Effects of Upstream Signalized Intersections on Two-Lane Highway Operations
A Paper Submitted for Presentation at the January 2004 Annual Meeting of the
Transportation Research Board
Prepared by
Michael P. Dixon
Assistant Professor
Civil Engineering
University of Idaho
P.O. Box 441022
Moscow, ID 83844-1022
Phone: 208-885-4338
E-mail:
Michael Kyte
Professor
Civil Engineering
University of Idaho
PO Box 440901
Moscow, ID 83844-0901
208-885-6002 (voice)
208-885-2877 (fax)
And
Satya Sai Kumar Sarepalli
Graduate Research Assistant
Department of Civil Engineering
University of Idaho
Moscow, ID 83844-0901
Submission date: 10/8/2004
Word count: 5716 + 2 Tables and 5 Figures = 7466
5
Dixon, Kyte, and Sarepalli
Abstract
Signalized intersections can significantly affect traffic operations on two-lane highways, such as increasing percent time-spent-following (PTSF). To date no deterministic or micro-simulation methods exist that allow this effect to be considered when evaluating two-lane highway sections. The primary purpose of this paper is to introduce the formulation of a methodology to assess the effects of signalized intersections on two-lane highways. In this paper, it is shown that the effect of signalized intersections on two-lane highway operations can be significant. Then the methodology formulation is introduced and is comprised of three steps for estimating the PTSF, one of the primary performance measures used in the current Highway Capacity Manual for assessing the quality of service on two-lane highways. The methodology is then applied to two hypothetical cases.
Introduction
Because of increased development in rural areas, more signals are being installed on two-lane highways. The current edition of the Highway Capacity Manual, HCM 2000, provides formal deterministic procedures for the analysis of two-lane highways, signalized intersections, and signalized arterials [1]. Stochastic simulation models can also be used to analyze these facilities. TWOPAS and TRARR, stochastic micro-simulation models, have been used to model two-lane highways. Other micro-simulation models can be used to model signalized intersections and arterials. However, no procedure currently exists, deterministic or otherwise, that accounts for the effects of upstream signalized intersections on two-lane highway operations, such as increased percent time-spent-following (PTSF).
The purpose of this paper is to develop and present the formulation of a methodology by which the effects of a simple isolated signalized intersection on a downstream two-lane highway section can be estimated in terms of PTSF, one of the two measures of effectiveness for Class I two-lane highways required to determine the Level of Service. The proposed methodology could be applied to the other measure, Average Travel Speed (ATS), as well but it is not addressed here. This paper does not address the effect of the signal on intersection traffic operations, for this the reader should refer the HCM signalized intersection chapter. For this paper, the intersection was assumed to be one with one through lane, where the primary demand volume at the intersection is carried on the through movement feeding the subject two-lane highway section. This assumption is reasonable if the left and right turn movements feeding the two-lane highway sections have low demand volumes, however the methodology presented can be expanded to include situations with significant turn movements.
A background is presented, discussing the relevant works and illustrating the problem in greater detail. Then the methodology for estimating the effects of upstream signals on two-lane highway operations is described. The authors’ conclusions and recommendations for future research are then offered.
Background
Previous traffic operations research involving two-lane highways investigated the effects of traffic control techniques such as passing lanes, turnouts, and passing zones [1-4]. However, no research has been done to determine the downstream effects of signalized intersections on PTSF.
TWOPAS and HCM 2000
It is important to understand the extent to which TWOPAS, a two-lane highway micro-simulation model, was implemented to develop the HCM 2000 two-lane highway procedure. It is difficult to collect field data over an entire highway section in order to quantify two-lane highway traffic operations. As a result, deterministic two-lane highway procedures rely heavily upon TWOPAS to quantify the relationship between two-lane highway characteristics and operations.
After some calibration of TWOPAS to observed field conditions, TWOPAS was run many times for different combinations of a wide range of highway conditions. The output of these simulation runs was used as the data to develop the parameters used in the HCM 2000 two-lane highway procedure, and this procedure predicts the level of service (LOS) of the facility through estimates of PTSF and ATS.
