Chapter 10, Problem 5P

To determine

The capacity of the lane group.

Answer to Problem 5P

The capacity of the lane group is $723\text{veh}/\text{h}/\text{lane}$.

Explanation of Solution

Given:

The base rate is $1900\text{pc}/\text{h/lane}$.

Lane width is $11\text{ft}$.

Heavy vehicles are $4\%$ of the traffic stream.

Approach grade is $+3\%$.

No on-street parking.

No bus stops.

Bicycle and pedestrian traffic conflicting with this lane group is negligible.

Intersection is in a central business district.

The effective green time for the movement is $35\text{s}$.

The total cycle length is $60\text{s}$.

Formula used:

The adjusted saturated flow rate for a lane group is given by

$s=\left(s_0\right)\left(f_w\right)\left(f_{HV}\right)\left(f_g\right)\left(f_p\right)\left(f_a\right)\left(f_{bb}\right)\left(f_{Lu}\right)\left(f_{RT}\right)\left(f_{LT}\right)\left(f_{LPb}\right)\left(f_{RPb}\right)$   ...... (I)

Here, $s$ is saturation flow rate for the subject lane group, $s_0$ is a base saturation flow rate per lane, $f_w$ is the adjustment factor for lane width, $f_{HV}$ is the adjustment factor for heavy vehicles in the traffic stream, $f_g$ is the adjustment factor for approach grade, $f_p$ is the adjustment factor for the existence of a parking lane adjacent to the lane group and parking activity on that lane, $f_a$ is the adjustment factor for area type, $f_{bb}$ is adjustment factor for blocking effect of local buses stopping within the intersection area, $f_{Lu}$ is the adjustment factor for lane utilization, is the adjustment factor for right turns in the lane group, $f_{RT}$ is the adjustment factor for right turns in the lane group, $f_{LT}$ s adjustment factor for left turns in the lane group, $f_{LPb}$ is pedestrian adjustment factor for left- turn movements, and $f_{RPb}$ is the pedestrian adjustment factor for right- turn movements.

The Heavy-vehicle adjustment factor is given by

$f_{HV}=\frac{100}{100+P_{HV}\left(E_T-1\right)}$   ...... (II)

Here, $f_{HV}$ is Heavy-vehicle adjustment factor, $P_{HV}$ is percent of Heavy-vehicle in the subject improvement ground, and $E_T$ is passenger car equivalent.

The grade adjustment factor is given by

$f_g=1-\frac{P_g}{200}$   ...... (III)

Here, $f_g$ is grade adjustment factor, and $P_g$ is approach grade for the subject movement group.

Parking adjustment factor is given by

$f_p=\frac{N-0.1-\frac{18N_m}{3600}}{N}\ge 0.050$   ...... (IV)

Here, $N_m$ is parking maneuver rate adjacent to lane group, and $N$ is number of lanes in lane group.

The bus blockage adjustment factor is given by

$f_{bb}=\frac{N-\frac{14.4N_b}{3600}}{N}\ge 0.050$   ...... (V)

Here, $N_b$ is bus stopping rate at the approach.

The lane utilization adjustment factor is given by

$f_{Lu}=\frac{v_g}{v_{gi}N}$   ...... (VI)

Here, $v_g$ is unadjusted demand flow rate for lane group, and $v_{gi}$ is unadjusted demand flow rate on the single lane in the lane group with the highest volume.

The right turn adjustment factor for protecting movement on exclusive lane is given by

$f_{RT}=\frac{1}{E_R}$   ...... (VII)

Here, $E_R$ is equivalent number of through cars for a protected right-turning vehicle the value of which is $1.18$.

The left turn adjustment factor for protecting movement on exclusive lane is given by

$f_{LT}=\frac{1}{E_L}$   ...... (VIII)

Here, $E_L$ is equivalent number of through cars for a protected left-turning vehicle the value of which is $1.05$.

The value of $f_{LPb}$, $f_{RPb}$, and $f_{Lu}$ is $1$, and the value of $f_a$ is $0.90$.

The capacity of the lane group is given by

$c=Ns\frac{g}{C}$   ...... (IX)

Here, $c$ is capacity, $g$ is effective green time for the lane group, $C$ is cycle length.

Calculation:

The Heavy-vehicle adjustment factor is calculated as

Substitute $4\%$ for $P_{HV}$, and $2$ for $E_T$ in equation (II).

$\begin{array}{c}{f}_{HV}=\frac{100}{100+4\%\left(2-1\right)}\\ =\frac{100}{100+\frac{4}{100}}\\ =0.9996\end{array}$

The grade adjustment factor is calculated as

Substitute $3\%$ for $P_g$ in equation (III).

$\begin{array}{c}{f}_g=1-\frac{3\%}{200}\\ =1-\frac{\frac{3}{100}}{200}\\ =1-0.00015\\ =0.999\end{array}$

Parking adjustment factor is calculated as

Substitute $1$ for $N$, and $0$ for $N_m$ in equation (IV).

$\begin{array}{c}{f}_p=\frac{1-0.1-\frac{18\times 0}{3600}}{1}\ge 0.050\\ =1-0.1\ge 0.050\\ =0.9\ge 0.050\end{array}$

The bus blockage adjustment factor is calculated as

Substitute $1$ for $N$, and $0$ for $N_b$ in equation (V).

$\begin{array}{c}{f}_{bb}=\frac{1-\frac{14.4\left(0\right)}{3600}}{1}\ge 0.050\\ =1-0\ge 0.050\\ =1\ge 0.050\end{array}$

The right turn adjustment factor for protecting movement on exclusive lane is calculated as

Substitute $1.18$ for $E_R$ in equation (VII).

$\begin{array}{c}{f}_{RT}=\frac{1}{1.18}\\ =0.847\end{array}$

The left turn adjustment factor for protecting movement on exclusive lane is calculated as

Substitute $1.05$ for $E_L$ in equation (VIII).

$\begin{array}{c}{f}_{LT}=\frac{1}{1.05}\\ =0.952\end{array}$

The adjusted saturated flow rate for a lane group is calculated as

Substitute $1900\text{pc}/\text{h/lane}$

$0.9996$ for $f_{HV}$, $0.999$ for $f_g$, $0.9$ for $f_p$, and $f_a$, $1$ for $f_{bb}$, $0.847$ for $f_{RT}$, $0.952$ for $f_{LT}$, $1$ for $f_{LPb}$, $f_{RPb}$, $f_w$, and $f_{Lu}$ in equation (I).

$\begin{array}{c}s=\left(1900\text{pc}/\text{h/lane}\right)\left(1\right)\left(0.9996\right)\left(0.999\right)\left(0.9\right)\left(0.90\right)\left(1\right)\left(0.847\right)\left(0.952\right)\left(1\right)\left(1\right)\left(1\right)\\ =1239.22\text{veh}/\text{h/lane}\end{array}$

The capacity of the lane group is calculated as

Substitute $35\sec$ for $g$, $1239.22\text{veh}/\text{h/lane}$ for $s$, $60\sec$ for $C$, and $1$ for $N$ in equation (IX).

$\begin{array}{c}c=\left(1\right)\left(1239.22\text{veh}/\text{h/lane}\right)\left(\frac{35\sec }{60\sec }\right)\\ =722.87\text{veh}/\text{h/lane}\\ \approx 723\text{veh}/\text{h/lane}\end{array}$

Conclusion:

The capacity of the lane group is $723\text{veh}/\text{h}/\text{lane}$.