Module 7 : Traffic Signal Design

Lecture 37 : Capacity and Los Analysis of a Signalized I/S

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	Determining capacity and v/c ratio: Capacity at signalized intersections is based on the concept of saturation flow and defined saturation flow rate. The flow ratio for a given lane group is defined as the ratio of the actual or projected demand flow rate for the lane group ($v_i$) and the saturation flow rate($s_i$). The flow ratio is given the symbol (v/s)i for lane group i. Capacity at signalized I/S is based on the saturation flow and saturation flow rate. $$C_i = s_i \times ( g_i /c )$$ (1) where $c_i$ = capacity of lane group i (veh/h), $s_i$ = saturation flow rate for lane group i (veh/h) and $g_i /C$ = effective green ratio for lane group i. v/c ratio: The ratio of flow rate to capacity (v/c), often called the volume to capacity ratio, is given the symbol X in intersection analysis $$X_i = (\frac{v}{c})_i = \frac{v_i}{s_i(\frac{g_i}{C})} =\frac{v_i c}{s_i g_i}$$ (2) where, $X_i$ = (v/c)i = ratio for lane group i, $v_i$ = actual or projected demand flow rate for lane group i (veh/h), $s_i$ = saturation flow rate for lane group i (veh/h), $g_i$ = effective green time for lane group i (s) and C = cycle length (s) Critical lane group: Another concept used for analyzing signalized intersections is the critical v/c ratio, $X_c$. This is the v/c ratio for the intersection as a whole, considering only the lane groups that have the highest flow ratio (v/s) for a given signal phase. For example, with a two-phase signal, opposing lane groups move during the same green time. Generally, one of these two lane groups will require more green time than the other (i.e., it will have a higher flow ratio). This would be the critical lane group for that signal phase. The critical v/c ratio for the intersection is determined by using Equation, $$X_c = \sum \left(\frac{v}{S}\right) (\frac{C}{C-L})$$ (3) where, $X_c$ = critical v/c ratio for intersection; The above eqn. is useful in evaluating the overall i/s w.r.t the geometric and total cycle length. A critical v/c ratio less than 1.0, however, does indicate that all movements in the intersection can be accommodated within the defined cycle length.