A Spatial Analysis of Multimodal Transport in Kisii Town Using the LWR Model
Abstract
Traffic flow in most urban areas is augmenting due to the growth in transport and continual demand for it. It is multimodal and includes use of different types of vehicles, motorcycles and even walking. The assessment of uninterrupted traffic flow is traditionally based on empirical methods. This study was based on the macroscopic model which is a mathematical model that
formulates the relationships among traffic flow characteristics like density, flow, mean and speed of a traffic stream. The study considered traffic models first developed by Lighthill and Whitham [14] and later Richards [20] shortly called LWR traffic flow model. Simulation by use of this method enables control strategies of congestion dissipation and has suggested some recommended measures to rationalize the design of roads and implementation of regulations of road users considering some regulations and infrastructural gaps in Kisii town. This paper focuses on two finite difference schemes, that is, first order Explicit Upwind Difference Scheme-EUDS (forward time, backward space) and second order Lax-Wendroff Difference Scheme-LWDS (forward time, centred space) for solving first order PDE as well as the traffic density $\rho(t,x)$ was computed by solving LWR macroscopic conservation form of traffic flow model using both schemes. The conditions of stability were numerically verified and it is shown that LWDS is superior to EUDS in terms of time step selection. The results obtained were compared with average key data, which provided the initial and boundary conditions used for numerical simulation.
References
Adams, W. F. (1936). Road traffic considered as a random series. Journal of the Institution of Civil Engineers, 4(1), 121–130. https://doi.org/10.1680/ijoti.1936.14802
Bosire, J. N., Sigey, J. K., Okelo, J. A., & Okwoyo, J. (2015). Zhang's second order traffic flow model and its application to the Kisii Kisumu highway within Kisii County. University of Nairobi.
Bretti, G., Natalini, R., & Piccoli, B. (2007). A fluid-dynamic traffic model on road networks. Archives of Computational Methods in Engineering, 14, 139–172. https://doi.org/10.1007/s11831-007-9004-8
Chandler, K. N., & Tanner, J. C. (1958). Estimates of the total miles run by road vehicles in Great Britain in 1952 and 1956. Journal of the Royal Statistical Society. Series A (General), 121(4), 420–437. https://doi.org/10.2307/2343311
Daganzo, C. F., & Geroliminis, N. (2008). An analytical approximation for the macroscopic fundamental diagram of urban traffic. Transportation Research Part B: Methodological, 42(9), 771–781. https://doi.org/10.1016/j.trb.2008.06.008
Greenshields, B. D., Bibbins, J. R., Channing, W. S., & Miller, H. H. (1935). A study of traffic capacity. In Highway Research Board Proceedings (Vol. 14, No. 1, pp. 448–477). Washington, DC.
Haberman, R. (1998). Mathematical models: mechanical vibrations, population dynamics, and traffic flow. SIAM. https://doi.org/10.1137/1.9781611971156
Helbing, D., Treiber, M., Kesting, A., & Schönhof, M. (2009). Theoretical vs. empirical classification and prediction of congested traffic states. The European Physical Journal B, 69, 583–598. https://doi.org/10.1140/epjb/e2009-00140-5
Huber, M., & Helmreich, B. (2016). Stormwater management: Calculation of traffic area runoff loads and traffic related emissions. Water, 8(7), 294. https://doi.org/10.3390/w8070294
Kimathi, M. E. M. (2012). Mathematical models for 3-phase traffic flow theory (Doctoral dissertation). Technische Universität Kaiserslautern.
Kronjäger, W., & Konhäuser, P. (1997). Applied traffic flow simulation. IFAC Proceedings Volumes, 30(8), 777–780. https://doi.org/10.1016/S1474-6670(17)43916-4
Kumar, R., Parida, P., Madhu, E., & Kumar, A. B. (2017). Does connectivity index of transport network have impact on delay for driver? Transportation Research Procedia, 25, 4988–5002. https://doi.org/10.1016/j.trpro.2017.05.377
Lévéque, L., Ranchet, M., Deniel, J., Bornard, J.-C., & Bellet, T. (2020). Where do pedestrians look when crossing? A state of the art of the eye-tracking studies. IEEE Access, 8, 164833–164843. https://doi.org/10.1109/ACCESS.2020.3021208
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. https://doi.org/10.1098/rspa.1955.0089
López, M. A., Martin, S., Aguado, J. A., & de la Torre, S. (2013). V2G strategies for congestion management in microgrids with high penetration of electric vehicles. Electric Power Systems Research, 104, 28–34. https://doi.org/10.1016/j.epsr.2013.06.005
Mackie, R. L., Smith, J. T., & Madden, T. R. (1994). Three-dimensional electromagnetic modeling using finite difference equations: The magnetotelluric example. Radio Science, 29(4), 923–935. https://doi.org/10.1029/94RS00326
Morgan, J. V. (2002). Numerical methods for macroscopic traffic models (Doctoral dissertation). Citeseer.
Munoz, J. C., & Daganzo, C. F. (2003). Structure of the transition zone behind freeway queues. Transportation Science, 37(3), 312–329. https://doi.org/10.1287/trsc.37.3.312.16043
Rahane, S. K., & Saharkar, U. R. (2014). Traffic congestion-causes and solutions: a study of Talegaon Dabhade City. Journal of Information, Knowledge and Research in Civil Engineering, 3(1), 160–163.
Richards, P. I. (1956). Shock waves on the highway. Operations Research, 4(1), 42–51. https://doi.org/10.1287/opre.4.1.42
Richards, C. W., & Thaller, M. L. (1978). United States railway traffic: An update. The Professional Geographer, 30(3), 250–255. https://doi.org/10.1111/j.0033-0124.1978.00250.x
Xiong, R., He, H., Guo, H., & Ding, Y. (2011). Modeling for lithium-ion battery used in electric vehicles. Procedia Engineering, 15, 2869–2874. https://doi.org/10.1016/j.proeng.2011.08.540
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