Module 7 : Traffic Signal Design

Lecture 38 : Coordinated Traffic Signal

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	Signal Progression on two-way streets Consider that the arterial shown in Fig.  is not a one-way but rather a two-way street. Figure 1: Moving southbound Fig. 1 shows the trajectory of a southbound vehicle on this arterial. Offset determination on a two-way street If any offset were changed in Fig. 1 to accommodate the southbound vehicle(s), then the northbound vehicle or platoon would suffer. The fact that offsets are interrelated presents one of the most fundamental problems of signal optimization. The inspection of a typical cycle (as in Fig. 2) yields the conclusion that the offsets in two directions add to one cycle length. For longer lengths (as in Fig. 3) the offsets might add to two cycle lengths. When queue clearances are taken into account, the offsets might add to zero lengths. Figure 2: Offsets on 2 way arterial are not independent- One cycle length Figure 3: Offsets on 2 way arterial are not independent- Two cycle length The general expression for the two offsets in a link on a two-way street can be written as $$t_{\mathrm{NB},i} + t_{\mathrm{SB},i} = nC$$ (1) where the offsets are actual offsets, n is an integer and C is the cycle length. Any actual offset can be expressed as the desired ideal offset, plus an error or discrepancy term: $$t_{\mathrm{actual}(j,i)} = t_{\mathrm{ideal}(j,i)} + e_{(j,i)}$$ (2) where $j$ represents the direction and $i$ represents the link. Offset determination in a grid Figure 4: Closure effect in grid A one-way street system has a number of advantages, not the least of which is traffic elimination of left turns against opposing traffic. The total elimination of constraints imposed by the closure of loops within the network or grid is not possible. Fig. 4 highlights the fact that if the cycle length, splits, and three offsets are specified, the offset in the fourth link is determined and cannot be independently specified. Fig. 4 extends this to a grid of one-way streets, in which all of the north-south streets are independently specified. The specification of one east-west street then locks in all other east-west offsets. The key feature is that an open tree of one-way links can be completely independently set, and that it is the closing or closure of the open tree which presents constraints on some links.