Values for h_LT,adj, h_RT,adj, and h_HV,adj are obtained from Exhibit 21-12. The values for geometry group 1 are as follows:

• h_LT,adj = 0.2
• h_RT,adj = −0.6
• h_HV,adj = 1.7

Step 5: Determine Initial Departure Headway

The process of determining departure headways (and thus service times) for each of the lanes on each of the approaches is iterative. For the first iteration, an initial departure headway of 3.2 s should be assumed. For subsequent iterations, the calculated values of departure headway from the previous iteration should be used if the calculation has not converged (see Step 11).

Step 6: Calculate Initial Degree of Utilization

• Equation 21-14: Degree of utilization.

  $x=\frac{v{h}_d}{3600}$

  (HCM7 Eq. 21-14)

Step 7: Compute Probability States

• Equation 21-15: Probability state; uses results from Exhibit 21-13 and Exhibit 21-14.

  $P\left(I\right)={\displaystyle \underset{j}{\prod }P\left(a_j\right)}$

  (HCM7 Eq. 21-15)

• Exhibit 21-13: Probability of a_j (two-lane approaches).

  aj	Vj	P(aj)
  1	0	0
  0	0	1
  1	> 0
  0	> 0	1 –

• Exhibit 21-14: Probability of DOC case: multilane AWSC intersections (two-lane approaches, by lane).

  The full exhibit contains 64 combinations of vehicle presence on three approach legs, with two lanes per approach, that can conflict with traffic on a subject approach. Since this method considers only single-lane approaches, just 8 degree-of-conflict (DOC) cases are applicable. These cases are shown as follows.

  i	DOC Case	Number of Vehicles	Opposing Approach	Conflicting Left Approach	Conflicting Right Approach
  1	1	0	0	0	0
  2	2	1	1	0	0
  5	3	1	0	1	0
  7	3	1	0	0	1
  13	4	2	0	1	1
  16	4	2	1	1	0
  21	4	2	1	0	1
  45	5	3	1	1	1

Step 8: Compute Probability Adjustment Factors

• Equation 21-16: Probability of DOC C1; uses results from Equation 21-15 and Exhibit 21-14.

  P(C₁) = P(1) (HCM7 Eq. 21-16)

• Equation 21-17: Probability of DOC C2; uses results from Equation 21-15 and Exhibit 21-14.

  $P\left(C_2\right)={\displaystyle \underset{i=2}{\overset{4}{\sum }}P\left(i\right)}$

  (HCM7 Eq. 21-17)

• Equation 21-18: Probability of DOC C3; uses results from Equation 21-15 and Exhibit 21-14.

  $P\left(C_3\right)={\displaystyle \underset{i=5}{\overset{10}{\sum }}P\left(i\right)}$

  (HCM7 Eq. 21-18)

• Equation 21-19: Probability of DOC C4; uses results from Equation 21-15 and Exhibit 21-14.

  $P\left(C_4\right)={\displaystyle \underset{i=11}{\overset{37}{\sum }}P\left(i\right)}$

  (HCM7 Eq. 21-19)

• Equation 21-20: Probability of DOC C5; uses results from Equation 21-15 and Exhibit 21-14.

  $P\left(C_5\right)={\displaystyle \underset{i=38}{\overset{64}{\sum }}P\left(i\right)}$

  (HCM7 Eq. 21-20)

• Equation 21-21: Probability adjustment factor 1; uses results from Equations 21-16, 21-17, 21-18, 21-19, and 21-20.

  $AdjP\left(1\right)=\alpha \left[P\left(C_2\right)+2P\left(C_3\right)+3P\left(C_4\right)+4P\left(C_5\right)\right]/1$

  (HCM7 Eq. 21-21)

• Equation 21-22: Probability adjustment factor 2-4; uses results from Equations 21-16, 21-17, 21-18, 21-19, and 21-20.

  $AdjP\left(2\right)\text{through}AdjP\left(4\right)=\alpha \left[P\left(C_3\right)+2P\left(C_4\right)+3P\left(C_5\right)-P\left(C_2\right)\right]/3$

  (HCM7 Eq. 21-22)

• Equation 21-23: Probability adjustment factor 5-10; uses results from Equations 21-16, 21-17, 21-18, 21-19, and 21-20.

