Platoon dispersion is the gradual spreading of a vehicle group as it travels between signalised intersections. A cluster of vehicles released together on a green phase doesn't arrive at the downstream stop line as a compact group. Faster drivers accelerate ahead, slower ones lag behind, and by the time the platoon reaches the next detector, it has smeared across a window of several seconds. That spreading is platoon dispersion, and it's one of the most consequential inputs in coordinated signal timing design.
Understanding dispersion matters because green wave corridors depend on a tight platoon arriving at the next intersection within a predictable offset window. When dispersion is underestimated, green time opens too early or too late, catching part of the platoon on red. The result isn't a failed corridor so much as a corridor that works at lower volumes and breaks down when demand rises.
Why platoons spread out
Three forces drive dispersion along a link. First, individual driver behaviour: reaction times, preferred following distances, and target speeds vary across every vehicle in the group. A 50 km/h approach speed with a 2-second headway variation across 20 vehicles produces a platoon tail that's already 40 metres longer than the head by the time it clears the stop line.
Second, link geometry introduces variance. Mid-block driveways, unsignalised side streets, and pedestrian crossings all cause individual drivers to brake or accelerate independently, which breaks the group's coherence. A 400-metre link with two active driveways disperses a platoon faster than an uninterrupted 400-metre arterial section.
Third, inter-vehicle speed variance compounds with distance. A 5 km/h speed spread across a platoon produces roughly 1.4 seconds of additional spread per 100 metres of travel. On a 600-metre link, that alone accounts for an 8-second arrival window at the downstream signal, even before driveway interference is counted.
The Robertson dispersion model
The most widely applied dispersion model in signal coordination software is the Robertson model, developed in the early 1970s and still embedded in tools like SIDRA Intersection and TRANSYT. The model treats each departing time slice of vehicles as a proportion that arrives at the downstream stop line over a distribution of future time steps.
The core parameter is the smoothing factor, usually denoted as F, which ranges from 0 to 1. A value of 1 means perfect platoon preservation: every vehicle that departs in second t arrives in second t at the downstream signal. A value closer to 0 means near-total dispersion: the departing group smears uniformly across future arrival intervals. Calibrated values for urban arterials in Australian conditions typically sit between 0.35 and 0.55, depending on link length and driveway density. Freeway off-ramp links, with no mid-block interference, can push to 0.7 or higher.
The travel time used in the model is the free-flow travel time for the link, not the congested travel time. That distinction matters. Using a congested travel time input shifts the predicted arrival window and causes the offset to be set against a condition that won't hold when the network is lightly loaded.
What dispersion does to offset selection
Signal offset is the time difference between the start of green at one intersection and the start of green at the next intersection along the corridor. In a perfectly coordinated system with zero dispersion, the offset equals the free-flow travel time between stops. Platoon dispersion changes this calculus in two ways.
First, it widens the effective arrival window, which means some portion of the platoon will always arrive outside the optimal green band. The objective shifts from serving the whole platoon to maximising the proportion served, which is the bandwidth efficiency metric used in TRANSYT and similar optimisation tools.
Second, it creates a trade-off between cycle length and coordination quality. Longer cycle lengths produce larger platoons at each release, which disperses more by the time it reaches the next stop line. Shorter cycles produce smaller, more coherent platoons that disperse less but leave less total green time available per phase. For most urban arterials, cycle lengths between 80 and 120 seconds offer the best balance, though link length and intersection spacing shift that range considerably.
This is directly related to the design of adaptive systems. Adaptive signal control can recalculate offsets in real time as measured arrival profiles diverge from modelled dispersion curves, which is one of its genuine advantages over fixed-time plans on corridors with variable demand.
Calibrating dispersion parameters in practice
Field calibration of dispersion parameters requires loop detector or radar data at both the upstream and downstream ends of each link. The process involves matching the modelled arrival profile at the downstream detector against the measured arrival profile across a sample of signal cycles, then adjusting F until the profiles align. In practice, three steps cover most calibration work.
- Collect departure profiles from the upstream stop line over at least 50 green phases, stratified by time of day.
- Record arrival profiles at the downstream detector using the same time resolution (typically 1-second counts).
- Iterate the Robertson smoothing factor in the model until the root mean square error between predicted and measured arrival distributions falls below the acceptable threshold, usually 5–8 vehicles per interval.
Link-specific calibration produces materially better coordination than applying default F values from literature. On one Melbourne arterial corridor assessed by Bob Panich Traffic Signals, applying calibrated dispersion parameters rather than a default F of 0.5 reduced the bandwidth efficiency loss during peak periods by 12 percentage points across a six-intersection run.
Dispersion and queue interaction
Dispersion models assume vehicles travel in free flow between intersections. When residual queues form at the downstream signal, the assumption breaks down. Vehicles at the rear of a dispersed platoon that encounter a standing queue decelerate sharply, and the arrival distribution at the stop line no longer matches the dispersion model's prediction. This is the point at which coordination analysis needs to incorporate queue length estimates, not just dispersion parameters.
The interaction between dispersion and queue growth is one reason that corridor models calibrated under light demand conditions underperform during peak periods without modification. Queue spillback adds a further complication: if the downstream queue extends back to the upstream detector, the arrival data collected there is no longer a clean platoon departure profile.
Practical implications for timing plan design
Several design decisions follow directly from dispersion behaviour on a corridor. Intersection spacing is the most fundamental. Intersections spaced less than 250 metres apart see relatively little dispersion between stops, and tight coordination offsets are achievable. Intersections 800 metres apart will see platoon arrival windows of 15 seconds or more, which demands either wider green bands or acceptance of lower bandwidth efficiency.
Split allocation also interacts with dispersion. Giving more green time to the coordinated through movement doesn't help if a dispersed platoon tail is still arriving when the phase ends. A split that accounts for the modelled arrival window, not just the average travel time, serves more vehicles than one calibrated only to the free-flow offset.
Finally, the direction of travel matters. A one-way corridor can be optimised for a single direction with tight offsets. A two-way arterial requires a compromise offset that serves both directions partially, since the dispersion profiles for inbound and outbound platoons rarely align to the same cycle split. Most Australian two-way arterials accept a bandwidth efficiency of 30–45% per direction as a realistic outcome, rather than the theoretical maximum achievable in a single direction.
Bob Panich Traffic Signals designs coordinated signal timing plans that account for link-specific dispersion parameters, measured arrival profiles, and two-way bandwidth constraints, producing corridor performance that holds up under variable demand rather than only under the conditions of the calibration run.