CALCULATION OF ENTRY CAPACITY

1. Solve for the capacity of right-turn lane and through and left-turn lane

2.1(1040) 1 1040
(4.1−2.92−2.1 )
𝐶𝐸, 𝑅south = 3600. (1 − ). .e 3600
3600 2.9

𝐶𝐸, 𝑅south = 416.544 𝑣𝑒ℎ/ℎ.

2.1(971) 1 971
𝐶𝐸, 𝑅north = 3600. (1 − ). .e 3600 (4.1−2.9 2−2.1 )
3600 2.9

𝐶𝐸, 𝑅north = 545.474 𝑣𝑒ℎ/ℎ.

6.4
−32 ( )
3600
e
𝐶𝐸, 𝑇𝐿𝑇𝑛𝑜𝑟𝑡ℎ = 32( 3.5 )
−32( )
3600
1−e

𝐶𝐸, 𝑇𝐿𝑇𝑛𝑜𝑟𝑡ℎ = 986.884 𝑣𝑒ℎ/ℎ.

6.4
−26 ( )
3600
e
𝐶𝐸, 𝑇𝐿𝑇south = 26( 3.5
)
−26( )
3600
1−e

𝐶𝐸, 𝑇𝐿𝑇south = 994.576 𝑣𝑒ℎ/ℎ.

2.1(838) 1 838
𝐶𝐸,𝑎𝑠𝑡 = 3600. (1 − ). .e 3600 (4.1−2.92−2.1 )
3600 2.9

𝐶𝐸,𝑎𝑠𝑡 = 558.3 𝑣𝑒ℎ/ℎ.

 2.1 ( 780 ) 1 780
𝐶𝐸,𝑇𝑒𝑎𝑠𝑡 = 3600. (1 − ). .e 3600 ( 4.1−2.9 2−2.1 )
3600 2.9

𝐶𝐸,𝑇𝑒𝑎𝑠𝑡 = 600.548 𝑣𝑒ℎ/ℎ.

2.1 ( 586 ) 1 586

𝐶𝐸,west = 3600. (1 − ). .e 3600 ( 4.1−2.9 2−2.1 )
3600 2.9

𝐶𝐸,west = 747.066 𝑣𝑒ℎ/ℎ.

2.1 ( 1239 ) 1 1239

𝐶𝐸,𝑇west = 3600. (1 − ). .e 3600 ( 4.1−2.9 2−2.1 )
3600 2.9

𝐶𝐸,𝑇west = 284.818 𝑣𝑒ℎ/ℎ.

2. Solve for the degree of saturation at each lane

360
𝑥𝑅south = = 0.864254437
416.544

707
𝑥𝑇𝐿𝑇south = = 0.716396253
986.884

475
𝑥𝑅north = = 0.870802275
545.474

843
𝑥𝑇𝐿𝑇north= = 0.847597368
994.576
 419
𝑥𝑅east = = 0.750492567
558.3

390
𝑥𝑇𝐿𝑇east = = 0.649406875
600.548

293
𝑥𝑅west = = 0.392200957
747.066

220
𝑥𝑇𝐿𝑇west= = 0.772423091
284.818

3. Solve for the utilization ratio at each lane

0.864254437
𝜌𝑅south = = 1.0
0.864254437

0.716396253
𝜌𝑇𝐿𝑇south = = 0.828918225
0.864254437

0.870802275
𝜌𝑅north = = 1.0
0.870802275

0.847597368
𝜌𝑇𝐿𝑇south = = 0.973352267
0.870802275
 0.750492567
𝜌𝑅east = = 1.0
0.750492567

0.649406875
𝜌𝑇𝐿𝑇east = = 0.865307538
0.750492567

0.392200957
𝜌𝑅west = = 0.507754055
0.772423091

0.772423091
𝜌𝑇𝐿𝑇west = = 1.0
0.772423091

4. Capacity at entries can be calculated using two different formulas

𝐶𝐸south = 1.0(416.544) + 0.828918225(986.884)

𝐶𝐸south = 1234.590133 𝑣𝑒ℎ/ℎ.

360+707
𝐶𝐸south =
0.864254437

𝐶𝐸south = 1234.590133 𝑣𝑒ℎ/ℎ.

Average entry capacity at north approach is 1234.590133 𝑣𝑒ℎ/ℎ.

 𝐶𝐸north = 1.0(545.474) + 0.973352267(994.576)

𝐶𝐸north = 1513.546804 𝑣𝑒ℎ/ℎ

475+ 843
𝐶𝐸north =
0.870802275

𝐶𝐸north = 1513.546804 𝑣𝑒ℎ/ℎ

Average entry capacity at north approach is 1513.546804 𝑣𝑒ℎ/ℎ.

