Module 4 : Macroscopic And Mesoscopic Traffic Flow Modeling

Lecture 18 : Cell Transmission Models

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	Merging and Diverging Consider two cells merging, here we have a beginning cell and its complimentary merging into ending cell, the constraints on the flow that can be sent and received are given by equation 1 and equation 1. $$y_k(t)\leq S_{Bk};y_{ck}(t) \leq S_{Ck} y_k(t)+y_{ck}(t) \leq R_{Ek}$$ (1) where, $S_I(t) = (Q_I,n_I)$, and $R_I(t)=(Q_I,\delta I,[N_I- n_I])$. A number of combinations of $y_k(t) +y_{ck}(t)$ are possible satisfying the above said constraints. Similarly for diverging a number of possible outflows to different links is possible satisfying corresponding constraints, hence this calls for an optimization problem. Ziliaskopoulos (2000), has given this LP formulations for both merging and diverging, this has been discussed later