HCM UNSIGNALIZED SAMPLE PROBLEM

(1)

PART D. EXAMPLE PROBLEMS

Problem No.

Description

Application

1 TWSC Unsignalized Intersection

Operational LOS

2 TWSC Unsignalized Intersection

Operational LOS

3 TWSC Unsignalized Intersection

Operational LOS

4 AWSC Unsignalized Intersection

Operational LOS

5 AWSC Unsignalized Intersection

Operational LOS

(2)

E

XAMPLE

P

ROBLEM

1 The Intersection

A TWSC T-intersection with an exclusive westbound left-turn lane.

The Question

What are the delay and level of service?

The Facts

√

Two-lane major street,

√

10 percent HV,

√

Two-lane minor street,

√

No special intersection geometry, and

√

Level grade,

√

No pedestrians.

√

Stop-controlled on minor street

approach,

Outline to Solution

The steps below show the northbound approach calculations only.

Calculations for other approaches are shown on the worksheets.

Steps

1. Data input.

Worksheets 1 and 2

2. Site characteristics.

Worksheet 3 - lane designation, grade,

right-turn channelization, and arrival type

3. t

_c

and t

_f

(use Equations 17-1 and

17-2 and Exhibit 17-5 ).

t

_c,x

= t

_c,base

+ t

_c,HV

P

_HV

+ t

_c,G

G – t

_{c, T}

– t

_3,LT

t

_f,x

= t

_f,base

+ t

_f,HV

P

_HV

t

_c,4

= 4.1 + 1.0(0.10) + 0 – 0 – 0 = 4.200 s

t

_f,x

= 2.2 + 0.9(0.10) = 2.290 s

4. Skip Worksheets 5a through 5e.

No upstream signals within 0.4 km

5. Movement capacity c

_m,x

accounting

for impedance (use Equation 17-4 ).

v

c,9

=

v

₂

N

+ 0.5v

3

+ v

14

+ v

15

v

_c,9

= 250 + 20 + 0 + 0 = 270 veh/h

c

_p,x

=

v

_c,x

e

−vc,xtc,x/ 3,600

1 −

e

−vc,xtf,x/ 3,600

c

_p,9

=

270 *

e

−270*6.300/ 3,600

1 −

e

−270*3.390/ 3,600

= 750 veh/h

c

_m,9

= c

_p,9

* P

_p,9

= 750 (1) = 750 veh/h

P

_0,i

=

1 −

v

i

c

_m,i

P

_0,9

=

1 −

120

750 =

0. 840

6. Skip Worksheets 7a and 7b.

No two-stage gap acceptance

7. Shared-lane capacity (use Equation

17-15).

Worksheet 8 - Movements 7 and 9 share the

same lane

(3)

9. Control delay and LOS (use

Equation 17-38 and Exhibit 17-2).

Worksheet 10

d

=

3, 600

c

_m,x

+

900T[... ]

+

5 d

_NB

=

3, 600

523 +

900 0. 25

(

)

[... ]

+

5 =

14. 9 s

,

LOS B

10. Skip Worksheet 11.

No Rank 1 vehicle delay

Example Problem 1

STOP STOP v1 v2 v3 v12 v7 v10 v9 v13 v14 v15 v16 v6 v4 S2 S5 v11 v8 v5

TWSC - UNSIGNALIZED INTERSECTIONS WORKSHEET

Worksheet 1

Worksheet 2

Vehicle Volumes and Adjustments

Pedestrian Volumes and Adjustments

Vehicle Volumes and Adjustments

Movement 1 2 3 4 5 6 7 8 9 10 11 12

Volume (veh/h) Peak-hour factor, PHF Hourly flow rate (veh/h) Proportion of heavy vehicles, P_HV

Movement 13 14 15 16

Flow, Vx (ped/h)

Lane width, w (m) Walking speed,1_S

p (m/s)

Percent blockage, fp (Equation 17-11) 1. Default walking speed = 1.2 m/s

General Information Site Information

Analyst ______________________ Intersection ________________________ Agency or Company ______________________ Jurisdiction ________________________ Date Performed ______________________ Analysis Year ________________________ Analysis Time Period ______________________

Geometrics and Movements

Length of study period = _____ h

grade = ______ grade = ______ grade = ______ grade = ______ Show North Street Street KMN Jones/Market

CEI Latah County

5/17/99 1999 AM Peak J ones Market 250 40 300 150 40 120 250 40 150 300 40 120 1.00 1.00 1.00 1.00 1.00 1.00 250 40 150 300 40 120 0.10 0.10 0.10 0.10 0.10 0.10 0% 0.25 0% 0% 0 0 0 0

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TWSC - UNSIGNALIZED INTERSECTIONS WORKSHEET Worksheet 3

Movement 9 " Yes " No Storage space, n ________________

(number of vehicles)

Type

Movements 7 and 8 " Yes _____ " No Storage space, m ________________ (number of vehicles) Movements 10 and 11 " Yes _____ " No Storage space, m ________________ (number of vehicles)

* Includes raised or striped median (RM), or two-way left-turn lane (TWLTL)

Lane Designation

Movements Lane 1 Lane 2 Lane 3 Grade, G Right Turn

Channelized? 1, 2, 3

4, 5, 6 7, 8, 9 10, 11, 12

Flared Minor-Street Approach

Median Storage*

Computing Delay to Major-Street Vehicles Upstream Signals

Data for Computing Effect of Delay to Major-Street Vehicles S2 Approach S5 Approach