𝐶𝐸east = 1.0(558.3) + 0.865307538(600.548)

𝐶𝐸east = 1077.958711 𝑣𝑒ℎ/ℎ

419+390
𝐶𝐸east =
0.750492567

𝐶𝐸east = 1077.958711 𝑣𝑒ℎ/ℎ.

Average entry capacity at north approach is 1077.958711 𝑣𝑒ℎ/ℎ

𝐶𝐸west = 0.507754055(747.066) + 1.0(284.818)

 𝐶𝐸west = 664.1437909 𝑣𝑒ℎ/ℎ

293+220
𝐶𝐸west =
0.772423091

𝐶𝐸west = 664.1437909 𝑣𝑒ℎ/ℎ

Average entry capacity at north approach is 664.1437909 𝑣𝑒ℎ/ℎ.

CALCULATION OF DELAY AND QUEUE LENGTH

Evaluation of delay at each lane

3600
𝐷𝑖 = + 900T¿ + 5
Ci

Use 0.25 reference time (T) for the peak 15-minute analysis

Refer to the tabulated data

Degree of Saturation Capacity

Approach Lane Ci
 Qi (𝑣𝑒ℎ/ℎ)
Ci
Right Turn 0.864254437 416.544
Through & Left Turn 0.716396253 545.474
South
Right Turn 0.870802275 986.884
Through & Left Turn 0.847597368 994.576
North
Right Turn 0.685272118 585.169
Through & Left Turn 0.601520644 623.42
East
Right Turn 0.808618306 536.718
Through & Left Turn 0.907884629 501.165
West

3600
𝐷Rsouth = + 900(0.25)¿ + 5
416.544

𝐷Rsouth = 48.594 𝑠/𝑣𝑒ℎ

3600
𝐷TLTsouth = + 900(0.25)¿ + 5
545.474

𝐷TLTsouth = 17.264 𝑠/𝑣𝑒ℎ

3600
𝐷Rnorth = + 900(0.25)¿ + 5
986.884

𝐷Rnorth = 41.134 𝑠/𝑣𝑒ℎ

3600
𝐷TLTnorth = + 900(0.25)¿ + 5
994.576

𝐷TLTnorth = 24.926 𝑠/𝑣𝑒ℎ

 3600
𝐷Reast = + 900(0.25)¿ + 5
585.169

𝐷Reast = 28.311 𝑠/𝑣𝑒ℎ

3600
𝐷TLTeast = + 900(0.25)¿ + 5
623.42

𝐷TLTeast = 21.41 𝑠/𝑣𝑒ℎ

3600
𝐷Rwest = + 900(0.25)¿ + 5
536.718

𝐷Rwest = 12.891 𝑠/𝑣𝑒ℎ

3600
𝐷TLTwest = + 900(0.25)¿ + 5
501.165

𝐷TLTwest = 49.9 𝑠/𝑣𝑒ℎ

Evaluation of 95th percentile of queue length at each lane

Ci
𝑁95, = 900T¿ .
3600

Use 0.25 reference time (T) for the peak 15-minute analysis

Refer to the tabulated data

Degree of Saturation Capacity

Approach Lane Qi Ci
Ci (𝑣𝑒ℎ/ℎ)
Right Turn 0.864254437 416.544
Through & Left Turn 0.716396253 545.474
South
Right Turn 0.870802275 986.884
Through & Left Turn 0.847597368 994.576
North
Right Turn 0.685272118 585.169
Through & Left Turn 0.601520644 623.42
East
Right Turn 0.808618306 536.718
Through & Left Turn 0.907884629 501.165
West
 416.544
𝑁95,Rsouth = 900(0.25)¿ .
3600

𝑁95,Rsouth = 8.604 ≈ 9 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠

545.474
𝑁95,TLTsouth = 900(0.25)¿.
3600

𝑁95,TLTsouth = 6.396 ≈ 7 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠

986.884
𝑁95,Rnorth = 900(0.25)¿ .
3600

𝑁95,Rnorth = 9.656 ≈ 10 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠

994.576
𝑁95,TLTnorth = 900(0.25)¿.
3600

𝑁95,TLTnorth = 10.69 ≈ 11 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠

623.42
𝑁95,Reast = 900(0.25)¿.
3600

𝑁95,Reast =6.545 ≈ 7 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠

623.42
𝑁95,TLTeast = 900(0.25)¿.
3600

𝑁95,TLTeast = 4.706 ≈ 5 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠

536.718
𝑁95,Rwest = 900(0.25)¿.
3600
𝑁95,Rwest = 1.872 ≈ 2 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠

501.165
𝑁95,TLTwest = 900(0.25)¿.
3600

𝑁95,TLTwest = 5.856 ≈ 6 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠

CALCULATION OF ENTRY CAPACITY

1. Solve for the capacity of right-turn lane and through and left-turn lane
 2.1(366) 1 366
(4.1−2.9 2−2.1 )
𝐶𝐸, 𝑅south = 3600. (1 − ). .e 3600
3600 2.9

𝐶𝐸, 𝑅south = 416.544 𝑣𝑒ℎ/ℎ.

