan, Z. H., Gulliver, T. A., Khattak, K. S., & Qazi, A. (2020a). A macroscopic traffic model based on reaction velocity. Iranian journal of science and technology, transactions of civil engineering, 44(1), 139–150.
Khan, Z. H., Imran, W., Gulliver, T. A., Khattak, K. S., Wadud, Z., & Khan, A. N. (2020b). An anisotropic traffic model based on driver interaction. IEEE access, 8, 66799–66812.
LeVeque, R. J. (2002). Finite volume methods for hyperbolic problems (Vol. 31). Cambridge university press.
Lighthill, M. J., & Whitham, G. B. (1955). On kinematic waves II. A theory of traffic flow on long crowded roads. Proceedings of the royal society of London. series A. mathematical and physical sciences, 229(1178), 317–345.
Mahdizadeh, H., Sharifi, S., & Omidvar, P. (2018). On the approximation of two-dimensional transient pipe flow using a modified wave propagation algorithm. Journal of fluids engineering, 140(7). https://doi.org/10.1115/1.4039248
Mahdizadeh, H., Stansby, P. K., & Rogers, B. D. (2011). On the approximation of local efflux/influx bed discharge in the shallow water equations based on a wave propagation algorithm. International journal for numerical methods in fluids, 66(10), 1295–1314.
Mahdizadeh, H., Stansby, P. K., & Rogers, B. D. (2012). Flood wave modeling based on a two-dimensional modified wave propagation algorithm coupled to a full-pipe network solver. Journal of hydraulic engineering, 138(3), 247–259.
Mohammadian, S. (2017). Numerical study on traffic flow prediction using different second-order continuum traffic flow models (Master Thesis, Ferdowsi University of Mashhad). (In Persian). Retrieved from https://ganj.irandoc.ac.ir/#/articles/478c9ea9bca65e2dcec30db90ae277dc
Mohammadian, S., & van Wageningen-Kessels, F. (2018). Improved numerical method for Aw-Rascle type continuum traffic flow models. Transportation research record: journal of the transportation research board, 2672(20), 262–276.
Moodi, S. (2017). Numerical modellig of flood flow in sewer networks considering the effects of the manhole (Master Thesis, University of Sistan and Baluchestan). (In Persian). Retrieved from https://ganj.irandoc.ac.ir/#/articles/1c341d46960c0b712dec3237302d1df5
Moodi, S., & Mahdizadeh, H. (2018). Numerical modelling of water influx falling into an empty tank using a modified wave propagation algorithm. Modares mechanical engineering, 18(6), 182–190. (In Persian). https://mme.modares.ac.ir/article-15-16901-fa.html
Payne, H. (1971). Models of freeway traffic and control, simulation councils. INC.: San Diego, CA, USA, 51–61.
Richards, P. I. (1956). Shock waves on the highway. Operations research, 4(1), 42–51.
Roe, P. (1981). Approximate riemann solvers, parameter vectors, and difference schemes. Journal of computational physics, 43(2), 357–372.
Sreekumar, M., Joshi, S. M., Chatterjee, A., & Mathew, T. V. (2019). Analyses and implications of higher order finite volume methods on first-order macroscopic traffic flow models. Transportation letters, 11(10), 542–557.
Zhang, H. M. (1998). A theory of nonequilibrium traffic flow. Transportation research part B: methodological, 32(7), 485–498.