Data collection

At signalized intersections, other than collecting data on arrival rate and pattern (which can be done in the usual manner of counting volume and recording time headways), data on delay and saturation flow rates may need to be collected. In this section, procedures for collecting data on delay and saturation flow rates are described.

Collecting data on average delay

In this section a procedure which can be easily used to collect data on stopped delay at a signalized intersection is described. The procedure relies on the principle that the area between the cumulative arrival and departure plots (see Figure 7) gives the total time all the vehicles spend stopped at the intersection; its unit is vehicle seconds. This divided by the total number of arrivals obviously gives the average delay.

The area can be obtained by either summing all the delays or queue lengths, that is,

$$\mbox{Total area between cum. arr. and dep. plots} = \sum_{n}d(n) = \int_t q(t) dt$$

where, all the variables are as explained in Figure 7.

Hence, the average delay can be obtained as

$$\mbox{Average Delay} = \frac{\int_t q(t)dt}{\mbox{Total number of arrivals}}$$

The data collection procedure uses the above expression to evaluate the average delay. The method relies on determining area by observing the queue lengths at short intervals of time over the entire experiment time period, and counting the total number of vehicles that arrive during the entire test period. The procedure is explained step-by-step as follows.

Step 1:

Decide the time period, $P$ for which the data will be collected. Decide the interval of time, $I$, at which queue length at the intersection will be counted. The cycle length, $C$, should not be an integral multiple of $I$. Let the number of intervals in $P$ be $m$.

Step 2:

Count the queue length, $q_i$, at the end of each interval. Continue counting till $P$ is over. Also over the time $P$ count the total number of vehicles that arrive at the intersection, $V_{total}$.

Step 3:

Estimate the area as $\sum_{i=1}^m I \times q_i$. See Figure 13, which is a figure similar to Figure 7. The area obtained using $\sum_{i=1}^m I \times q_i$ is generally seen to be more than the actual area, and hence the estimate obtained above is reduced by $10 \%$ in order to get a closer estimate of the true area.

図 13: Plot of cumulative number of arrivals and departures versus time showing the area obtained by numerically integrating the queue lengths.

Step 4:

Estimate the average delay as

$$\mbox{Average delay} = \frac{0.9 \times I \sum_{i=1}^m q_i}{V_{total}}$$

Collecting data on saturation flow rate

The saturation flow rate is the reciprocal of the saturation headway. The saturation headway, as suggested in the section on Departure Processes, is the headway at which latter vehicles discharging from a queue crosses the stop line. In general the HCM [#!hcm98!#] suggests that the average value of the saturation headway for sample $i$, $s_i$ can be obtained using

$$s_i = \frac{T_{L,i} - T_{4,i}}{L-4}$$

where, $T_{j,i}$ is the time at which the $j^{th}$ vehicle of the queue crosses the stop line for the $i^{th}$ sample, and $L$ stands for the last vehicle in the queue. The assumption here is that from the fourth vehicle onwards all vehicles more or less maintain the saturation headway. According to the HCM [#!hcm98!#], the average value of the saturation headway should be estimated as the mean of $s_i$'s after repeated sampling.