Shared-lane volume, major-street through vehicles, vi1, blocked by LT

Shared-lane volume, major-street right-turn vehicles, vi2, blocked by LT

Saturation flow rate, major-street through vehicles, s_i1 Saturation flow rate, major-street right-turn vehicles, s_i2 Number of major-street through lanes

Length of study period, T (h)

Movements Distance to Prog Speed, Cycle Green Time, Arrival Saturation Flow Progressed Flow, Signal, D (m) S_prog (km/h) Length, C (s) g_eff (s) Type Rate, s (veh/h) V_prog (veh/h)

protected LT 3 TH protected LT 3 TH S2 S₅ General Information Project Description _________________________________________________________________________________

Example Problem 1

2, 3 0 N 4 5 0 N 7, 9 0 N X X X X Example Problem 1

(5)

t_f = t_f,base + t_f,HV P_HV t_c = t_c,base + t_c,HV P_HV + t_c,G G - t_c,T - t_3,LT

Major LT Minor RT Minor TH Minor LT

Movement 1 4 9 12 8 11 7 10 t_f,base (Exhibit 17-5) t_f,HV P_HV (from Worksheet 2) t_f(Equation 17-2) Worksheet 5a

Time to Clear Standing Queue (Computation 1)

Movement 2 Movement 5

v_T,prog v_L,prot v_T,prog v_L,prot

Effective green, g_eff (s) Cycle length, C (s) Saturation flow rate, s (veh/h)

Arrival type 3 3

vprog (veh/h)

Rp (from Chapter 16) 1.00 1.00

Proportion of vehicles arriving on green, P (Equation 17-17) gq1 (Equation 17-18)

gq2 (Equation 17-19)

g_q (Equation 17-20)

Movement 1 4 9 12 8 11 7 10 tc,base (Exhibit 17-5) tc,HV PHV (from Worksheet 2) tc,G - - 0.1 0.1 0.2 0.2 0.2 0.2 G (from Worksheet 3) t3,LT single stage two stage single stage two stage t_c,T t_c (Equation 17-1)

Worksheet 4

Critical Gap and Follow-Up Time General Information Project Description _________________________________________________________________________________

Example Problem 1

4.1 6.2 7.1 1.0 1.0 1.0 0.10 0.10 0.10 0 0 0 0.0 0.0 0.7 0.0 0.0 0.0 4.200 6.300 6.500 2.2 3.3 3.5 0.9 0.9 0.9 0.10 0.10 0.10 2.290 3.390 3.590 Example Problem 1

(6)

7 7 7 10 10 10 0,4 0,1

Step 1: RT from Minor Street v9 v12

Conflicting flows (Exhibit 17-4) vc,9= vc,12 =

Potential capacity (Equation 17-3 or 17-29) cp,9= cp,12 =

Ped impedance factor (Equation 17-12) p_p,9= p_p,12 =

Movement capacity (Equation 17-4) c_m,9 = c_p,9 p_p,9= c_m,12 = c_p,12 p_p,12 = Prob of queue-free state (Equation 17-5) p_0,9= p_0,12 =

Step 2: LT from Major Street v₄ v₁

Ped impedance factor (Equation 17-12) pp,4= pp,1 =

Movement capacity (Equation (17-4) c_m,4 = c_p,4 p_p,4= c_m,1 = c_p,1 p_p,1 = Prob of queue-free state (Equation 17-5) p_0,4= p_0,1 = Major left shared lane prob of queue-free state (Equation 17-16) p*₌ _p*₌

Step 3: TH from Minor Street (4-leg intersections only) v₈ v₁₁

Capacity adjustment factor due to impeding movement f₈ = p_0,4 p_0,1 p_p,8= f₁₁ = p_0,4 p_0,1 p_p,11 = (shared lane use p*_{) (Equation 17-13)}

Movement capacity (Equation 17-7) cm,8 = cp,8 f8= cm,11 = cp,11 f11 =

Prob of queue-free state p_0,8= p_0,11 =

Step 4: LT from Minor Street (4-leg intersections only) v₇ v₁₀

Conflicting flows (Exhibit 17-4) v_c,7= v_c,10 =

Potential capacity (Equation 17-3 or 17-29) c_p,7= c_p,10 =

Major left, minor through impedance factor p'' _{= p}_0,11_f₁₁₌ _p''_{= p}_0,8_f₈₌

Major left, minor through adjusted impedance factor p'₌ _p'₌

(Equation 17-8)

Capacity adjustment factor due to impeding movements f7 = p' p0,12 pp,7= f10 = p' p0,9 pp,10 =

(Equation 17-14)

Movement capacity (Equation 17-10) cm,7 = f7 cp,7= cm,10 = f10 cp,10 =

Step 5: LT from Minor Street (T-intersections only) v7 v10

Capacity adjustment factor due to impeding movement f₇ = p_0,4 p_0,1 p_p,7= f₁₀ = p_0,4 p_0,1 p_p,10 = (shared lane use p*_{) (Equation 17-13)}

Movement capacity (Equation 17-7) c_m,7 = c_p,7 f₇= c_m,10 = c_p,10 f₁₀ =

Impedance and Capacity Calculation General Information

Project Description _________________________________________________________________________________

Notes

1. For 4-leg intersections use Steps 1, 2, 3, and 4. 2. For T-intersections use Steps 1, 2, and 5.

270 750 1.000 750 0.840 1.000 290 1227 1.000 1227 0.878 1.000 870 312 1.000 0.878 274 Example Problem 1

Example Problem 1

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Example Problem 1

Worksheet 8

Movement v (veh/h) cm (veh/h) cSH (veh/h)

