V. Coordination Timing Issues

There are three parameters that determine how a controller functions in a coordination mode: cycle length, offset, and split. While all three parameters are important to the efficient operation of a signalized arterial or network, it might be argued that the cycle length is the most important of these parameters because it determines the periodicity of the system.

Resonant Cycle

In the discussion of the cycle length, we introduce the concept of the resonant cycle length.⁸ That is, for regular linear and grid networks, there are one, two, and sometimes three cycle lengths that provide much better operation than other cycles. In other words, the concept of a resonant cycle is a cycle length that accommodates good two-way progression. The resonance (and non-resonance) of a cycle time stems from the principle that intersection spacing precludes good progression at certain cycle lengths, and conversely some cycle lengths necessarily preclude progression on an arterial due to their incompatibility to the network geometry. The second essential element of a resonant cycle is that it continues to provide good two-way arterial progression over a range of volumes.

Resonant cycles naturally arise on arterials as a function of what cycle provides good two-way progression for given intersection spacing, vehicle speeds, volume levels, saturation flow rates, and phase sequencing. Time-space diagrams can be used to provide a convenient means of conveying the traffic flow mechanics that give rise to the resonant cycle. The results of the experiments, taken as a whole, suggest that well-chosen cycle lengths scheduled by time-of-day or selected from a table dynamically could yield better progression, delay, and travel time performance than an on-line incremental adjustment strategy based on maintaining a constant, target degree of saturation for the single most congested intersection—a typical adaptive control strategy.

Optimizing an arterial signal-timing plan (cycle, splits, and offsets) for a singular set of input volumes can be handled in a straightforward manner by using signal-timing optimization software such as Transyt-7F or Synchro. However, a much more challenging task is compiling a set of time-of-day (TOD) signal-timing plans and a TOD schedule for each day of the week, in order to accommodate all hourly and daily fluctuations in traffic conditions typically experienced during the week.

There are currently no commercially available off-the-shelf tools to address this problem and even the literature offers very little in terms of structured guidance to accomplish this task. The decisions to be made include the following:

Select a workable number of plans. For example, 15 signal-timing plans usually are not practical. A typical day might minimally consist of four plans: the AM peak, the PM peak, off-peak day, and off-peak night. Also, for areas in the vicinity of major shopping facilities one might consider a special plan to accommodate shopping traffic demand.

Construct a schedule. Each hour of the week must be covered by a signal-timing plan. For example, the schedule determines when the AM peak plan starts and ends, subsequently switching to the off-peak plan.

Determine the input volumes to generate each plan. Over the hours that each signal-timing plan will be in operation, traffic conditions may fluctuate significantly. However, signal-timing optimization software only accepts a single set of input volumes to generate a corresponding plan. For example, a user might use the peak-hour flows observed over the whole time frame a plan will be in effect.

The decisions are all interrelated. For example, the number of workable plans may depend on the number of “distinct” traffic conditions that can be discerned. The construction of the schedule will depend on the number of timing plans that are appropriate through a given day. The input volumes will depend on what time of day a plan is in effect. Until very recent publications, engineering judgment was the only guide to making these decisions.

A paper published in 2002 suggests that a statistical clustering algorithm, based on volumes approach the arterial’s critical intersection be used to determine “break-points” (or switch points) between TOD plans in the daily schedule.⁹

A subsequent paper,published in 2004, suggested flaws with using volume clusters, and suggested that instead, 90th percentile volumes (of a set of several TOD observations) of the critical intersection be used to optimize its cycle length based on a uniform delay equation.¹⁰ These plans would then be evaluated over several TOD intervals (using a genetic algorithm) to optimize the TOD schedule of the critical intersection.

Intersection Categories

In the signal network to be retimed, all intersections can be divided into two categories: primary intersections and secondary intersections. The primary intersections have the highest demand-to-capacity ratio and will therefore require the longest cycles. These intersections are usually well-known to the Traffic Engineer. They are the intersection of two arterials, the intersections with the worst accident experience, the intersections that service the major shopping centers, and the intersections that generate the most complaints. The secondary intersections are the ones that generally serve the adjacent residential areas and local commercial areas. They are usually characterized by heavy demand on the two major approaches and much less demand on the cross-street approaches.

The purpose of assigning intersections to one of these two categories is to reduce the locations where traffic counts are required. The primary intersections require turning movement traffic counts—there is simply no other way to measure demand. However, the secondary intersections usually have side street demand that can be met with phase minimum green times. The strategy, therefore, is to concentrate the counting resources at the locations where there is no substitute, and to use minimum green times for the minor phases at secondary intersections.

