Learning ObjectivesTo define lost, effective green time, and saturation flowTo design signal timing for pretimed isolated signals (Websters method)To understand the operation of actuated signalsTo perform warrant analysis for signal control(Chapter 8, p.306-313; 322-330)

Basic Timing ElementsElements within a phase:Green interval: the period of the phase during which the green signal is illuminated. Yellow/amber interval: the portion of the phase during which the yellow light is illuminated. All-red interval: the period during which the red light is illuminated for all approaches Intergreen interval: the interval between the end of green for one phase and the beginning of green for another phaseStreet AStreet BAll-redIntergreen

Intergreen PeriodTo Eliminate dilemma zone:

Dilemma Zone

Practice ProblemGiven the following information pertaining an intersection and its signal timing:Intergreen time of 6 secIntersection width of 60ftLevel grade with coefficient of friction of 0.5Does a dilemma zone exist for a 18ft-long vehicle approaching at 50mph? Assume a perception-reaction time of 1sec

Solution

Types of Signal ControllersPretimedFixed interval lengths in fixed sequenceSemi-actuated (traffic-adjusted)Predefined timing schemes selected based on traffic flow informationActuatedVaried length and/or sequence of signal indications React to arrivals of vehicles/pedestriansIsolated or coordinated

Condition at Start-up

Queue PositionObserved Avg.HeadwaySaturation HeadwayDifference(Obs.-Est.)13.142.14 1.0022.742.140.5032.522.140.3842.372.140.23 52.142.140.00Start-up Lost Time2.11

Saturation FlowGTime (sec)Flow Rate (vphpl)YSaturation Flow SNumber of vehicles that would pass through the intersection during an entire hour of green

Effective Green TimeEffective Green GGTime (sec)Flow Rate (vphgpl)YSaturation FlowTime during which the flow is assumed to take place at saturation flow

Lost TimeEffective Green GGTime (sec)Flow Rate (vphgpl)YSaturation FlowTime during which no flow takes placeLost Time l2Lost Time l1

Lost TimeEffective Green GGTime (sec)Flow Rate (vphgpl)YLost Time l2Lost Time l1Saturation Flow

Critical Approach or LaneThe approach or lane for a given phase that requires the most green time (highest flow ratio)Flow should be in straight-through passenger-car units per hour (e.g. 1 HV = 1.75 PCU)

Cycle Length Determination for Pretimed SignalsLong enough to serve all critical movements, but no longerIf too short: high lost/green time ratioIf too long: lengthened queues

Websters MethodMost prevalentMinimizes intersection delayCo = Optimum cycle length (sec)L = Total lost time per cycle, usually taken as the sum of the total yellow and all-red intervals (sec) (i.e. total intergreen intervals)Yi = Ratio of the observed flow rate (in straight-through passenger cars per hour) to the saturation flow rate for the critical approach or lane in each phase

Allocate Green Time to PhasesSplit according to critical flow ratios across phases Co-L= Available green timeYi = As before

Traffic-Actuated SignalsBegin with GminIf no calls from detectorSwitch to the next phaseOtherwise extend green time by h, i.e. the unit extension of green or critical gaph small for high arrival rates, and vice versaIf vehicles keep arriving at headways shorter than or equal to h, then terminate only when Gmax is reachedEquivalent to pretimed, fixed cycle if saturated

Benefits of Traffic SignalsReduce right-angle collisionsOrderly trafficContinuous flowAllow other vehicles and pedestrians to cross a heavy traffic streamControl traffic more economically than by manual methods

Drawbacks of Traffic SignalsUnjustified, ill-designed, improperly operated signalsIncreased rear-end collisionsExcessive delayDisregard of signal indicationsCircuitous travel by alternative routes

Signal Warrants Eight warrants to considerEight-hour vehicular volumeFour-hour vehicular volumePeak hourPedestrian volumeSchool crossingCoordinated signal systemCrash experienceRoadway networkhttp://mutcd.fhwa.dot.gov/HTM/2003r1/part4/part4c.htm

Capacity AnalysisFlow (v/s) ratio

Capacity

Volume to capacity (v/c) ratio

Capacity AnalysisCritical v/c ratiov/c ratio for the intersection as a whole

Average Control DelayThe basis for LOS determinationFor a given lane group:

Aggregated Delay EstimatesDelay for an ApproachDelay for an Intersection

Determine LOSmeasure of the acceptability of delay levels to motoristsUse the total control delay for the given intersection:

Interpretation of ResultsA critical v/c ratio of greater than 1.0 indicates that the signal and geometric design cannot accommodate the combination of critical flows at the intersection. The condition may be ameliorated by increased cycle length, changes in the phasing plan, and basic changes in geometrics.When the critical v/c ratio is acceptable but the v/c ratios for critical lane groups vary widely, the green-time allocation should be reexamined, because disproportionate distribution of available green is indicated.

Interpretation of ResultsLOS measure is somewhat subjective: what might be acceptable in a large city is not necessarily acceptable in a smaller city or rural areaWhen delay levels are acceptable for the intersection as a whole but are unacceptable for certain lane groups, the phase plan, allocation of green time, or both might be examined to provide for more efficient handling of the disadvantaged movement(s)When delay levels are unacceptable but v/c ratios are relatively low, the cycle length may be too long for prevailing conditions, the phase plan may be inefficient, or both. When both delay levels and v/c ratios are unacceptable, the situation is critical. The full range of potential geometric and signal design improvements should be considered.

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