7 8 9 10 11 12 Worksheet 9

Movement 7 Movement 8 Movement 9 Movement 10 Movement 11 Movement 12 csep (from Worksheet 6 or 7)

Volume (from Worksheet 2) Delay (Equation 17-38) Q_sep (Equation 17-34) Q_sep + 1 Round (Q_sep + 1) nmax (Equation 17-35) cSH c_sep n c_act (Equation 17-36)

Effect of Flared Minor-Street Approaches Shared-Lane Capacity General Information Project Description _________________________________________________________________________________ (Equation 17-15) cSH = ∑vy ∑ y y v_y cm,y

( )

40 274 523 120 750 Example Problem 1

(8)

Example Problem 1

*

Worksheet 10

Delay to Rank 1 Vehicles

Worksheet 11

Control Delay, Queue Length, Level of Service

S2 Approach S5 Approach

p_0,j (Equation 17-5) vi1, volume for Stream 2 or 5

vi2, volume for Stream 3 or 6

s_i1, saturation flow rate for Stream 2 or 5 si2, saturation flow rate for Stream 3 or 6

p0,j (Equation 17-16)

d_{major left}, delay for Stream 1 or 4 N, number of major-street through lanes d_{Rank 1}, delay for Stream 2 or 5 (Equation 17-39)

Lane v (veh/h) cm (veh/h) v/c Queue Length Control Delay LOS Delay and LOS

(Equation 17-37) (Equation 17-38) (Exhibit 17-2) 1 2 3 1 2 3

Movement v (veh/h) c_m (veh/h) v/c Queue Length Control Delay LOS (Equation 17-37) (Equation 17-38) (Exhibit 17-2) 1 4 General Information Project Description _________________________________________________________________________________ 12 11 10 12 11 10 12 11 10 9 8 7 9 8 7 9 8 7 p_0,1₌ _{p0,4 =} p* =0, 1 p* =0, 4 Example Problem 1 160 523 0.306 < 2 14.9 B 14.9 B

X X X

150 1227 0.12 < 1 8.3 A

(9)

E

XAMPLE

P

ROBLEM

2 The Intersection

A TWSC intersection with upstream signals. The major street is

Walnut St. (EB/WB) and the minor street is Elm St. (NB/SB).

The Question

What are the delay and level of service of the minor-street approaches?

The Facts

√

Four-lane major street,

√

10 percent HV,

√

Two-lane minor street,

√

Upstream signals in both major-street directions, and

√

Level grade,

√

No pedestrians.

Outline to Solution

The steps below show the northbound approach calculations only.

Calculations for other approaches are shown on the worksheets.

Steps

1. Data input.

Worksheets 1 and 2

2. Site characteristics.

Worksheet 3 - lane designation, grades, right-turn

channelization, and upstream signals

3. t

_c

and t

_f

(s) (use

Equations 1 and

17-2 and Exhibit 17-5).

t

_c,x

= t

_c,base

+ t

_c,HV

P

_HV

+ t

_c,G

G – t

_{c, T}

– t

_3,LT

t

_c,1

= 4.1 + 2.0(0.10) + 0 – 0 – 0 = 4.300 s

t

_f,x

= t

_f,base

+ t

_f,HV

P

_HV

t

_f,x

= 2.2 + 1.0(0.10) = 2.300 s

4. Effect of upstream

signals

Worksheets 5a through 5e

Proportion of vehicles

arriving during green, P

(use Equation 17-17).

P = R

_p

g

eff

C

P = 0.33

30

80 = 0.124

Discharge time (use

Equations 18,

17-19, and 17-20 ).

For Movement 2

g

_q

= g

_q1

+ g

_q2

g

_q1

=

v

prog

C(1

−

P)

s

=

250(80)(1

−

0.124)

3, 600

=

4. 867

g

_q2

=

v

prog

CPg

q1

sg

_eff

−

v

_prog

CP

=

250(80)(0.124)(4. 867)

3, 600(30)

−

250(80)(0.124)

=

0.114 g

_q

= 4.867 + 0.114 = 4.981

Maximum platoon flow

rate, v

_c,max

(use

Equation 17-21).

v

_c,max

= sf[1 – (1 – F)

gq

_]

v

_c,max

= 3,600(0.751)[1 – (1 – 0.253)

4.981

_{] = 2,071 veh/h}

Minimum platoon flow

rate, v

_c,min

.

v

_c,min

= 1,000(2) = 2,000

Duration of blocked

period, t

_p,i

(use

Equation 17-22).

t

_p,i

=

g

_q

−

ln 1

−

v

c,min

sf









v

_c,max

−

v

_prog

R

_p

f

v

_c,min

−

v

_prog

R

_p

f

























ln(1

−

F)

t

p,2

=

4.981 −

ln

1 −

2,000

3,600(0.751)









2,071

−

250(0.33)(0.751)

2,000

−

250(0.33)(0.751)





















ln(1

−

0.253)

=

0.489 Proportion of time

blocked (use Equation

17-23).

p

_i

=

t

P,T

+

t

P,L

C

p

₂

=

0.489

(10)

4. (continued) Dominant

and subordinate

platoons (use

Equations 17-24 and

17-25).

p

_dom

= max(p

₂

, p

₅

)

p

_subo

= min(p

₂

, p

₅

)

p

_dom

= P

₂

= 0.006

p

_subo

= P

₅

= 0.000

Conflicting flow during

unblocked period (use

Equation 17-28).

v

_c,u,x

=

v

c,x

−

s(1

−

p

x

)

p

_x

v

_c,u,1

=

400 −

3, 600(1

−

1. 000)

1. 000

=

400 veh/h

Capacity during

unblocked period, c

_r,x

(use Equation 17-3).

