Module 7 : Traffic Signal Design

Lecture 38 : Coordinated Traffic Signal

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	Bandwidth concept The bandwidth concept is very popular in traffic engineering practice, because the windows of green (through which platoons of vehicles can move) are easy visual images for both working professionals and public presentations good solutions can often be obtained manually, by trial and error. Bandwidth and efficiency of a progression The efficiency of a bandwidth (measured in seconds) is defined as the ratio of the bandwidth to the cycle length, expressed as a percentage: $$\mathrm{efficiency} = \frac {\mathrm{bandwidth}}{\mathrm{cycle~length}} \times 100\%$$ (1) An efficiency of 40% to 50% is considered good. The bandwidth is limited by the minimum green in the direction of interest. Figure 1: Bandwidths on a time space diagram Fig. 1 illustrates the bandwidths for one signal-timing plan. The northbound efficiency can be estimated as $(17/60)100\% = 28.4\%$. There is no bandwidth through the south-bound. The system is badly in need of re-timing at least on the basis of the bandwidth objective. In terms of vehicles that can be put through this system without stopping, note that the northbound bandwidth can carry $17/2.0 = 8.5$ vehicles per lane per cycle in a nonstop path through the defined system. The northbound direction can handle $$\frac{8.5 veh}{\mathrm{cycle}} \times \frac{\mathrm{cycle}}{60 sec} \times \frac{3600 sec}{hr} = 510 \mathrm {vph~per~lane}$$ very efficiently if they are organized into 8-vehicle platoons when they arrive at this system. If the per lane demand volume is less than $510 vphpl$ and if the flows are so organized, the system will operate well in the northbound direction, even though better timing plans might be obtained. The computation can be formalized into an equation as follows: $$\mathrm{nonstop~volume} = \frac {3600(BW)(L)} {(h)(C)} \mathrm{vph}$$ (2) where: $BW$ = measured or computed bandwidth, sec, $L$= number of through lanes in indicated direction, $h$ = headway in moving platoon, sec/veh,and $C$ =cycle length. Trial-and-error approach to find bandwidth The engineer usually wishes to design for maximum bandwidth in one direction, subject to some relation between the bandwidths in the two directions. There are both trial-and-error and somewhat elaborate manual techniques for establishing maximum bandwidths. Refer to Fig. 2, which shows four signals and decent progressions in both the directions. For purpose of illustration, assume it is given that a signal with 50:50 split may be located midway between Intersections 2 and 3. The possible effect as it appears in Fig. 3 is that there is no way to include this signal without destroying one or the other through band, or cutting both in half. The offsets must be moved around until a more satisfactory timing plan develops. A change in cycle length may even be required. The changes in offset may be explored by: copying the time-space diagram of Fig. 3 cutting the copy horizontally into strips, one strip per intersection placing a guideline over the strips, so as to indicate the speed of the platoon(s) by the slope of the guideline sliding the strips relative to each other, until some improved offset pattern is identified Figure 2: Case study:Four intersections with good progressions Figure 3: Effect of inserting a new signal into system There is no need to produce new strips for each cycle length considered: all times can be made relative to an arbitrary cycle length `C. The only change necessary is to change the slope(s) of the guidelines representing the vehicle speeds. The northbound vehicle takes $3600/60 = 60 sec$ to travel from intersection 4 to intersection 2. If the cycle length $C = 120 sec$, the vehicle would have arrived at intersection 2 at $C/2$, or one half of the cycle length. To obtain a good solution through trial-and-error attempt, the following should be kept in consideration: If the green initiation at Intersection 1 comes earlier, the southbound platoon is released sooner and gets stopped or disrupted at intersection 2. Likewise, intersection 2 cannot be northbound without harming the southbound. Nor can intersection 3 help the southbound without harming the northbound. A historical perspective on the use of bandwidth An elegant mathematical formulation requiring two hours of computation on a supercomputer is some-what irrelevant in most engineering offices. The determination of good progressions on an arterial must be viewed in this context:only 25 years ago, hand held calculators did not exist; 20 years ago, calculators had only the most basic functions. 15 years ago, personal computers were at best a new concept. Previously, engineers used slide rules. Optimization of progressions could not depend on mathematical formulations simply because even one set of computations could take days with t he tools available. Accordingly,graphical methods were developed. The first optimization programs that took queues and other details into account began to appear, leading to later developments that produced the signal-optimization programs in common use in late 1980s. As computers became more accessible and less expensive, the move to computer solutions accelerated in the 1970s. New work on the maximum-bandwidth solution followed with greater computational power encouraging the new formulations.