A4.6 Worked examples of trip reliability procedure

Introduction

Three worked examples of the calculations for trip reliability benefits are given below.

Example 1 - Signalised intersection upgrade

An urban arterial project involves the addition of traffic lanes to the north and south approaches of a 4-leg intersection. This will improve the reliability of travel time. The traffic volumes for the north, south, east and west approaches are 1,506 veh/h, 168 veh/h, 1,662 veh/h and 57 veh/h respectively.

The average delay for do minimum is 30 seconds and average delay for the project option is 20.8 seconds. Total flow is 3,393 veh/h.

Travel time savings

Travel time savings = $15.13 × 3393 × (30 - 20.8) / 3600 = $131.19/h
where $15.13 is value of travel time for morning commuter peak hour (table A4.3)

Trip reliability savings

The standard deviation of delay (in min) is calculated by:

SD(TT) = S₀ + (S - S₀) / (1 + e^{b*(VC ratio − a)})

For signalised intersections: S =1.25, b = −32, a = 1, S₀ =0.120 (table A4.5).

Do minimum

For the do minimum, the total standard deviation in delay for the intersection is 774.950 veh-min.

Project option

With additional traffic lanes for the north and south approaches, the standard deviation drops to 411.574 veh-min.

The drop in standard deviation of delays is due to:

1. Increase in capacity for North and South approaches as an extra lane is added for the through traffic.
2. Increase in capacity for East and West approaches as the signal controller can allocate a higher proportion of cycle time to movements on these approaches.

Variability benefits per hour of the time period are calculated as:

0.9 × $15.13 × (774.950 − 411.574) / 60 × 30 % = $24.74/h.

Where $15.13 is the value of travel time for morning commuter peak hour (table A4.3), 0.9 is the variability travel time factor and the correction factor for an intersection model of 30 percent has been judged to be appropriate.

Example 2 - rural highway: 4 laning

A section of rural strategic road is approaching capacity. One option is 4 laning part of this section. The road carries 20,000 veh/day in level terrain, with a peak period intensity of 2,050 veh/h, 70/30 directional split, 7 percent heavy truck component and has 60 percent no-passing.

For the do minimum, the capacity is calculated as 2800 × f_d × f_t = 2,800 × 0.89 × 0.92 = 2,290 veh/h. The values for f_d and f_t are drawn from appendix A3.11. With a traffic volume of 2,050 veh/h, the VC ratio = 2,050 / 2,290 = 0.90. The standard deviation of travel time (denoted as SD(TT)) is 0.09 min (from table A4.7).

For the project option, assuming there are no restrictions requiring a reduction in the lane capacity, a capacity of 2,200 veh/h/lane is applicable (see appendix A3.10). The VC ratio is 2,050 / (4 × 2,200) = 0.23.

The standard deviation of delay (in min) is calculated by:

SD(TT) = S₀ + (S − S₀) / (1 + e^{b* (VC ratio − a)})

For a rural highway (2 lanes in each direction of travel):

S = 1.03, b = −22, a = 1, S₀ = 0.033 (from table A4.5)

SD(TT) = 0.033 + (1.030 - 0.033) / (1 + e^{−22 * (0.23 −1)})

= 0.033 min

Variability benefits per hour are calculated as:

0.9 × $25.34 × (0.09 − 0.033) × 2,050 / 60 × 30 % = $13.32/h

where: $25.34 is the value of travel time for weekday period for rural strategic roads (from table A4.3)

0.9 is the variability travel time factor and

30% is selected as the appropriate adjustment factor

(from table A4.6).

Example 3 - Township bypass project

A project provides a township (urban arterial) bypass from A to E to remove through traffic from the town centre. The existing through-traffic between A and E is 2,400 veh/h with 1,200 vehicles in each direction. It is expected that the traffic volumes between A and E will remain the same once the bypass is built, but 1400 vehicles will use the new bypass each hour (700 in each direction).

Traffic volume and VC ratio at the signalised intersection I are summarised on the following page.

Do minimum

Project option

Matrices of flows

For road section, standard deviations of travel times in minutes are calculated by:

SD(TT) = S₀ + (S − S₀) / (1 + e^{b*(VC ratio − a)})

For urban arterial:

S = 0.89, b = −28, a = 1, S₀ =0.117 (table A4.5)

For urban retail road:

S = 0.87, b = −16, a = 1, S₀ =0.150 (table A4.5)

For intersection C, standard deviations of delays in minutes for each movement are calculated by:

SD(TT) = S₀ + (S − S₀) / (1 + e^{b*(VC ratio − a)})

For signalised intersection: S =1.25, b = −32, a = 1, S₀ =0.120 (table A4.5)

The total variability is the square root of the sum of individual link / intersection variability. For instance, from origin A to destination C, the total variability for do minimum and project option are calculated by:

Matrices of standard deviations of travel times

Network-wide estimate of variability

Multiply the element in the flow matrix with the corresponding element in the standard deviation matrix to derive the variability for each movement. Sum each line to get the total for the approach. Add the final column together to derive the network-wide variability.

Matrixes of flow × standard deviation of travel time

The total variability for 'do minimum' is 704.353 veh-min and for 'project option' is 467.666 veh/min. Variability benefits per peak hour are calculated as:

0.9 × $15.13 × (704.353 − 467.666) / 60 × 30 % = $16.11/h

Where $15.13 is the value of travel time for morning commuter peak hour for urban arterial (table A4.3), 0.9 is the variability travel time factor, and 30 percent is the adjustment factor as there is only one major source of variability.