c

_r,x

=

v

_c,u,x

e

−vc,u,xtc,x/ 3,600

1 −

e

−vc,u,xtf,x/ 3,600

c

_r,1

=

400 e

−400(4.300)/ 3,600

1 −

e

−400(2.300)/ 3,600

=

1,100 veh/h

Potential capacity,

c

_plat,x

, accounting for

platooning (use

Equation 17-29).

c

_plat,x

= p

_x

c

_r,x

c

_plat,1

= 1.000(1,100) = 1,100 veh/h

5. Movement capacity,

c

_m,x

, accounting for

impedance (use

Equation 17-4, 17-7, or

17-10).

c

_m,x

= c

_plat,x

f

_x

c

_m,1

= 1,100(1.000) = 1,100 veh/h

6. Skip Worksheets 7a

and 7b.

No two-stage gap acceptance

7. Shared-lane capacity

Worksheet 8 (use

Equation 17-15).

c

SH

=

v

_y y

∑

v

_y

c

_m,y y

∑

c

_SH(NB)

=

44 +

132 +

55

44

202 +

132

254 +

55

867 =

288 veh/h

8. Skip Worksheet 9.

No flared minor-street approaches

9. Control delay and LOS

(use Equation 17-38

and Exhibit 17-2).

d

=

3, 600

c

_m,x

+

900T[... ]

+

5 d

_NB

=

3, 600

288 +

900 0. 25

(

)

[... ]

+

5 =

53. 5 s , LOS F

(11)

Example Problem 2

Worksheet 1

Worksheet 2

Movement 1 2 3 4 5 6 7 8 9 10 11 12

Volume (veh/h) Peak-hour factor, PHF Hourly flow rate (veh/h) Proportion of heavy vehicles, PHV

Flow, V_x (ped/h) Lane width, w (m) Walking speed,1_S_p_(m/s)

Percent blockage, f_p (Equation 17-11)

1. Default walking speed = 1.2 m/s

Length of study period = _____ h grade = ______

grade = ______ grade = ______ grade = ______ Show North Street Street JME Walnut/Elm

CEI Latah County

5/7/99 1999 AM Peak 28 110 11 100 300 66 44 132 55 33 250 50 33 250 50 66 300 100 44 132 55 11 110 28 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 33 250 50 66 300 100 44 132 55 11 110 28 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0 0 0 0 Walnut Elm 0.25 0% 0% 0% 0%

(12)

Example Problem 2

Type

4, 5, 6 7, 8, 9 10, 11, 12

Median Storage*

Data for Computing Effect of Delay to Major-Street Vehicles S₂Approach S₅Approach Shared-lane volume, major-street through vehicles, v_i1, blocked by LT

Shared-lane volume, major-street right-turn vehicles, v_i2, blocked by LT Saturation flow rate, major-street through vehicles, s_i1

Saturation flow rate, major-street right-turn vehicles, si2

Number of major-street through lanes Length of study period, T (h)

Movements Distance to Prog Speed, Cycle Green Time, Arrival Saturation Flow Progressed Flow, Signal, D (m) Sprog (km/h) Length, C (s) geff (s) Type Rate, s (veh/h) Vprog (veh/h)

protected LT 3 TH protected LT 3 TH S2 S5 General Information Project Description _________________________________________________________________________________ 1 2 2, 3 0 N 4 5 5, 6 0 N 7, 8, 9 0 N 10, 11, 12 0 N X X X X 135 55 80.0 30.0 1 3600 250 200 50 70.0 20.0 1 3600 250 Example Problem 2

(13)

Example Problem 2

Worksheet 4

Critical Gap and Follow-Up Time

t_c = t_c,base + t_c,HV P_HV + t_c,G G - t_c,T - t_3,LT

t_f = t_f,base + t_f,HV P_HV

Movement 1 4 9 12 8 11 7 10 t_f,base (Exhibit 17-5) t_f,HV PHV (from Worksheet 2) tf (Equation 17-2) t_c,T t_c (Equation 17-1) Worksheet 5a

Arrival type 3 3

vprog (veh/h)

R_p (from Chapter 16) 1.00 1.00

Proportion of vehicles arriving on green, P (Equation 17-17) gq1 (Equation 17-18) gq2 (Equation 17-19) g_q (Equation 17-20) General Information Project Description _________________________________________________________________________________

Movement 1 4 9 12 8 11 7 10 tc,base (Exhibit 17-5) tc,HV PHV (from Worksheet 2) tc,G - - 0.1 0.1 0.2 0.2 0.2 0.2 G (from Worksheet 3) t3,LT single stage two stage single stage two stage 4.1 4.1 6.9 6.9 6.5 6.5 7.5 7.5 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0 0 0 0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 - - - -4.300 4.300 7.100 7.100 6.700 6.700 7.700 7.700 - - - -2.2 2.2 3.3 3.3 4.0 4.0 3.5 3.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 2.300 2.300 3.400 3.400 4.100 4.100 3.600 3.600 30.0 20.0 80.0 70.0 3600 3600 1 1 250 250 0.33 0.33 0.124 0.094 4.867 4.404 0.114 0.103 4.981 4.507 Example Problem 2

(14)

Example Problem 2

Proportion of Time TWSC Intersection Is Blocked (Computation 2)

Worksheet 5b

v_T,prog v_L,prot v_T,prog v_L,prot α (Exhibit 17-13) β = (1 + α)-1 ta = D/Sprog (s) F = (1 + αβta)-1 f = v_prog/Vc ≥ 0 vc,Max (Equation 17-21) vc,Min = 1000N t_p (Equation 17-22) p (Equation 17-23) Worksheet 5c

