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Two Way Coordination

Optimization

Case Study 9

Case Study 10

### One Way Coordination

Coordination on a one way street is a relatively simple process.  To start out with, we will define some terms that are commonly used with signal coordination.

The diagram at the right is a time-space diagram that shows five intersections that are coordinated for eastbound traffic.  In this simple example, the intersections are all the same distance apart (4 and 5 are twice the normal distance), the cycle lengths are all the same, and the splits are 50/50.  That is to say, half of the time the through movement gets green, and half of the time the cross streets get the green.

The through band is the strip bordered by dark green.  This indicates the length of time available for vehicles going a certain speed to travel without stopping.  If the bandwidth (the width of the through band in time) were 12 seconds, and we assume a minimum headway of 2 seconds per vehicle, we could have a maximum of 6 cars per lane per cycle travel through this system without stopping.

The offset is the time from when the signal turns green until the succeeding signal turns green.  If the offset was zero, then the lights would turn green at the same time.

The efficiency of the bandwidth is defined by the following equation:

[Roess, et al, 1998]

• e = Bandwidth efficiency (%)

• bw = Bandwidth (sec)

• C = Cycle length (sec)

For the example above the bandwidth happens to be the same as the green time at the first intersection.  This intersection has a green time of 50%, so the efficiency is 50% of the cycle length.  While the bandwidth efficiency is a good measure of effectiveness, it should not be the only requirement you use when you are coordinating a signal.  The most efficient bandwidth does not necessarily provide the best service over the system.  This is because the system serves cross-street and turning traffic, which may or may not benefit from large bandwidth efficiencies being given to the major through movement.

The progression of the system is the order in which the signals turn green.  The progression of the system in the example is known as forward or simple progression.  The forward comes from the fact that if you stand at street 1 and watch the lights, it looks like a green wave moving forward down the street as the lights change.  Progression speed is the speed at which the through band (or "green wave") travels across the system.  In the diagram, it is the reciprocal of the slope of the through band.  In more concrete terms, it is the maximum speed a vehicle could travel down the street and still hit every green light.   The progression speed depends largely on the offsets and block lengths.

For one way coordination, the first step is to calculate the cycle lengths for each intersection.  The cycle lengths must be equal or be multiples of each other (such as 45 seconds and 90 seconds) or else they will not always align properly for uniform through bands and coordination will not be possible.  The image below shows this phenomenon.  The first line depicts cycles half as long as the cycles in the second line.  Even though the greens don't match up perfectly, they at least are always in the same position relative to each other, which will allow through bands to be created for every other short cycle.  The phases in the third line tend to "wander" relative to those in the other two lines and, as a result, it is not possible to coordinate the third line with the other two.  The requirement that the cycle lengths be multiples of each other creates a tendency for cycle lengths to be equal except at major intersections where exceptionally long cycle lengths are necessary.

Although cycle lengths must be multiples of each other, the phases within the cycles can be any length.  This is because the green times will still occur at the same point relative to each other, that is to say, the offset will be constant.  Differing phase lengths arise when cross streets have different volumes, where some will need significantly more green time than others.  In cases of differing phase lengths, the bandwidth will be limited to the smallest green time given to the through movement on the coordinated street.

Once the cycle length has been set for your street, the next step will be to determine the offsets.  The ideal offsets can be determined by the following equation:

[Roess, et al, 1998]

• ti = Ideal Offset

• D = Distance Between Intersections (ft)

• S = Ideal Vehicle Speed (ft/s)

While this equation gives you the ideal offsets, it does not take into account internal queues.  Internal queues are queues created at intersections by mid-block traffic, such as traffic from parking lots, side streets, or stragglers from the last platoon that are waiting for the light to turn green.  Internal queues adversely affect coordination because there is now a clearance time needed before a platoon can go through the intersection.  For this reason, if there is internal queuing the offsets will need to be lower than the ideal offsets.  The following figure demonstrates the effects of internal queuing.  The short blue line represents the time necessary to clear the queue before the arrival of the upstream platoon.  This is the same amount of time that is lost to the through band due to the shortened offset.

The new offset time is given by:

[Roess, et al, 1998]

• ti, D, S are as defined above

• Q = Number of vehicles queued per lane (veh)

• h = Startup headway (sec) generally 2 seconds

As you can see from the equation, it is possible to have no offsets or negative offsets.  The disadvantage with small or negative offsets is that this limits the width of the through band.  This is discussed in more detail on the 2 Way Coordination page.

With your offset times and cycle lengths you have the beginnings of a coordinated system.  However, this says nothing of two way coordination.  For more on that, please go here.