State Highway Administration

QUEUING ANALYSIS

• Queue lengths can be determined by the following procedure: 1.25 x Volume = Q Length
• When large intersections are involved or it is known that a cycle length greater then 120 seconds is needed, the procedures described below will be used.

SIGNALIZED INTERSECTIONS
This procedure can be used at intersections with existing signals and intersections where it is felt a signal may be installed.

1. Perform critical lane analysis
2. Select Cycle length
   • use existing timing if available
   • if timing is not available, use the suggested cycle lengths

   Recommended Maximum Cycle Lengths
   

   LOS	2 Phase	3-5Phase	6-8 Phase
   A B C D E F	90 90 100 120 135 150	100 100 120 135 150 165	120 120 135 150 165 180

   NOTE: These cycle lengths are to be used as a guide, knowledge of the intersection may result in using a Higher or lower cycle.

3. Use Poisson Distribution Chart/Formula to determine maximum number of vehicles per cycle of a specific movement.

   FORMULA:

   Avg Veh/Cycle =

   Critical Lane Volume (veh/hr) x Cycle Length(sec.) 3600 (sec/hr)

4. Assume a vehicle length of 25 ft.
5. Once the average vehicles per cycle (specific movement) is determined, the chart can be used to find the maximum vehicles per cycle for that movement.
6. The queue length will be the maximum vehicles per cycle times 25 ft. per vehicle.
7. It is noted that the chart ends at an average of 20 vehicles per cycle. In cases where the average number of vehicles per cycle exceeds 20 the following formula can be used to determine the queue length. This formula can also be used in lieu of the chart.
   Q. = Avg No. of Veh x 1.4 (Surge Factor) x 25 ft.

   POISSON DISTRIBUTION
   

   Average No. of Vehicle Per Cycle ---------------------- 0.1 - 0.3 0.4 - 0.8 0.9 - 1.3 1.4 - 1.9 2.0 - 2.6 2.7 - 3.2 3.3 - 3.9 4.0 - 4.7 4.8 - 5.4 5.5 - 6.1 6.2 - 6.9 7.0 - 7.7 7.8 - 8.4 8.5 - 9.2 9.3 - 10.0 10.1 - 10.8 10.9 - 11.6 11.7 - 12.4 12.5 - 13.2 13.3 - 14.0 14.1 - 14.9 15.0 - 15.7 15.8 - 16.5 16.6 - 17.3 17.4 - 18.2 18.3 - 19.0 19.1 - 19.8 19.9 - 20.0

   Maximum No. of Vehicle Per Cycle ---------------------- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

1. Determine the critical gap needed for the movement (from chart) this chart is also found in the 1985 HCM unsignalized intersections. BASIC CRITICAL GAP FOR PASSENGER CARS, SEC
   

   Vehicle Maneuver and Type of Control	Average Running Speed, Major Road
   	30 MPH		55 MPH
   	Number of Lanes on Major Road
   	2	4	2	4
   RT from Minor Road STOP YIELD	5.5 5.0	5.5 5.0	6.5 5.5	6.5 5.5
   LT from Major Road	5.0	5.5	5.5	6.0
   Cross Major Road STOP YIELD	6.0 5.5	6.5 6.0	7.5 6.5	8.0 7.0
   LT from Minor Road STOP YIELD	6.5 6.0	7.0 6.5	8.0 7.0	8.5 7.5

   Note: If restricted sight distance exists add one second to the gap needed. Where average running speeds are between 30 mph and 55 mph, interpolate.
2. Determine average gap between opposing vehicles
   
   Average Gap Opposing Vehicle 3600 sec / (Volume Per/Hour)
3. If the average gap is greater than the gap needed for the maneuver the same procedure as signalized intersections can be used with the cycle length equal to the critical gap required (from chart) plus 4 seconds (start up time).
4. If the average gap is less than or equal to the gap needed, this maneuver should be analyzed as if a signal were in place.