Platoon Event Periods (Computation 3) General Information Project Description _________________________________________________________________________________ p₂ (from Worksheet 5b) p₅ (from Worksheet 5b) p_dom (Equation 17-24) p_subo (Equation 17-25)

Constrained or unconstrained (Equation 17-26, 17-27)

Proportion for Minor Movements, p_x

Single-Stage Two-Stage

(Exhibit 17-16) Stage I Stage II

p1 p₄ p₇ 1 - p₂ 1 - p₅ p8 1 - p2 1 - p5 p₉ p10 1 - p5 1 - p2 p₁₁ 1 - p₅ 1 - p₂ p12 0.50 0.50 0.667 0.667 8.836 14.400 0.253 0.172 0.751 0.536 2071 1105 2000 2000 0.489 0.000 0.006 0.000 0.006 0.000 0.006 0.000 Unconstrained 1.000 0.994 0.994 0.994 0.994 0.994 0.994 1.000 Example Problem 2

(15)

TWSC - UNSIGNALIZED INTERSECTIONS WORKSHEET Worksheet 5d

Worksheet 5e

Conflicting Flows During Unblocked Period (Computation 4)

Two-Stage

Movements 7 8 10 11

Stage I Stage II Stage I Stage II Stage I Stage II Stage I Stage II p_x (from Worksheet 5c) c_r,x (Equation 17-3) cplat,x (Equation 17-29) Single-Stage Movements 1 4 7 8 9 10 11 12 v_c,x (Exhibit 17-4) s (veh/h) px (from Worksheet 5c) v_c,u,x (Equation 17-28) Single-Stage Movements 1 4 7 8 9 10 11 12 px (from Worksheet 5c) c_r,x (Equation 17-3) c_plat,x (Equation 17-29)

Capacity During Unblocked Period (Computation 5)

Two-Stage

Movements 7 8 10 11

Stage I Stage II Stage I Stage II Stage I Stage II Stage I Stage II vc,x (Exhibit 17-4) s (veh/h) p_x (from Worksheet 5c) vc,u,x (Equation 17-28) General Information Project Description _________________________________________________________________________________

Example Problem 2

400 300 678 873 150 739 848 200 3600 3600 3600 3600 3600 3600 3600 3600 1.000 0.994 0.994 0.994 0.994 0.994 0.994 1.000 400 280 660 857 129 722 831 200 1.000 0.994 0.994 0.994 0.994 0.994 0.994 1.000 1100 1223 333 279 872 300 289 783 1100 1216 331 277 867 298 287 783 Example Problem 2

(16)

7 7 7 10 10 10 0,4 0,1

Step 1: RT from Minor Street v9 v12

Movement capacity (Equation 17-4) c_m,9 = c_p,9 p_p,9= c_m,12 = c_p,12 p_p,12 = Prob of queue-free state (Equation 17-5) p0,9= p0,12 =

Step 2: LT from Major Street v4 v1

Movement capacity (Equation (17-4) c_m,4 = c_p,4 p_p,4= c_m,1 = c_p,1 p_p,1 = Prob of queue-free state (Equation 17-5) p0,4= p0,1 =

Major left shared lane prob of queue-free state (Equation 17-16) p*₌ _p*₌

Step 3: TH from Minor Street (4-leg intersections only) v8 v11

Capacity adjustment factor due to impeding movement f₈ = p_0,4 p_0,1 p_p,8= f₁₁ = p_0,4 p_0,1 p_p,11 = (shared lane use p*_{) (Equation 17-13)}

Movement capacity (Equation 17-7) c_m,8 = c_p,8 f₈= c_m,11 = c_p,11 f₁₁ =

Prob of queue-free state p_0,8= p_0,11 =

Step 4: LT from Minor Street (4-leg intersections only) v7 v10

Major left, minor through impedance factor p'' _{= p}

0,11 f11= p'' = p0,8 f8 =

(Equation 17-8)

Capacity adjustment factor due to impeding movements f₇ = p'_p

0,12 pp,7= f10 = p' p0,9 pp,10 =

(Equation 17-14)

Movement capacity (Equation 17-10) c_m,7 = f₇ c_p,7= c_m,10 = f₁₀ c_p,10 =

Step 5: LT from Minor Street (T-intersections only) v₇ v₁₀

Capacity adjustment factor due to impeding movement f7 = p0,4 p0,1 pp,7= f10 = p0,4 p0,1 pp,10 =

(shared lane use p*_{) (Equation 17-13)}

Notes

150 200 867 783 1.000 1.000 867 783 0.937 0.964 300 400 1216 1100 1.000 1.000 1216 1100 0.946 0.970 873 848 277 287 1.000 1.000 0.917 0.917 254 263 0.480 0.582 678 739 331 298 1.000 1.000 0.534 0.440 0.634 0.556 0.611 0.521 202 155 Example Problem 2

Example Problem 2

(17)

(Equation 17-15) v_y c_m,y c_SH=

( )

∑v_y ∑ y y

Worksheet 8

Movement v (veh/h) c_m (veh/h) c_SH (veh/h)

7 8 9 10 11 12 Worksheet 9

Volume (from Worksheet 2) Delay (Equation 17-38) Q_sep (Equation 17-34) Qsep + 1 Round (Q_sep + 1) n_max (Equation 17-35) c_SH csep n c_act (Equation 17-36)

Effect of Flared Minor-Street Approaches Shared-Lane Capacity General Information Project Description _________________________________________________________________________________

Example Problem 2

44 202 132 254 288 55 867 11 155 110 263 284 28 783 Example Problem 2

(18)