Number of Timing Plans

A unique timing plan is required whenever a cycle length, offset, or split is different from the previous setting. When a new timing plan is selected, the controller must “transition” to the new plan. During this transition period, systematic operation in the network is interrupted while each controller adjusts to the new parameters. Because of this disruption, transitions are minimized and one must be assured that the benefits of the new plan overcome the disbenefits of the transition period.

One way to determine how many timing plans are needed is to assume that a new plan is needed whenever there is a significant change in the traffic demand. This may be assessed by evaluating the changes in demand by hour and by direction. For the network, array the northbound, southbound, eastbound and westbound in a table where the directional flows are in columns and the rows represent the hourly data. Have a column of the table represent the sum of the four directional flows. Examine this column to identify the time during which there is a significant change in the total demand: this is an indication that different cycle length (new timing plan) may be warranted.

Assuming that the major flows are on the north-south street, calculate the basic split by dividing the greater of the northbound or southbound by the total intersection demand for the period. When this ratio changes is a good indication of the need for a new plan to accommodate a new offset. Periods when a new plan may be warranted are identified by the changes in either the total demand or the split demand.

Using the Tool Box

We have placed a significant emphasis on discussing resonant cycle lengths because plan changes involving different cycle lengths are very disruptive during the transition period. In contrast, timing plan changes that involve different offsets with the same cycle length are relatively benign, and plan changes that only involve split differences are generally unnoticed. It is important therefore, to identify the resonant cycle and use this cycle for as many plans as possible.

When a computer model is not available, we suggest that the following procedure be followed:

1. Cycle—For each Primary intersection, calculate the Cycle Length required using Webster’s equation as defined in Section 4.1. For each signal group, determine the Resonant Cycle Length using the equations provided in Section 4.2. Select the longest Cycle for the timing plan.

2. Split—For each Primary intersection determine the intersection splits using the Critical Movement Method explained in Section 4.5 and the selected Cycle. For each Secondary intersection, determine the time required for each minor movement using the Greenshields-Poisson Method and the Cycle explained in Section 4.6. Check both Primary and Secondary intersections for pedestrian timing requirements and adjust as necessary.
   
   The purpose of obtaining count data is to use it as input to a timing model. The timing model then generates the appropriate signal settings. There is an alternative way, which is to estimate the settings directly. This is being performed when estimating the minimum phase time for the cross-street movements at a secondary intersection. The turning movement data at the primary intersection might show that the cycle length for the group should be 100 seconds. If we allow a phase minimum of 10 seconds and assume 5 seconds for the change and clearance intervals, then we can determine that the side street split should be 15 percent. To work the numbers another way, there will be thirty-six100-second cycles per hour. Ten seconds is sufficient time to discharge three to four vehicles per cycle. In other words, this strategy will provide enough capacity to discharge approximately 125 vehicles per lane in an hour. As long as the demand is less than the 125 vehicles per lane, this approach will work fine.
   
   This example describes one way to estimate secondary intersection split, given the cycle length. For system timing, we must also have a means of estimating the third parameter, the offset. We can do this for two conditions: when the demand in one direction is predominant and when the demand is relatively balanced.

3. Offset—Determine the offsets using the Kell Method as outlined in Section 4.4. When using the Kell Method (or any maximum bandwidth method), the practitioner has several options. The most obvious, and most frequently used, is to consider an arterial as single entity. This will generally result in balanced bandwidths in both directions.
   
   During periods of directional flow, however, it may be useful to consider a minor variation. Within any arterial group, the signals can be clustered in subgroups. The intent is to cluster signals that have similar link lengths into subgroups. The Kell Method is then applied to each cluster which by virtue of the similar link lengths will have good progression in each direction. The offsets within the subgroups are those generated by the Kell Method. The offset between clusters is set using the one-way method defined in Section 4.3 to favor the peak directional movement. This technique assures good progression in the peak direction while providing good progression within the clusters in the counter-flow direction.
   
   During periods of heavy directional flow, it may be necessary to ignore the contra-flow traffic to accommodate the peak directional demand. In this instance, all of the offsets are developed using the One-way Method as described in Section 4.3.

8 “Resonant Cycles in Traffic Signal Control;” Shelby, S.G., Darcy Bullock, and Douglas Gettman, TRB Meeting, January 2005.

9 Smith, B. L., W. T. Scherer, T. A. Hauser, and B. Park, “Data-Driven Methodology for Signal Timing Plan Development: A Computational Approach.” Computer-Aided Civil and Infrastructure Engineering, Vol. 17, 2002, pp. 287-395.

10 Park, B., P. Santra, I. Yun, D. Lee, “Optimization of Time-of-Day Breakpoints for Better Traffic Signal Control.” In TRB 83rd Annual Meeting Compendium of Papers. CD-ROM. Transportation Research Board, National Research Council, Washington, DC, 2004.