  $AdjP\left(5\right)\text{through}AdjP\left(10\right)=\alpha \left[P\left(C_4\right)+2P\left(C_5\right)-3P\left(C_3\right)\right]/6$

  (HCM7 Eq. 21-23)

• Equation 21-24: Probability adjustment factor 11-37; uses results from Equations 21-16, 21-17, 21-18, 21-19, and 21-20.

  $AdjP\left(11\right)\text{through}AdjP\left(37\right)=\alpha \left[P\left(C_5\right)-6P\left(C_4\right)\right]/27$

  (HCM7 Eq. 21-24)

• Equation 21-25: Probability adjustment factor 38-64; uses results from Equations 21-16, 21-17, 21-18, 21-19, and 21-20.

  $AdjP\left(38\right)\text{through}AdjP\left(64\right)=-\alpha \left[10P\left(C_5\right)\right]/27$

  (HCM7 Eq. 21-25)

• Equation 21-26: Adjusted probability; uses results from Equations 21-16, 21-17, 21-18, 21-19, 21-20, 21-21, 21-22, 21-23, 21-24, and 21-25.

  $P\text{'}\left(i\right)=P\left(i\right)+AdjP\left(i\right)$

  (HCM7 Eq. 21-26)

Step 9: Compute Saturation Headways

• Equation 21-27: Saturation headway; uses results from Exhibit 21-15 and Equation 21-13.

  h_si = h_base + h_adj (HCM7 Eq. 21-27)

• Exhibit 21-15: Saturation headway values by case and geometry group.

  Values for h_base are obtained from Exhibit 21-15. The values for geometry group 1 are as follows:

  Case	Base Headway (s)
  1	3.9
  2	4.7
  3	5.8
  4	7.0
  5	9.6

Step 10: Compute Departure Headways

• Equation 21-28: Departure headway; uses results from Equations 21-26 and 21-27.

  $h_d={\displaystyle \underset{i=1}{\overset{64}{\sum }}P\text{'}\left(i\right)h_{si}}$

  (HCM7 Eq. 21-28)

Step 11: Check for Convergence

The calculated values of h_d are checked against the initial values assumed for h_d. If the values change by more than 0.1 s (or a more precise measure of convergence), Steps 5 through 10 are repeated until the values of departure headway for each lane do not change significantly.

Step 12: Compute Capacity

This is an iterative procedure. Check the HCM7 for more information.

Step 13: Compute Service Times

• Equation 21-29: Service time; uses results from Equation 21-28.

  t_s = h_d − m (HCM7 Eq. 21-29)

Step 14: Compute Control Delay and Determine LOS for Each Lane

• Equation 21-30: Calculation of the control delay; uses results from Equations 21-14, 21-28, and 21-29.

  $d=t_s+900T\left[\left(x-1\right)+\sqrt{{\left(x-1\right)}^2+\frac{h_{d}x}{450T}}\right]+5$

  (HCM7 Eq. 21-30)

Step 15: Compute Control Delay and Determine LOS for Each Approach and the Intersection

• Equation 21-31: Control delay for an approach; uses results from Equations 21-30 and 21-12.

  $d_a=\frac{{\displaystyle \sum d_i{v}_i}}{{\displaystyle \sum v_i}}$

  (HCM7 Eq. 21-31)

• Equation 21-32: Control delay for the intersection; uses results from Equations 21-30 and 21-12.

  $d_{intersection}=\frac{{\displaystyle \sum d_a{v}_a}}{{\displaystyle \sum v_a}}$

  (HCM7 Eq. 21-32)

• Exhibit 21-8: LOS criteria (motorized vehicle mode); the LOS is determined for the major roadway through movement for the analysis direction.

  Control Delay (s/veh)	LOS
  –10	A
  >10–15	B
  >15–25	C
  >25–35	D
  >35–50	E
  >50	F

  If the v/c > 1.0, the LOS is F.

Step 16: Compute Queue Lengths

10.2 Nomenclature