Worksheet 10

Worksheet 11

Movement v (veh/h) c_m (veh/h) v/c Queue Length Control Delay LOS (Equation 17-37) (Equation 17-38) (Exhibit 17-2) 1 4 General Information Project Description _________________________________________________________________________________

Example Problem 2

12 11 10 12 11 10 12 11 10 9 8 7 9 8 7 9 8 7 p_0,1₌ _{p0,4 =} p* =0, 1 p* =0, 4 * Example Problem 2 231 288 0.802 6 53.5 F 53.5 F 149 284 0.525 3 30.9 D 30.9 D

X X X

33 1100 0.030 - 8.4 A 66 1216 0.054 - 8.1 A

X X X

(19)

E

XAMPLE

P

ROBLEM

3 The Intersection

A TWSC intersection with flared approaches and a median storage.

The major street is Walnut St. (EB/WB), and the minor street is Elm St. (NB/SB).

The Question

What are the delay and level of service of the minor-street approaches?

The Facts

√

Four-lane major street,

√

10 percent HV,

√

Two-lane minor street,

√

Flared approach, storage for one vehicle, and

√

Level grade,

√

Median storage, storage for two vehicles.

√

No pedestrians,

Outline to Solution

The steps below show the northbound approach calculations only.

Calculations for other approaches are shown on the worksheets.

Steps

1. Data input.

Worksheets 1 and 2

2. Site characteristics.

Worksheet 3 - lane distribution, grades, right-turn

channelization, flared minor-street approach, and

median storage

3. t

_c

and t

_f

(use Equations 17-1 and

17-2).

Worksheet 4 - Movement 1

t

_c

= t

_c,base

+ t

_c,HV

P

_HV

+...

t

_c

= 4.1 + 2.0(0.10) + 0.0 – 0.0 – 0.0 = 4.300 s

t

_f

= t

_f,base

+ t

_f,HV

P

_HV

t

_f

= 2.2 + 1.0(0.10) = 2.300 s

4. Skip Worksheets 5a through 5e.

No upstream signals within 0.4 km

5. Movement capacity, c

_m,x

, for

minor RT and major LT

movements accounting for

impedance (use Equations 17-3,

17-4, 17-5, and 17-12).

Worksheet 6 - Movement 9

v

_c,9

=

v

2

N

+ 0.5v

3

+ v

14

+ v

15

v

_c,9

=

250

2 + 0.5(50) + 0 + 0 = 150 veh/h

c

_p,9

= v

_c,9

e

−vc,9tc,9/ 3,600

1 −

e

−vc,9tf,9/ 3,600

c

_p,9

=

150 e

−150(7.1)/ 3,600

1 −

e

−150(3.4)/ 3,600

=

845 veh/h

p

_p,9

= 1.0 – f

_p

= 1.0 – 0.000 = 1.000

c

_m,9

= c

_p,9

p

_p,9

= (845)(1.000) = 845 veh/h

p

_0,9

= 1 –

v

9

c

_m,9

= 1 –

55

845 = 0.935

6. Movement capacities, c

_m,x

, for

minor TH and minor LT

movements, accounting for

impedance and two-stage gap

process (use Equations 17-32,

17-33, or 17-7 and Exhibit 17-4).

Worksheets 7a and 7b

v

_c,I,8

= 341 veh/h

v

_c,II,8

= 532 veh/h

v

_c,8

= 873 veh/h

Single Stage

c

_m,8

= c

_p,8

f

₈

= 273(0.917) = 250 veh/h

Two-Stage

c

_T

=

α

y

m+1

−

1 y(y

m

₋

_1)...

[

]

c

_T

=

0. 949

1. 808

2+1

−

1 1. 808(1. 808

2

₋

_1)...

[

]

=

390 veh/h

(20)

7. Shared-lane capacity (use

Equation 17-15).

Worksheet 8

c

_SH

=

v

_y y

∑

v

_y

c

_m y

∑

c

_SH

(NB)

=

44 +

132 +

55

44

370 +

132

390 +

55

845 =

442 veh/h

8. Flared approach capacity (use

Equations 17-36 and 17-38).

Worksheet 9 - Movement 7

d

=

3, 600

c

_m,x

+

900T ...

[ ]

+

5 d

=

3, 600

369 +

900 0. 25

(

)

[ ]

...

+

5 =

16. 070 s

Q

_sep

=

d

7

v

7

3, 600

=

16. 0

(

)

( )

44 3, 600

=

0.196 c

_act

(NB)

=

c

_sep i

∑

−

c

_SH









n

_Max

+

c

SH

c

_act

= (1,605 – 442)

1

2 + 442 = 1,024 veh/h

9. Control delay and LOS (use

Equation 17-38 and Exhibit

17-2).