2.1(1014) 1 1014
𝐶𝐸, 𝑅north = 3600. (1 − ). .e 3600 (4.1−2.9 2−2.1)
3600 2.9

𝐶𝐸, 𝑅north = 545.474 𝑣𝑒ℎ/ℎ.

6.4
−45( )
3600
e
𝐶𝐸, 𝑇𝐿𝑇south = 45 ( 3.5
)
−45 ( )
3600
1−e

𝐶𝐸, 𝑇𝐿𝑇south = 986.884 𝑣𝑒ℎ/ℎ.

6.4
−28 ( )
3600
e
𝐶𝐸, 𝑇𝐿𝑇north = 28 ( 3.5 )
−28( )
3600
1−e

𝐶𝐸, 𝑇𝐿𝑇north = 994.576 𝑣𝑒ℎ/ℎ.

2.1(801) 1 801
𝐶𝐸,𝑎𝑠𝑡 = 3600. (1 − ). .e 3600 (4.1−2.9 2−2.1 )
3600 2.9

𝐶𝐸,𝑎𝑠𝑡 = 585.169 𝑣𝑒ℎ/ℎ.

2.1 ( 749 ) 1 749

𝐶𝐸,𝑇𝑒𝑎𝑠𝑡 = 3600. (1 − ). .e 3600 ( 4.1−2.9 2−2.1 )
3600 2.9

𝐶𝐸,𝑇𝑒𝑎𝑠𝑡 = 623.42 𝑣𝑒ℎ/ℎ.

2.1 ( 868 ) 1 868

𝐶𝐸,west = 3600. (1 − ). .e 3600 ( 4.1−2.9 2−2.1 )
3600 2.9
 𝐶𝐸,west = 536.718 𝑣𝑒ℎ/ℎ.

2.1 ( 918 ) 1 918

𝐶𝐸,𝑇west = 3600. (1 − ). .e 3600 ( 4.1−2.9 2−2.1 )
3600 2.9

𝐶𝐸,𝑇west = 501.165 𝑣𝑒ℎ/ℎ.

2. Solve for the degree of saturation at each lane

183
𝑥𝑅south = = 0.19821305
923.249

851
𝑥𝑇𝐿𝑇south = = 0.876946207
970.413

380
𝑥𝑅north = = 0.874916825
434.327

995
𝑥𝑇𝐿𝑇north= = 1.003019138
992.005

401
𝑥𝑅east = = 0.685272118
585.169
 375
𝑥𝑇𝐿𝑇east = = 0.601520644
623.42

434
𝑥𝑅west = = 0.808618306
536.718

455
𝑥𝑇𝐿𝑇west= = 0.907884629
501.165

3. Solve for the utilization ratio at each lane

0.19821305
𝜌𝑅south = = 0.226026463
0. 876946207

0. 876946207
𝜌𝑇𝐿𝑇south = = 1.0
0. 876946207

0. 874916825
𝜌𝑅north = = 0.872283282
1.003019138

1.003019138
𝜌𝑇𝐿𝑇south = = 1.0
1.003019138

0.685272118
𝜌𝑅east = = 1.0
0.685272118
 0.601520644
𝜌𝑇𝐿𝑇east = = 0.87783626
0.685272118

0.808618306
𝜌𝑅west = = 0.890661963
0.907884629

0.907884629
𝜌𝑇𝐿𝑇west = = 1.0
0.907884629

4. Capacity at entries can be calculated using two different formulas

𝐶𝐸south = 0.226026463(923.249) + 1.0(970.413)

𝐶𝐸south = 1179.0917 𝑣𝑒ℎ/ℎ.

183+851
𝐶𝐸south =
0. 874916825

𝐶𝐸south = 1179.0917 𝑣𝑒ℎ/ℎ.

Average entry capacity at north approach is 1179.0917 𝑣𝑒ℎ/ℎ.

𝐶𝐸north = 0.872283282(434.327) + 1.0(992.005)

𝐶𝐸north = 1370.8612 𝑣𝑒ℎ/ℎ

 380+995
𝐶𝐸north =
1.003019138

𝐶𝐸north = 1370.8612 𝑣𝑒ℎ/ℎ

Average entry capacity at north approach is 1370.8612 𝑣𝑒ℎ/ℎ.

