Traffic Engineering – Intersection Capacity

Intersection Capacity is more than the volume of vehicles the intersection can accommodate in a given time interval. First, as transportation engineers we must give consideration to pedestrians, mass transit, and other forms of travel. Second, we must design for the time required for an intersection to fill up and then empty given the various speeds of pedestrians, private vehicles, buses, light rail, etc. And third, we must be able to coordinate each intersection with the overall traffic configuration of other intersections, traffic flow patterns, access points, speed limits, etc.

The study of intersection capacity utilization is filled with opportunities for creativity and problem-solving.

Intersection Capacity

Using information from Traffic Engineering – Street Segment Interrupted Flow and based on the traffic counts for the intersection shown (assume up is north):

Intersection Capacity

1. Calculate the East-West Critical Lane Volumes:

  • East bound traffic turning left + (West bound traffic + West bound traffic turning right) = 105 + (250 + 130) = 105 + 380 = 485 vph
  • West bound traffic turning left + (East bound traffic + East bound traffic turning right) = 70 + (215 + 60) = 70 + 275 = 345 vph

2. Calculate the North-South Critical Lane Volumes:

  • North bound traffic turning left + (South bound traffic + South bound traffic turning right) = 75 + (245 + 65) = 75 + 310 = 385 vph
  • South bound traffic turning left + (North bound traffic + North bound traffic turning right) = 110 + (225 + 125) = 110 + 350 = 460 vph

3. Calculate the Critical Volume for Phase (Vci):

  • Vci = 485 vph (from calculations in steps 1 and 2)

4. Calculate the Total Critical Volume (Vc):

  • Vc = sum of Critical Lane Volumes = 380 + 275 + 310 + 350 = 1315 vph

5. Calculate the Saturation Flow Rate (given: headway (h) = 2.3 sec/veh):

  • Saturation Flow Rate (s) = 3600/h = 3600/2.3 = 1565 veh/hr

6. Calculate the Cycle Length (C) if the number of phases (N) = 4, the total lost time per phase (tL) = 4 sec, the Peak Hour Factor (PHF) = 1.0, and the desired volume/capacity (v/c) ratio = 0.97:

  • C = (N x tL) ÷ [1 – (Vc ÷ (PHF x (v/c) x s))]
  • C = (4 x 4) ÷ [1 – (1315 ÷ (1.0 x 0.97 x 1565))] = 120 sec

7. Calculate the Effective Green Time (gi):

  • gi = (Vci ÷ Vc) x (C – L), where Vci = Critical Volume for Phase, Vc = Total Critical Volume, and L = Total Lost Time = N x tL
  • gi = (485 ÷ 1315) x (120 – (4 x 4)) = 38.4 sec

8. Calculate the capacity of one approach lane:

  • c = 3600gi ÷ hC = (3600 x 38.4) ÷ (2.3 x 120) = 500vph
Related Content:

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Fire Protection PE Exam Prep Course

Intersection Capacity

NCEES

Traffic Engineering – Street Segment Interrupted Flow

Street Segment Interrupted Flow is traffic flow regulated by an external means such as a traffic signal.

Vehicle-vehicle interactions and vehicle-roadway interactions play a secondary role in defining the traffic flow under interrupted flow conditions.

Street Segment Interrupted Flow

Concepts and Equations

From Signal Timing Tutorial:

  • Critical Lane Volume

Maximum volume per lane during a signal phase.

  • Critical Volume (Vc)

Sum of all critical lane volumes during a signal cycle.

  • Through Car Equivalent Units (TCUS)

A hypothetical vehicle generated from vehicle types, vehicle turning movements, etc. for use in calculating traffic signal cycles.

TCUS are generated by multiplying traffic volumes by tabulated factors to account for the added congestion created by vehicles turning left or right from the flow of traffic.

  • Saturation Flow Rate (s)

Number of vehicles served by a lane for one hour of green time (vehicles/hr).

The maximum number of vehicles that can be serviced in an hour of green is: s = 3600 ÷ h.

  • Saturation Headway

Headway of the vehicles in a “stable moving platoon” passing through a green light.

  • Lost Time

Elapsed time when no cars are present in an intersection. Equal to Start-Up Lost Time and Clearance Lost Time.

  • Start-Up Lost Time

Sum of time difference between the saturation headway and the first four headways.

  • Clearance Lost Time

Elapsed time required during right-of-way changes.

  • Current Flow Rate (v)

Obtained from traffic counts.

  • Desired v/c Ratio

Ratio of current flow rate to capacity of the facility. Equal to Rate of Flow divided by Capacity.

  • Peak Hour Factor (PHF)

Calculated by: Hourly Volume divided by Maximum Rate of Flow.

Also, PHF = V ÷ (V15 x 4)

    • where:
      • V = Peak Hourly Volume (vehicles/hr)
      • V15 = maximum 15-minute volume within the peak hour
  • Cycle Length (C)

Amount of time from when a movement is given the right-of-way until that movement receives it again.

C = (N x tL) ÷ (1 – (Vc ÷ (PHF x (v/c)des x 3600/h)))

    • where:
      • N = the number of phases in one cycle
      • tL = total lost time per phase (sec)
      • Vc = Critical Volume (vehicles/hr)
      • PHF = Peak Hour Factor
      • (v/c)des = desired volume/capacity ratio
      • h = saturation headway (sec)
  • Green Time Calculations
    • Green Split – how long each phase will have the right-of-way.

    • Effective Green Time (gi) – time that a movement is going, regardless of the indication shown.

gi = (Vci ÷ Vc) x (C – L)

      • where:
        • gi = Effective Green Time (sec)
        • Vci = Critical volume for phase (vehicles/in-hr)
        • Vc = Total Critical Volume (vehicles/in-hr)
        • C = Cycle length (sec)
        • L = Total Lost Time (tL x N) (sec)
  • Actual Green Time (Gi)

Gi = gi + tL – Yi

    • where:
      • tL = Lost time per phase (sec)
      • Yi = Yellow and all-red time (sec)
  • Intersection Capacity (ci)

ci = (3600/h) x (gi/C) = s(gi/C)

    • where:
      • ci = Capacity of one approach lane (passenger cars per lane per hour)
      • h = Saturation Headway
      • gi = Effective Green Time for the approach (sec)
      • C = Cycle length (sec)
      • s = Saturation Flow Rate = 3600/h

Related Content:

If there is anything we can do to help you prepare for the Civil Engineering Transportation PE Exam, please do not hesitate to Contact Us.

For additional PE Exam resources, go to EngineeringDesignResources.com.

To Your Success …

Jeff Setzer, PE
Fire Protection PE Exam Prep Course

Street Segment Interrupted Flow

NCEES