Worksheet 10

d

_NB

=

3, 600

c

_m,x

+

900T[... ]

+

5 d

_NB

=

3, 600

1, 024

+

900 0. 05

(

)

[... ]

+

5 =

9. 5 s

LOS A

(21)

Example Problem 3

Worksheet 1

Worksheet 2

Movement 1 2 3 4 5 6 7 8 9 10 11 12

Volume (veh/h) Peak-hour factor, PHF Hourly flow rate (veh/h) Proportion of heavy vehicles, PHV

Flow, V_x (ped/h) Lane width, w (m) Walking speed,1_S_p_(m/s)

Percent blockage, f_p (Equation 17-11)

1. Default walking speed = 1.2 m/s

Length of study period = _____ h grade = ______

grade = ______ grade = ______ grade = ______ Show North Street Street JME Walnut/Elm

CEI Latah County

5/7/99 1999 AM Peak 28 110 132 55 33 250 50 33 250 50 66 300 100 44 132 55 11 110 28 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 33 250 50 66 300 100 44 132 55 11 110 28 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0 0 0 0 Walnut Elm 0% 0% 0% 0% 0.25 100 300 66 44 11

(22)

Type

4, 5, 6 7, 8, 9 10, 11, 12

Median Storage*

Data for Computing Effect of Delay to Major-Street Vehicles S2 Approach S5 Approach

Shared-lane volume, major-street through vehicles, vi1, blocked by LT

Shared-lane volume, major-street right-turn vehicles, v_i2, blocked by LT Saturation flow rate, major-street through vehicles, s_i1

Saturation flow rate, major-street right-turn vehicles, s_i2 Number of major-street through lanes

Length of study period, T (h)

Movements Distance to Prog Speed, Cycle Green Time, Arrival Saturation Flow Progressed Flow, Signal, D (m) S_prog (km/h) Length, C (s) g_eff (s) Type Rate, s (veh/h) V_prog (veh/h)

protected LT 3 TH protected LT 3 TH S₂ S5 General Information Project Description _________________________________________________________________________________

Example Problem 3

1 2 2, 3 0 N 4 5 5, 6 0 N 7, 8, 9 0 N 10, 11, 12 0 N X X X X 1 1 2 2 RM RM Example Problem 3

(23)

2.2 2.2 3.3 3.3 4.0 4.0 3.5 3.5

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10

2.300 2.300 3.400 3.400 4.100 4.100 3.600 3.600

Worksheet 4

Critical Gap and Follow-Up Time

t_c = t_c,base + t_c,HV P_HV + t_c,G G - t_c,T - t_3,LT

tf = tf,base + tf,HV PHV

tc,T

tc (Equation 17-1)

Worksheet 5a

Arrival type 3 3

vprog (veh/h)

R_p (from Chapter 16) 1.00 1.00

Proportion of vehicles arriving on green, P (Equation 17-17) gq1 (Equation 17-18) g_q2 (Equation 17-19) g_q (Equation 17-20) General Information Project Description _________________________________________________________________________________

Movement 1 4 9 12 8 11 7 10 tc,base (Exhibit 17-5) t_c,HV P_HV (from Worksheet 2) t_c,G - - 0.1 0.1 0.2 0.2 0.2 0.2 G (from Worksheet 3) t_3,LT single stage two stage single stage two stage

Example Problem 3

Movement 1 4 9 12 8 11 7 10 t_f,base (Exhibit 17-5) t_f,HV P_HV (from Worksheet 2) t_f(Equation 17-2) 4.1 4.1 6.9 6.9 6.5 6.5 7.5 7.5 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0 0 0 0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 .0 - - - - 1.0 1.0 1.0 1.0 4.300 4.300 7.100 7.100 6.700 6.700 7.700 7.700 - - - - 5.700 5.700 6.700 6.700 Example Problem 3

(24)

7 7 7 10 10 10 0,4 0,1

Step 1: RT from Minor Street v₉ v₁₂

Movement capacity (Equation 17-4) cm,9 = cp,9 pp,9= cm,12 = cp,12 pp,12 =

Prob of queue-free state (Equation 17-5) p0,9= p0,12 =

Step 2: LT from Major Street v4 v1

Movement capacity (Equation (17-4) cm,4 = cp,4 pp,4= cm,1 = cp,1 pp,1 =

Major left shared lane prob of queue-free state (Equation 17-16) p*₌ _p*₌

Step 3: TH from Minor Street (4-leg intersections only) v₈ v₁₁

(shared lane use p*_{) (Equation 17-13)}

Movement capacity (Equation 17-7) c_m,8 = c_p,8 f₈= c_m,11 = c_p,11 f₁₁ =

Prob of queue-free state p0,8= p0,11 =

Step 4: LT from Minor Street (4-leg intersections only) v7 v10

Major left, minor through impedance factor p'' _{= p}

0,11 f11= p'' = p0,8 f8 =

(Equation 17-8)

Capacity adjustment factor due to impeding movements f₇ = p'_p

0,12 pp,7= f10 = p' p0,9 pp,10 =

(Equation 17-14)

Movement capacity (Equation 17-10) c_m,7 = f₇ c_p,7= c_m,10 = f₁₀ c_p,10 =

Step 5: LT from Minor Street (T-intersections only) v₇ v₁₀

Capacity adjustment factor due to impeding movement f₇ = p_0,4 p_0,1 p_p,7= f₁₀ = p_0,4 p_0,1 p_p,10 = (shared lane use p*_{) (Equation 17-13)}

Notes

Example Problem 3

150 200 845 783 1.000 1.000 845 783 0.935 0.964 300 400 1202 1100 1.000 1.000 1202 1100 0.945 0.970 Example Problem 3

(25)

TWSC - UNSIGNALIZED INTERSECTIONS WORKSHEET

Worksheet 7a

Effect of Two-Stage Gap Acceptance

Step 3: TH from Minor Street v8 v11

Part I - First Stage

Conflicting flows (Exhibit 17-4) vc,I,8= vc,I,11 =

Potential capacity (Equation 17-3 or 17-29) cp,I,8= cp,I,11 =

Ped impedance factor (Equation 17-12) pp,I,8= pp,I,11 =

Capacity adjustment factor due to impeding movement fI,8 = p0,1 pp,I,8= fI,11 = p0,4 pp,I,11 =