PTSF Measurement in TWOPAS
TWOPAS can be used to estimate the performance measures for a two-lane highway section and one of these measures is “Overall % time not in state 1.” This performance measure is taken over the space of the facility and is the TWOPAS measure of PTSF, which was used to develop the HCM 2000 two-lane highway procedure.
TWOPAS does offer a more disaggregate measure of PTSF, percent impeded (PI). The difference between PI and PTSF is that PTSF is a measure of the proportion of time that vehicles are in the state of following as they progress down the highway section [5]. In contrast, PI is a measure of the proportion of vehicles that are in the state of following for smaller subsections, where a PI measure is given for each subsection. A detailed picture of how PTSF varies along the length of the facility can be obtained by specifying many subsections. During the course of this research it was found that the average of the TWOPAS PI measurements, taken over the length of the facility, is within 3% of the PTSF value output by TWOPAS. The average of the PI measurements was calculated as a weighted average, consistent with Equation 20-23 in the HCM 2000 for aggregating PTSF across multiple highway sections [1].
Given the proximity of the aggregated PI over the highway section and the PTSF of the highway section, the measurement PI can be used as a reliable measure of how PTSF varies over the highway section. This is significant because the approximate downstream distance at which traffic operations return to normal, as measured by PTSF, is needed and this can be done using PI.
TWOPAS Sensitivity to Upstream Effects
To illustrate the potential effects of a signalized intersection on two-lane highway operations, two types of TWOPAS runs were made with four replicate runs for each. This sample size, or number of replicate runs, was selected because it results in a mean PTSF with a 95% confidence interval of +/-10% of the mean. The condition with no signalized intersection is represented by assuming randomly distributed headways for entering traffic. The distribution of headways is defined in TWOPAS through the parameter, entering percent following (EPF). When assuming random headways, this parameter is calculated using a cumulative negative exponential distribution of headways less than 3.0 seconds, shown in Equation 1, consistent with the HCM 2000 definition of vehicles following [1]. A value of EPF = 40% was used for the condition with no signalized intersection, assuming a volume of 600 vph. A higher value for EPF = 60%, was used to represent the situation where a signalized intersection is present and modifying the headway distribution of the traffic stream entering the two-lane highway. This value for EPF was decided upon based on field data and research determining feasible values for EPF. The method for determining EPF is discussed later in the methodology section, where discussion is given regarding the validity of the EPF values. A 47 km section of highway was simulated using TWOPAS with the following conditions:
· Directional volume = 600 vph
· No heavy vehicles
· 0% no-passing zones
· level terrain (i.e., no vertical or horizontal curves)
· 50/50 directional split
· desired speed and speed standard deviation were set equal to those used to develop the HCM 2000 procedures and can be found in the NCHRP 3-55(3) Task 6 report [5].
(1)
Where
q hourly flow rate of traffic entering the two-lane highway (veh/hr) and
t headway criteria used to define when vehicles are following (3.0 sec).
Figure 1 shows the PI as it varies along the facility. To maintain consistency with the HCM 2000, the y-axis on Figure 1 was labeled PTSF instead of PI [1]. This convention is maintained throughout this paper for all figures illustrating how PTSF varies along the length of a highway and for all references to these figures. However, the actual values shown in the figure were those output by TWOPAS as PI, which are a consistent measure of PTSF variation along a highway section [5].
In this paper, it is assumed that it is appropriate to represent the effects of a signalized intersection through the EPF parameter, as long as the percent following immediately downstream of a signalized intersection can be determined. Note that the first PTSF values on Figure 1 are different than what was entered for EPF = 60. This was investigated further by reducing the size of the subsections from 0.5 km to 30 meters and reducing the highway length to 3000 meters. TWOPAS output of PI and percent following (PF) were compared, where a measurement of PF is the percentage of vehicles following at headways of 3.0 seconds or less at specific points on the highway, similar to entering percent following, EPF. It was found that the PF value at the first observation interval was 59, given a value of 60 for entering percent following. This suggests that the entering percent following is being modeled correctly. It was also found that the difference in PI and EPF persisted. This can be explained by realizing that the measurement of PI is not the same as PF, as can be seen from their descriptions above.
