Original language | English (US) |
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Pages (from-to) | 185-189 |
Number of pages | 5 |
Journal | Mechanics Research Communications |
Volume | 11 |
Issue number | 3 |
DOIs | |
State | Published - 1984 |
Bibliographical note
Funding Information:Numerical example Consider the problem of a coordinated link consisting of two signalized intersections in succession governed by equation (3) subjected to boundary and initial conditions described in reference \[3\]. This problem has been solved analytically in \[3\] and numerically by a second order accuracy finite difference method (FDM) in \[5\]. The same problem was also solved here by the proposed FEM and the results, together with those of refernces \[3\] and \[5\], are shown in Fig. I. It is apparent from this Figure that both numerical methods are in good agreement with the analytical solution with the FEM yielding slightly better results than the FDM. It was found, however, that the computational cost associated with the FEM was higher than that of the FDM. Conclusions The FEM has been employed for the numerical solution of traffic flow problems for the first time in the literature° The method is slightly better in accuracy but more time consuming than the FDM. It is expected that for more advanced traffic flow modelling involving two spatial dimensions and/or governing equations consisting of both the continuity and momentum equations the FEM would become more accurate and efficient than the FDM. This, however, needs proof through further investigation. Acknowledgment Financial support for this study was provided by NSF (Project No. CEE-8210189) References I. M. Ao l ighthill and Whitham, "On kinematic waves; II. A theory of traffic flow on long crowded roads," Proc. R. Soc., Ser. A229, N. 1178, 317-345 (1955). 2. Do Co Gazis, "Mechanics and traffic theory," Developments in Mechanics, Z, 17-30 (1973). 3. P. G. Michalopoulos, G. Stephanopoulos and Vo B. Pisharody, Modelling of traffic flow at signalized links, Transp. Sci., 14, 9-41 (1980). 4. P. G. Michalopoulos and V. B. Pisharody, Platoon dynamics at signal controlled arterials, Transp. Sci., I__4, 365-396 (1980). 5. P. G. Michalopoulos, D. E. Beskos and J. Lin, Analysis of interrupted traffic flow by finite difference methods, Transp. Res. (in press)° 6. P. G. Michalopoulos, D. E. Beskos and Y. Yamauchi, Multilane traffic flow dynamics: Some macroscopic considerations, Transp. Reso (in press). 7o B. D. Greenshields, "A study of traffic capacity," Proc. Hwy, Res. Board, I_44, 448-477 (1934).