Tradeoffs among free-flow speed, capacity, cost, and environmental footprint in highway design

Abstract

This paper investigates differentiated design standards as a source of capacity additions that are more affordable and have smaller aesthetic and environmental impacts than modern expressways. We consider several tradeoffs, including narrow versus wide lanes and shoulders on an expressway of a given total width, and high-speed expressway versus lower-speed arterial. We quantify the situations in which off-peak traffic is sufficiently great to make it worthwhile to spend more on construction, or to give up some capacity, in order to provide very high off-peak speeds even if peak speeds are limited by congestion. We also consider the implications of differing accident rates. The results support expanding the range of highway designs that are considered when adding capacity to ameliorate urban road congestion.

Appendix: Speeds and capacities from the highway capacity manual (2000)

This appendix briefly discusses the HCM’s methodology for calculating speeds and capacities for expressways, which the HCM calls “freeways” (based on HCM ch. 13, 23), and arterials (based on HCM, ch. 10, 12, 15, 16, 21). A more detailed explanation of the equations and parameter values are presented in the online version of this Appendix (see Online Resource).

Expressways/Freeways

Capacity varies by free-flow speed, and equation 23-1 in the HCM is used to estimate free-flow speed (FFS) of a basic freeway segment:

$$ \text{FFS} = \text{BFFS} \,-\, f_{LW} - \,f_{LC} - f_{N} - f_{ID} $$

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A brief description of each parameter and the parameter values used in the paper are given in Table 5. As shown in Appendix N of the highway performance monitoring system (HPMS) field manual (FHWA 2002), the relationship between base capacity (BaseCap, measured in passenger-car equivalents per hour per lane) and free-flow speed is:

Table 5 Parameter values for expressways

$$ BaseCap = \left\{ {\begin{array}{*{20}c} {1,700 + 10FFS} \hfill \\ {2,400} \hfill \\ \end{array} \begin{array}{*{20}c} {{\text{ for }}\text{FFS} < 70} \hfill \\ {{\text{ for }}FFS \ge 70} \hfill \\ \end{array} } \right. $$

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Equation 23-2 in the HCM is used to convert hourly volume V, which is typically in vehicles per hour, to v _p , which is in passenger-car equivalents per hour per lane (pce/h/ln) and is used later on to estimate speed:

$$ \upnu_{p} = V/(PHF \times N \times f_{HV} \times f_{p} ) $$

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See Table 5 for the parameter values used in this paper. Equation (3) can also be used to calculate capacity in terms of vehicles per hour for all lanes, which we call V _K in this paper, by replacing V = V _K and v _p  = BaseCap.

We use the HCM speed-flow diagrams in Exhibit 23-3 to calculate average passenger-car speed S (min/h) as a function of the flow rate v _p (pce/h/ln).

Urban arterials

The high-type unsignalized arterial analyzed in the comparison between freeways and arterials in Sect. 4 is an example of a “multilane highway” in the HCM’s terminology. The capacity and free-flow speed of this arterial are calculated using the procedures outlined in Chapters 12 and 21 of the HCM (which are very similar to the expressway calculations). However, we make the following modification to the HCM speed-flow function since the HCM function results in the high-type arterial having a higher speed at capacity than the expressway. For free-flow speeds between 55 and 60 min/h, that speed-flow function (Exhibit 21-3 of the HCM) is:

$$ S_{a} = \text{FFS} - \left[ {\left( {\frac{3}{10}\text{FFS} - 10} \right)\left( {\frac{{v_{p} - 1,400}}{28\text{FFS} - 880}} \right)^{1.31} } \right] $$

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The high-type arterial’s speed at capacity (which we shall denote as $S_{a}^{\text{cap}}$) can be calculated from this equation by setting flow rate v _p equal to capacity. Denoting the expressway’s speed at capacity as $S_{e}^{cap}$, we then define a modified speed-flow function for the high-type arterial so that $S_{a}^{\text{cap}} = S_{e}^{\text{cap}}$, essentially by increasing the rate at which speed falls with traffic volume. Specifically we use:

$$ \tilde{S}_{a} = \left( {\frac{{S_{a} - S_{a}^{\text{cap}} }}{{\text{FFS} - S_{a}^{\text{cap}} }}} \right)(\text{FFS} - S_{e}^{\text{cap}} ) + S_{e}^{\text{cap}} $$

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where S _a is given by equation (14).

For the signalized urban arterials in Sect. 3 (which the HCM calls “urban streets”; see Chapters 10, 15 and 16), we focus on high-speed principal arterials (design category 1). These arterials have speed limits of 45–55 min/h and a default free-flow speed of 50 min/h (Exhibits 10-4 and 10-5 of the HCM). Using the procedure recommended by Zegeer et al. (2008, pp. 66–73), if we assume the speed limits on the “regular” and “narrow” arterials in Sect. 3 are 55 and 45 min/h respectively, this gives us free-flow speeds of 51.5 and 46.8 min/h.

A vehicle’s travel time on an urban street (ignoring queuing due to volumes exceeding capacity, computed separately in the text) consists of running time plus “control delay” at a signalized intersection. Based on Exhibit 15-3 of the HCM, running time for an urban arterial longer than one mile is calculated as the length divided by the free-flow speed.

The formula for calculating control delay (Eq.16–9 in the HCM) is the sum of three components: (1) uniform control delay, which assumes uniform arrivals; (2) incremental delay, which takes into account random arrivals and oversaturated conditions (volume exceeding capacity); and (3) initial queue delay, which considers the additional time required to clear an existing initial queue left over from the previous green period.¹² Because the initial queue limits entry flow to the road’s capacity, the initial queue occurs only once at the entry to the road (prior to the first signal) since the traffic volume arriving at each intersection is never greater than the intersection’s capacity. As a result, the control delay in this paper consists only of uniform control delay and incremental delay. Using Eqs. 16–9, 16–11 and 16–12 of the HCM, the control delay at a signal is:

$$ d = \frac{{0.5C(1 - g/C)^{2} }}{{1 - \left[ {\min (1,X)(g/C)} \right]}} \cdot PF + 900T\left[ {(X - 1) + \sqrt {(X - 1)^{2} + \frac{8kIX}{cT}} } \right] $$

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Table 6 provides a description of the parameters and the values used in this paper.

Table 6 Parameter values for urban arterials

The arterial’s capacity, V _K, is based on the saturation flow rates of the through and shared right-turn/through lane groups, along with the fraction of time the signal is green and the proportion of traffic at each intersection that is making left turns. Saturation flow means the highest flow rate that can pass through the intersection while the light is green and is calculated based on equations 16–4 and 16–6 of the HCM. Saturation flow rates depend on the number of lanes, lane width, proportion of vehicles turning right, and other factors. For the most part, we use the default values recommended by the HCM and we assume that 7.5 % of the total traffic volume will be vehicles turning left, and similarly for vehicles turning right. Complete details are available in the online version of this Appendix (see Online Resource).