It could also be expected that the measurements in Figure 1 for EPF-60 would first decrease because of passing and platoon dispersion and then increase because of natural bunching that occurs on two-lane highways. This decrease would only occur if passing maneuvers and platoon dispersion occurred more quickly than vehicles catching up to the platoon. Conditions such as these are not likely to exist because vehicles are less likely to pass when in a platoon and because of higher volume conditions that would typically exist where a traffic signal is operating.
For the simulation conditions described above for the TWOPAS runs shown in Figure 1, the PTSF values reported by TWOPAS for the highway section with and without a signal were 67 and 60, respectively. Figure 1 also shows this difference between the two-lane highway operations with differing EPF values. This difference in traffic operations indicates that there is an interaction between two-lane highway PTSF and entering traffic conditions resulting with and without a signalized intersection. While the difference in the PTSF values is not very remarkable, it is important to note that the relative difference would increase as the highway section length decreased. Note that if the highway were 10 km in length, the proportional difference in area under the two curves relative to the area under the low curve would be larger. Given the potential impacts of signalized intersections on two-lane highway operations, it is important to investigate these impacts further and to develop a possible methodology whereby these impacts can be assessed.
Methodology
The analysis of two-lane highway sections affected by signalized intersection operations can be broken down into three steps. First, determine the percentage of vehicles following, EPFa, where ‘a’ denotes a location immediately downstream of the signalized intersection. Second, estimate the PTSF for the downstream highway section with the upstream signalized intersection, PTSFsig, using TWOPAS. Third, estimate the level-of-service based on the criteria suggested in the HCM 2000 two-lane highway analysis procedure. The first two steps are discussed in detail in this paper. For the third step, refer to the HCM 2000 [1].
The mathematical relationships shown in this paper are limited to the conditions below.
· No pedestrian traffic
· Uniform arrivals
· No shared lanes
· Intergreen time is assumed equal to the lost time
· Two phases
· No passing lanes
· No lane drops
· Saturation flow rate of 1800 pcphpl
· 50/50 directional split
Additional conditions such as three phase signal timing or shared lanes can also be included using the same mathematical relationships, though with some modifications.
Step 1: Determining Entering Percent Following (EPFa) Downstream of Signal
Estimation of the percentage of traffic following, EPFa, is based on a flow profile immediately downstream of the signalized intersection at location A shown in Figure 2. Because of the immediate downstream location of A, no platoon dispersion model is needed to augment estimation of EPFa. As shown in the figure, there are three movements that contribute to the flow profile. Movement 1 is the primary contributing movement, while the others are secondary. Also shown in Figure 2 is the flow profile representing three basic flow states at A and they are defined as follows:
· First state: discharged from the through movement queue during the first phase;
· Second state: discharged from the through movement without a queue plus any right-turns-on-red executed during the first phase; and
· Third state: discharged from the right and left turn movements during the second phase.
Third state traffic flow is a simplistic representation of how traffic is actually discharged from the right and left turn movements. This was justified by the assumption that these flows would be minor compared to the through movement.
Entering percent following at location A shown in Figure 2 (EPFa) can be estimated using Equation 2:
(2)
Where
VFa total number of vehicles following per cycle at location A (veh),
VFi total number of vehicles following per cycle from movement i (veh), and
Va total number of vehicles per cycle at location A (veh).
Because Va is the summation of the cycle-by-cycle volumes from movements 1, 2, and 3, it can be determined if volumes for movements 1, 2 and 3 and the cycle length are known. This leaves the estimation of VFa, the number of vehicles following at location A, which can be estimated by movement.
Vehicles following in movement one
Movement one is discharged during flow states one and two. Because vehicles discharged during state one are in a platoon, it can be assumed that all of the queued vehicles are in a platoon at location A and are following except the platoon leader, as represented in Equation 3. As tQ1 increases, the number of vehicles following per cycle for movement 1 increases. Furthermore, tQ1 increases as the difference between C and g1, the red time for movement 1, increases. As a result, as the g/C ratio for movement 1 decreases, the number of vehicles following, VF1, increases resulting in an increase in EPFa. Note that Equation 3 is based on a deterministic queue length model, consistent with queue length equations used in the HCM 2000 signalized intersection analysis procedure. Stochastic queue length models could be used instead to provide more realistic representations of the effects of random vehicle arrivals on queue length.