Module 6 : Traffic Intersection Control
Lecture 30 : Uncontrolled Intersection
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Potential Capacity

Capacity is defined as the maximum number of vehicles, passengers, or the like, per unit time, which can be accommodated under given conditions with a reasonable expectation of occurrence. Potential capacity describes the capacity of a minor stream under ideal conditions assuming that it is unimpeded by other movements and has exclusive use of a separate lane.

Once of the conflicting volume, critical gap and follow up time are known for a given movement its potential capacity can be estimated using gap acceptance models. The concept of potential capacity assumes that all available gaps are used by the subject movement i.e.; there are no higher priority vehicular or pedestrian movements and waiting to use some of the gaps it also assumes that each movement operates out of an exclusive lane. The potential capacity of can be computed using the formula:

$\displaystyle c_{px} = v_{cx} \times \frac{e^{-v_{cx}t_{cx}/3600}}{1-e^{-v_{cx}t_{fx}/3600}}$ (1)

where, $ c_{px}$ is the potential capacity of minor movement $ x$ (veh/h), $ v_{cx}$ is the conflicting flow rate for movement $ x$ (veh/h), $ t_{cx}$ is the critical gap for minor movement $ x$, and $ t_{fx}$ is the follow-up time movement $ x$.

Movement capacity and impedance effects

Vehicles use gaps at a TWSC intersection in a prioritized manner. When traffic becomes congested in a high-priority movement, it can impede lower-priority movements that are streams of Ranks 3 and 4 as shown in Fig. [*] from using gaps in the traffic stream, reducing the potential capacity of these movements. The ideal potential capacities must be adjusted to reflect the impedance effects of higher priority movements that may utilize some of the gaps sought by lower priority movements. This impedance may come due to both pedestrians and vehicular sources called movement capacity.

The movement capacity is found by multiplying the potential capacity by an adjustment factor. The adjustment factor is the product of the probability that each impeding movement will be blocking a subject vehicle. That is

$\displaystyle C_{mx}= C_{px} \times \sum_{i} P_{vi} \times P_{pi}$ (2)

where, $ C_{mx}$ is the movement capacity in vph, $ C_{px}$ is the potential capacity movement x in vph, $ P_{vi}$ is the probability that impeding vehicular movement $ i$ is not blocking the subject flow; (also referred to as the vehicular impedance factor for movement $ i$, $ P_{pi}$ is the probability that impeding pedestrian movement $ j$ is not blocking the subject flow; also referred to us the pedestrian impedance factor for the movement $ j$.

Vehicular movements

Priority 2 vehicular movements LTs from major street and RTs from minor street are not impeded by any other vehicular flow, as they represent the highest priority movements seeking gaps. They are impeded, however, by Rank 1 pedestrian movements. Priority 3 vehicular movements are impeded by Priority 2 vehicular movements and Priority l and 2 pedestrian movements seeking to use the same gaps. Priority 4 vehicular movements are impeded by Priority 2 and 3 vehicular movements, and Priority 1 and 2 pedestrian movements using the same gaps. Table. 1 lists the impeding flows for each subject movement in a four leg. Generally the rule stated the probability that impeding vehicular movement $ i$ is not blocking the subject movement is computed as

$\displaystyle P_{vi} = 1 - \frac{v_i}{C_{mi}}$ (3)

where, $ vi$ is the demand flow for impeding movement $ i$, and $ C_{mi}$ is the movement capacity for impeding movement $ i$ vph. Pedestrian impedance factors are computed as:

Pedestrian Movements

One of the impeding effects for all the movement is pedestrians movement. Both approaches of Minor-street vehicle streams must yield to pedestrian streams. Table. 1 shows that relative hierarchy between pedestrian and vehicular streams used. A factor accounting for pedestrian blockage is computed by Eqn. 4 on the basis of pedestrian volume, the pedestrian walking speed, and the lane width that is:

$\displaystyle P_{pj} = 1- \frac{V_j(W/S_p)}{3600}$ (4)

where, $ p_{pj}$ is the pedestrian impedance factor for impeding pedestrian movement $ j$, $ v_j$ is the pedestrian flow rate, impeding movement $ j$ in peds/hr, $ w$ is the lane width in m, and $ S_p$ is the pedestrian walking speed in m/s.
Table 1: Relative pedestrian/vehicle hierarchy
Vehicle Stream Must Yield to Impedance Factor for
  Pedestrian Stream Pedestrians, $ P_{p,x}$
$ V_1$ $ V_{16}$ $ P_{p,16}$
$ V_4$ $ V_{15}$ $ P_{p,15}$
$ V_7$ $ V_{15},V_{13}$ $ (P_{p,15}) (P_{p,13})$
$ V_8$ $ V_{15},V_{16}$ $ (P_{p,15}) (P_{p,16})$
$ V_9$ $ V_{15},V_{14}$ $ (P_{p,15}) (P_{p,14})$
$ V_{10}$ $ V_{16},V_{14}$ $ (P_{p,16}) (P_{p,14})$
$ V_{11}$ $ V_{15},V_{16}$ $ (P_{p,15}) (P_{p,16})$
$ V_{12}$ $ V_{16},V_{13}$ $ (P_{p,16}) (P_{p,13})$

Determining Shared Lane Capacity

The capacities of individual streams (left turn, through and right turn) are calculated separately. If the streams share a common traffic lane, the capacity of the shared lane is then calculated according to the shared lane procedure. But movement capacities still represent an assumption that each minor street movement operates out of an exclusive lane. Where two or three movements share a lane its combined capacity computed as:

$\displaystyle C_{SH} = \Sigma \frac{\Sigma_y V_y}{\Sigma_y(\frac{V_y}{C_{my}})}$ (5)

where, $ C_{SH}$ is the shared lane capacity in veh/hr, $ V_y$ is the flow rate, movement $ y$ sharing lane with other minor street flow, and $ C_{my}$ is the movement capacity of movement $ y$ sharing lane with other minor street.