𝐶𝐸east = 1.0(585.169) + 0.87783626 (623.42)

𝐶𝐸east = 1132.396868 𝑣𝑒ℎ/ℎ

401+375
𝐶𝐸east =
0.685272118

𝐶𝐸east = 1132.396868 𝑣𝑒ℎ/ℎ.

Average entry capacity at north approach is 1132.396868 𝑣𝑒ℎ/ℎ

𝐶𝐸west = 0.890661963(536.718) + 1.0(501.165)

𝐶𝐸west = 979.199307 𝑣𝑒ℎ/ℎ

434+ 455
𝐶𝐸west =
0.907884629

𝐶𝐸west = 979.1993077 𝑣𝑒ℎ/ℎ

Average entry capacity at north approach is 979.1993077 𝑣𝑒ℎ/ℎ.

 CALCULATION OF DELAY AND QUEUE LENGTH

Evaluation of delay at each lane

3600
𝐷𝑖 = + 900T¿ + 5
Ci

Use 0.25 reference time (T) for the peak 15-minute analysis

Refer to the tabulated data

Degree of Saturation Capacity

Approach Lane Qi Ci
Ci (𝑣𝑒ℎ/ℎ)
Right Turn 0.19821305
923.249
South
Through & Left Turn
0.876946207 970.413

Right Turn 0.874916825 434.327

 North Through & Left Turn
1.003019138 992.005

Right Turn 0.685272118

585.169
East
Through & Left Turn
0.601520644 623.42

Right Turn 0.808618306

536.718
West
Through & Left Turn
0.907884629 501.165

3600
𝐷Rsouth = + 900(0.25)¿ + 5
923.249

𝐷Rsouth = 9.859 𝑠/𝑣𝑒ℎ

3600
𝐷TLTsouth = + 900(0.25)¿ + 5
970.413

𝐷TLTsouth = 28.257 𝑠/𝑣𝑒ℎ

3600
𝐷Rnorth = + 900(0.25)¿ + 5
434.327

𝐷Rnorth = 48.84 𝑠/𝑣𝑒ℎ

3600
𝐷TLTnorth = + 900(0.25)¿ + 5
992.005

𝐷TLTnorth = 49.781 𝑠/𝑣𝑒ℎ

3600
𝐷Reast = + 900(0.25)¿ + 5
585.169
𝐷Reast = 23.461 𝑠/𝑣𝑒ℎ

3600
𝐷TLTeast = + 900(0.25)¿ + 5
623.42

𝐷TLTeast = 19.12 𝑠/𝑣𝑒ℎ

3600
𝐷Rwest = + 900(0.25)¿ + 5
536.718

𝐷Rwest = 34.221 𝑠/𝑣𝑒ℎ

3600
𝐷TLTwest = + 900(0.25)¿ + 5
501.165

𝐷TLTwest = 49.48 𝑠/𝑣𝑒ℎ

Evaluation of 95th percentile of queue length at each lane

Ci
𝑁95, = 900T¿ .
3600

Use 0.25 reference time (T) for the peak 15-minute analysis

Refer to the tabulated data

Degree of Saturation Capacity

Approach Lane Qi Ci
Ci (𝑣𝑒ℎ/ℎ)
Right Turn 0.19821305
923.249
South
Through & Left Turn
0.876946207 970.413

Right Turn 0.874916825

434.327
North
Through & Left Turn
1.003019138 992.005

Right Turn 0.685272118

585.169
East
Through & Left Turn
0.601520644 623.42

Right Turn 0.808618306

536.718
West
Through & Left Turn
0.907884629 501.165
 416.544
𝑁95,Rsouth = 900(0.25)¿ .
3600

𝑁95,Rsouth = 0.735 ≈ 1 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠

545.474
𝑁95,TLTsouth = 900(0.25)¿.
3600

𝑁95,TLTsouth = 12

986.884
𝑁95,Rnorth = 900(0.25)¿ .
3600

𝑁95,Rnorth = 9.018 ≈ 10 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠

994.576
𝑁95,TLTnorth = 900(0.25)¿.
3600

𝑁95,TLTnorth = 19.503≈ 20 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠

623.42
𝑁95,Reast = 900(0.25)¿.
3600

𝑁95,Reast = 5.303≈ 6 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠

623.42
𝑁95,TLTeast = 900(0.25)¿.
3600

𝑁95,TLTeast = 4.017 ≈ 5 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠

 536.718
𝑁95,Rwest = 900(0.25)¿.
3600

𝑁95,Rwest = 7.871≈ 8 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠

501.165
𝑁95,TLTwest = 900(0.25)¿.
3600

𝑁95,TLTwest = 10.5≈ 11 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