Question 1 of 7: Definitions and discussion (5 × 4 marks)

Question 1: Definitions and discussion (5 × 4 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Approach. Each part is a short essay: define the term precisely, give the governing relation where one exists, then say what the distinction is for in design or operations.

Part (a) — effective green and effective red. The displayed green is what the driver sees; the effective green is the portion of the cycle during which vehicles actually discharge at the saturation flow rate. Two losses separate them. At the start of green the first few drivers react and accelerate, so departures build up to saturation flow over roughly the first two seconds — the start-up lost time $\ell_1$. At the end of the display some of the amber (and any all-red) is used productively by vehicles still crossing the stop line, and the remainder is wasted — the clearance lost time $\ell_2$. Writing the displayed green as $G$, the amber as $Y$ and the all-red as $R_{ar}$,

so the effective red is everything left in the cycle. The distinction is not academic: capacity is $c = s\,g/C$, using the effective green, and the total lost time $L = \sum \ell_i$ summed over the phases is exactly the quantity that appears in Webster’s optimum cycle $C_o = (1.5L + 5)/(1 - Y)$. Every extra phase buys another dose of lost time, which is why phasing plans are kept as simple as the conflicts allow. In this paper Questions 3 and 7 give a lost time of 3.5 s per phase and an all-red of 1.5 s per phase, so $L = 10$ s over two phases.

Part (b) — cordon counts versus screenline counts. Both are network-level volume studies, and both count vehicles (or persons) crossing a line, but the line is drawn for different purposes. A cordon count encloses an area — a downtown core, a campus, a hospital precinct — with a closed boundary, and every entry and exit point on that boundary is counted simultaneously, usually by direction and by time period. Because the boundary is closed, the running difference between entries and exits gives the accumulation inside the cordon at any moment, which is what parking-supply studies, curb-management studies and downtown trip-generation estimates need. A screenline count uses an open line that cuts across the study area, conventionally along a natural or artificial barrier such as a river, a rail corridor or a ridge, so that the number of crossing points is small and every crossing can be counted. Its purpose is different: the observed crossing volume is compared with the volume that a travel-demand model assigns across the same line, and the ratio is used to validate or calibrate the assignment. In short, a cordon answers “how much traffic is inside this area and when?”, a screenline answers “does my model reproduce the real directional flow across this barrier?” Canadian practice couples both with household travel surveys such as the Transportation Tomorrow Survey, and TAC guidance treats screenline agreement within roughly ±10 per cent as the benchmark for a validated assignment.

Part (c) — semi-actuated versus fully-actuated control. Both are demand-responsive: detectors on one or more approaches decide when a phase ends. In semi-actuated control only the minor approaches are detected. The major street is the non-actuated phase and rests in green indefinitely; a call from a minor-street detector (or a pedestrian push-button) terminates the major green after its minimum has been served, the minor phase is served for as long as its extensions require up to a maximum, and the controller returns to the major street. This suits an arterial crossed by a lightly used local street, and because the major street can be forced to yield green only at fixed points in a background cycle, semi-actuated controllers can be coordinated in a signal system. In fully-actuated control every approach is detected and every phase is variable, so both the phase sequence and the cycle length float with demand and there is no fixed cycle at all. The governing parameters are the minimum green (long enough to clear the vehicles stored between the detector and the stop line), the passage time or unit extension (the gap that keeps the phase alive), and the maximum green (the ceiling that protects the other approaches). Fully-actuated control gives the lowest delay at an isolated intersection with fluctuating or unbalanced demand, but its variable cycle makes coordination impossible, so it is not used inside a progression system.

Part (d) — protected phase versus permissive phase. The distinction is about right of way, and it applies chiefly to left turns. In a protected phase the movement has exclusive right of way: it is displayed a green arrow, and all conflicting vehicular movements and all conflicting pedestrian movements are held on red. The turn therefore discharges at its own saturation flow and its capacity is simply $c = s\,g/C$, independent of the opposing volume. In a permissive (permitted) phase the movement is displayed a circular green and the driver must yield — to the opposing through traffic and to pedestrians lawfully in the crosswalk — turning only in acceptable gaps. Its capacity is therefore a gap-acceptance quantity that falls as the opposing flow rises, and vanishes when the opposing flow saturates. Protection costs a phase, and therefore lost time and cycle length; permission costs safety, because the permitted left turn is the classic sight-restricted, judgement-dependent conflict. Canadian practice under the MUTCDC also uses the intermediate protected-permissive display, in which a leading or lagging green arrow is followed by a circular green or a flashing yellow arrow, giving protection during the heaviest part of the demand and permission for the remainder. Questions 3 and 7 of this paper adopt permitted left turns precisely because the four-phase protected alternative is shown to be infeasible.

Part (e) — the eight MUTCD signal warrants. The Manual on Uniform Traffic Control Devices (Part 4, Section 4C) lists eight warrants; a signal should not be installed unless at least one is met, and meeting a warrant is a necessary but not a sufficient condition — engineering judgement still governs. The eight are: (1) Eight-Hour Vehicular Volume; (2) Four-Hour Vehicular Volume; (3) Peak Hour; (4) Pedestrian Volume; (5) School Crossing; (6) Coordinated Signal System; (7) Crash Experience; and (8) Roadway Network. Four discussed in detail:

• Warrant 1, Eight-Hour Vehicular Volume. The base volume warrant, satisfied on either of two conditions for any eight hours of an average day. Condition A (minimum vehicular volume) requires both the major-street total and the higher-volume minor-street approach to exceed tabulated thresholds — roughly 500 and 150 veh/h respectively for one lane each way — and captures the case where the minor street simply cannot find gaps. Condition B (interruption of continuous traffic) uses a higher major-street threshold with a lower minor-street one, and captures the opposite case, where the major stream is so dense that even a modest minor demand is trapped. Thresholds are reduced to 70 per cent where the 85th-percentile major-street speed exceeds 70 km/h or the community has fewer than 10,000 people.
• Warrant 2, Four-Hour Vehicular Volume. Plots the major-street total against the higher minor-street approach for each of any four hours of an average day; the warrant is met if all four points fall above the applicable curve. It is the right test for an intersection with a pronounced but short peak that would fail the eight-hour test — a suburban school, an industrial shift change, a ferry terminal.
• Warrant 4, Pedestrian Volume. Applies where pedestrians, not vehicles, are the constrained movement. It is met when the pedestrian crossing volume and the vehicular volume are jointly high enough that adequate gaps do not occur, and it explicitly requires that fewer than the stated number of adequate gaps be available during the analysis period. It matters directly to Questions 3 and 7 of this paper, whose 850–1,200 ped/h crossing volumes are heavy enough to make the pedestrian clearance interval a binding constraint on cycle length.
• Warrant 7, Crash Experience. Met when adequate trial of less restrictive remedies has failed, five or more reported crashes susceptible to correction by signal control have occurred within a twelve-month period, and the volumes reach 80 per cent of the Warrant 1 thresholds. It is the only warrant driven by safety history rather than volume, and the “susceptible to correction” qualifier is essential: signals reliably reduce angle collisions but reliably increase rear-end collisions, so a rear-end-dominated crash history is an argument against signalisation, not for it.