(shared lane use p*_{) (Equation 17-6 or 17-13)}

Movement capacity (Equation 17-7) cm,I,8 = cp,I,8 fI,8= cm,I,11 = cp,I,11 fI,11 =

Prob of queue-free state (Equation 17-5) p0,I,8= p0,I,11 =

Part II - Second Stage

Conflicting flows (Exhibit 17-4) vc,II,8= vc,II,11 =

Potential capacity (Equation 17-3 or 17-29) cp,II,8= cp,II,11 =

Ped impedance factor (Equation 17-12) pp,II,8= pp,II,11 =

Capacity adjustment factor due to impeding movement fII,8 = p0,4 pp,II,8= fII,11 = p0,1 pp,II,11 =

Movement capacity (Equation 17-7) cm,II,8 = cp,II,8 fII,8= cm,II,11 = cp,II,11 fII,11 =

Prob of queue-free state (Equation 17-5) p0,II,8= p0,II,11 =

Part III - Single Stage

Result for Two-Stage Process

a (Equation 17-30) a = a =

y (Equation 17-31) y = y =

cT (Equation 17-32 or 17-33) cT= cT =

General Information Project Description _________________________________________________________________________________

Example Problem 3

341 482 618 532 1.000 1.000 0.970 0.945 599 503 0.780 0.781 532 366 504 601 1 .000 1.000 0.945 0.970 476 583 0.723 0.811 873 848 273 283 1.000 1.000 0.917 0.917 250 260 0.949 0.949 1.808 0.946 390 405 0.662 0.728 Example Problem 3

(26)

7 7 7 10 10 10

Worksheet 7b

Effect of Two-Stage Gap Acceptance

Step 4: LT from Minor Street v7 v10

Part I - First Stage

Conflicting flows (Exhibit 17-4) v_c,I,7= v_c,I,10 =

Potential capacity (Equation 17-3 or 17-29) c_p,I,7= c_p,I,10 = Ped impedance factor (Equation 17-12) pp,I,7= pp,I,10 =

Capacity adjustment factor due to impeding movements fI,7 = p0,1 pp,I,7= fI,10 = p0,4 pp,I,10 =

Movement capacity (Equation 17-7) c_m,I,7 = f_I,7 c_p,I,7= c_m,I,10 = f_I,10 c_p,I,10 = Part II - Second Stage

Conflicting flows (Exhibit 17-4) v_c,II,7= v_c,II,10 =

Potential capacity (Equation 17-3 or 17-29) cp,II,7= cp,II,10 =

Ped impedance factor (Equation 17-12) pp,II,7= pp,II,10 =

Capacity adjustment factor due to impeding movements f_II,7 = p_0,4 p_0,I,11 p_0,12 p_p,II,7= f_II,10 = p_0,1 p_0,I,8 p_0,9 p_p,II,10 = Movement capacity (Equation 17-7) c_m,II,7 = fI_I,7 c_p,II,7= c_m,II,10 = f_II,10 c_p,II,10 = Part III - Single-Stage

Major left, minor through impedance factor p"_{= p}

0,11 f11= p" = p0,8 f8 =

(Equation 17-8)

Capacity adjustment factor due to impeding movements f7 = p' p0,12 pp,7= f10 = p' p0,9 pp,10 =

(Equation 17-9 or 17-14)

Movement capacity (Equation 17-7) cm,7 = f7 cp,7= cm,10 = f10 cp,10 =

Result for Two-Stage Process

a (Equation 17-30) a = a = y (Equation 17-31) y = y = cT (Equation 17-32 or 17-33) cT= cT = General Information Project Description _________________________________________________________________________________

Example Problem 3

341 482 626 514 1.000 1.000 0.970 0.945 607 486 337 257 629 703 1.000 1.000 0.711 0.707 447 497 678 739 323 291 1.000 1.000 0.668 0.607 0.742 0.694 0.715 0.649 231 189 0.949 0.949 2.055 1.227 369 347 Example Problem 3

(27)

(Equation 17-15) vy c_m,y c_SH=

( )

∑v_y ∑ y y

Worksheet 8

Movement v (veh/h) c_m (veh/h) c_SH (veh/h)

7 8 9 10 11 12 Worksheet 9

Volume (from Worksheet 2) Delay (Equation 17-38) Qsep (Equation 17-34) Q_sep + 1 Round (Qsep + 1) n_max (Equation 17-35) c_SH csep n cact (Equation 17-36)

Effect of Flared Minor-Street Approaches Shared-Lane Capacity General Information Project Description _________________________________________________________________________________

Example Problem 3

44 369 132 390 442 55 845 11 347 110 405 439 28 783 369 390 845 347 405 783 44 132 55 11 110 28 16.070 18.881 9.557 15.714 17.171 9.768 0.196 0.692 0.146 0.048 0.525 0.076 1.196 1.692 1.146 1.048 1.525 1.076 1 2 1 1 2 1 2 2 442 439 1604 1535 1 1 1023 987 Example Problem 3

(28)

Worksheet 10

Worksheet 11

Movement v (veh/h) c_m (veh/h) v/c Queue Length Control Delay LOS (Equation 17-37) (Equation 17-38) (Exhibit 17-2) 1 4 General Information Project Description _________________________________________________________________________________

Example Problem 3

* 12 11 10 12 11 10 12 11 10 9 8 7 9 8 7 9 8 7 p_0,1₌ _{p0,4 =} p* =0, 1 p* =0, 4 Example Problem 3 231 1024 0.226 < 1 9.5 A 9.5 A 149 987 0.151 < 1 9.3 A 9.3 A

X X X

33 1100 0.030 < 1 8.4 A 66 1216 0.055 < 1 8.2 A