What is a time-distance diagram (time-space diagram) for traffic signals?

A time-distance diagram shows, on one drawing, when every traffic signal along a corridor is green and where a vehicle travelling at the design speed would be at each moment. It is the working drawing of signal coordination: if the sloped line of a vehicle passes through green at every intersection, the corridor has a green wave.

· SigTDD

Two names, one drawing

Time-distance diagram is the usual term in Australia, New Zealand and the United Kingdom; time-space diagram is the North American term used in the ITE and FHWA signal timing literature. Both describe the same plot: distance along the corridor on one axis, time on the other. Construction schedulers use the same words for a different chart (a linear schedule of chainage against date), which is why searching the bare phrase turns up scaffolding and railway timetables; the traffic-signal version is the one on this page.

The axes

SigTDD, like the desktop tools before it, puts distance up the vertical axis in metres from the first intersection and time across the horizontal axis in seconds. Each signalised intersection sits at its cumulative distance from the start of the corridor, so a 450 m link is drawn one and a half times as tall as a 300 m link. Time starts at an arbitrary reference, normally the start of the first intersection's cycle, and repeats every cycle length.

Time-distance diagram of the Riverside Drive example corridor with a northbound green waveSix intersections from 0 to 1850 metres, a 120-second cycle, phase bars at each intersection shifted by their offsets, and a translucent northbound band 59 seconds wide that meets green at every intersection.ABCDEABCDE#1 Oak St · offset 0sEABCDEABCD#2 Elm Ave · offset 21sCDEABCDEABC#3 Pine Rd · offset 45sCDEABCDEAB#4 Cedar Ln · offset 63sABCDEABCDEA#5 Birch Way · offset 90sABCDEABCDEA#6 Maple Ct · offset 111s0306090120150180210240050010001500Time (seconds)Distance north (m)
The six-intersection Riverside Drive example that ships with SigTDD (NB-Green-Wave.csv), drawn from its CSV values. The blue band is the set of northbound departures from Oak Street that meet green at every signal north of it.

Phase bars

At each intersection's distance a horizontal bar shows the signal sequence in time: phase A, then B, then C and so on, each ending in amber, then the sequence repeats. The bar is shifted right by the intersection's offset, the number of seconds between the corridor reference and the start of that intersection's cycle. Colour says which through movement each phase serves:

  • Cyan — both northbound and southbound through movements run (an "NS" or "NBSB" phase).
  • Purple — northbound only, typically a leading or lagging northbound turn phase that also carries the through.
  • Green — southbound only.
  • Grey — a phase outside the corridor progression: a cross-street phase, a pedestrian phase, a protected turn that stops the through.
  • Amber — the last seconds of each green run, deducted from usable green.

The cycle length is the sum of the phase durations. In the example every intersection runs a 120-second cycle: 40 s both directions, 22 s northbound, 22 s southbound, 18 s cross street, 18 s both directions. A corridor can only be coordinated when every signal runs the same cycle length, or an exact multiple of it, because otherwise the offsets drift apart cycle by cycle.

Vehicle trajectories

A vehicle moving along the corridor at a steady speed traces a straight sloped line: it covers distance up the page at a rate set by its speed. At 60 km/h it covers 16.7 m every second, so a 400 m link takes 24 s and the line rises 400 m while moving 24 s to the right. A faster vehicle draws a shallower line, a slower one a steeper line, and a stopped vehicle draws a horizontal line. Northbound lines rise to the right; southbound lines fall to the right.

Where a trajectory crosses a phase bar the colour under it tells you what the driver sees: green for a movement that includes their direction, or red. Reading the diagram is nothing more than following a line from the first signal to the last and checking what it crosses.

Green wave and bandwidth

Draw the trajectory that leaves the first intersection at the very start of its northbound green, and the one that leaves at the very end. If both lines, and every line between them, cross green at every downstream signal, the set of departure times between them is the green wave, also called the progression band or through band. Its width in seconds is the bandwidth; divided by the cycle length it gives the efficiency.

In the example above the northbound green at Oak Street is 58 s (phases A and B together, less 4 s of amber), and because every offset equals the cumulative travel time at 60 km/h, the full 59 s reaches Maple Court unbroken: an efficiency of 49 percent. SigTDD reports the bandwidth for each direction in the corridor header and shades the band on the canvas as the Sequence display option.

A second band, Next Green, shows only the departures that arrive on green at the very next intersection rather than all of them; it is the tool for adjusting one pair of signals at a time. Dashed Phase Extent lines project the start and end of each green at the design speed, so you can see exactly which phase at the next signal a platoon will meet.

What engineers use the diagram for

  • Setting offsets. Slide an intersection's phase bar left or right until the band passes through. On paper this took a ruler and a fresh sheet per attempt; on screen the band redraws as the slider moves. The arithmetic is on the green wave offset page.
  • Choosing a direction to favour. Two-way progression is only perfect when the spacing suits the cycle length; the diagram makes the trade-off visible, so the AM plan can favour inbound traffic and the PM plan outbound.
  • Checking a design speed. Tilting the trajectory shows whether a platoon at the posted speed, or at the speed drivers actually use, still fits the band.
  • Explaining a plan. A council committee or a client can see why a cycle length was chosen from one picture where a table of offsets says nothing.

Building one in SigTDD

The intersection table needs, per intersection: the distance to the next signal, the northbound and southbound design speeds, the offset and the phase durations with their directions. Type them, or import a CSV, a SigTDD JSON export or a Synchro UTDF file, and the diagram is drawn. The worked example goes through every number for the corridor drawn above.