For the segments without a non-motor lane
For this situation, the capacity of a road segment with curb parking should be affected significantly in the parking lane and its medial adjacent lane. Accordingly, the analysis and calculation of capacity should focus on the two kinds of lanes mentioned above. For the other lanes, the influence should be far less than on the two lanes mentioned above. Experience shows that the transverse space of a road will be occupied by curb parking. However, the transverse remaining width with curb parking will affect the travelling situation of dynamic traffic directly. Thus, the influence of curb parking on capacity should be divided into two situations and discussed according to the transverse remaining width.
-
1.
The reduction of effective lane width
The distance from the inner lane line of the medial lane adjacent to the parking zone to the inner edge of the curb parking zone is defined as the transverse remaining width and is marked as W
S
. Traffic investigation shows that when W
S
is larger than a certain value the transverse remaining space of the curb parking segment can be used as two lanes, as shown in Fig. 2. According to previous research [14], by considering the transverse safety distance of travelling vehicles and the vehicle’s standard width, the critical value of the transverse remaining width W
S
can be calculated. These values for low speed situations are listed in Table 3.
Table 3 The critical value of transverse residual width W
S
In Table 3, the standard width of both the car and truck is a statistical parameter, which is appropriate for a huge majority of modern cars and trucks. According to the analysis above, when the transverse remaining width W
S
is larger than the critical value listed in Table 3, the reduction of the lane’s effective width is the main reason why the capacity of the lane is reduced. Because of this, the modified method about lane width mentioned in Highway Capacity Manual (HCM 2010) [15] can be used to modify the capacity of a lane under this situation, as shown by Eq. (1) and Eq. (2).
$$ {C}_{l1}={C}_{l2}={C}_0\cdot {f}_w $$
(1)
$$ {f}_w=1+\frac{{\left(0.5\cdot {W}_S-W\right)}_c}{9.144} $$
(2)
Where.
C
l1 and C
l2the capacity of lane 1 and lane 2, as Fig. 2 shows (pcu/h),
C
0the basic capacity of one lane (pcu/h),
f
w
the correction coefficient of lane width.
W
c
the standard lane width in certain country. Its value is 3.66 m(12 ft) for USA, 3.75 m in China.
In Eq. (2), the 9.144 is caused by unit conversion from English to metric unit. Further analysis indicates that, although two vehicles can travel abreast within this transverse remaining width for the situation above, the lateral clearance for vehicle travelling is insufficient. In addition, because the medial lane line of parking zone loses the traffic function, there will be a very adverse effect on traffic safety.
-
2.
The Gap Acceptance model
When the transverse remaining width is less than the critical value listed in Table 3, mainline traffic flow cannot travel parallel. Thus, vehicles in the parking lane will be forced to change lane and travel using the acceptable gap of the fleet in its medial adjacent lane, as shown in Fig. 3. For this situation, there will be a serious bottleneck of capacity in the road segment with curb parking. This is because a large number of motor vehicles in lane 1 are forced to combine travel using the acceptable gap. This kind of traffic operation condition will lead to a large number of traffic conflicts and the capacity of lane 2 will also be affected.
The headway of the fleet in lane 2 h(s) is assumed to follow negative exponential distribution with parameter λ. Then, the distribution function of h is shown as Eq. (3).
$$ F(t)=P\left(h\le t\right)=1-{e}^{-\lambda t} $$
(3)
If t
0
(s) is the critical time interval of the fleet in lane 2, it means the minimum headway of this fleet for vehicles travelling through this fleet. t(s) is the car-following headway in lane 1 for successive travelling through the fleet in lane 2. There are n vehicles in lane 1 waiting for driving into lane 2. Then, the probability of the headway in lane 2 which allows n vehicles to driving into it fitly can be expressed by Eq. (4).
$$ P(n)=P\left[{t}_0+\left(n-1\right)t\le h<{t}_0+ nt\right]={e}^{-\lambda {t}_0}\left[{e}^{-\lambda \left(n-1\right)t}-{e}^{-\lambda nt}\right] $$
(4)
When the headway is longer than t
0
+ nt, there are also n vehicles can travel into lane 2. Because there are only n vehicles in lane 1. So, this probability can be marked as P′(n), as Eq. (5) shown.
$$ P^{\prime }(n)=P\left[h>{t}_0+ nt\right]=1-P\left[h\le {t}_0+ nt\right]={e}^{-\lambda {t}_0}{e}^{-\lambda nt} $$
(5)
Given the traffic volume q
l2, that is also the total number of headways in lane 2 in one hour. Thus, the number of vehicles in lane 1 can travel into lane 2 can be marked as Q. It can be calculated by Eq. (6).
$$ Q={q}_{l2}{\displaystyle \sum \left[P(n)\cdot n\right]}+{q}_{l2}P^{\prime }(n)\cdot n={q}_{l2}{e}^{-\lambda {t}_0}\frac{1-{e}^{-\lambda nt}}{1-{e}^{-\lambda t}} $$
(6)
According to the definition of capacity, the number of vehicles in lane 1 should be assumed to approach infinity. So, the capacity of lane 2 of the segment with curb parking C’
l2(pcu/h) should be expressed as Eq. (7). It also can be plotted as Fig. 4 shown. The meaning of parameter λ(pcu/s) is the average arrival rate of the vehicles in lane 2. It also equals to q
l2/3600 s.
$$ C{\prime}_{l2}={q}_{l2}\frac{e^{-\lambda {t}_0}}{1-{e}^{-\lambda t}}+{q}_{l2} $$
(7)
It can be known from Fig. 4, all the curves of the capacity of lane 2 C’
l2
decrease first and then increase with different t
0 and t. However, all of them are less than the basic traffic capacity of one lane with the corresponding design speed of the road. By analyzing the model above, it can be shown that the capacity of lane 2 for this traffic condition is mainly determined by the traffic volume of lane 2, besides the critical acceptance gap in lane 2 and the car-following headway in lane 1. In addition, this effect is bidirectional. That means when the volume in lane 2 is less, the number of vehicles in lane 1 which can travel through lane 2 using an acceptable gap is greater. So the capacity will be compensated. On the contrary, when this volume is larger, only a few vehicles in lane 1 can realize the combined travelling with an acceptance gap. It needs to be added that, The essence of the conflict between the parking vehicle when it leaves and the passing vehicles is also similar to this situation.
For segments with a non-motor lane
For this situation, there will be no conflicts between motor vehicles. However, some non-motor vehicles will be forced to travel in the medial adjacent motor lane. These non-motor vehicles will occupy the space of the motor lane. This phenomenon will lead to the reduction of the motor lane effective width, which is W
E
, as shown in Fig. 5. Thus, the influence mechanism of curb parking on capacity is similar to the reduction of effective lane width, as discussed above in section 3.1. However, the correction coefficient of the lane width f
w
should be calculated by Eq. (8).
$$ {f}_w=1+\frac{\left({W}_E-{W}_C\right)}{9.144} $$
(8)