1 Transportation Research Record: Journal of the Transportation Research Board, No. 2395, Transportation Research Board of the National Academies, Washington, D.C., 2013, pp. 1–11. DOI: 10.3141/2395-01 Department of Civil, Construction, and Environmental Engineering, Marquette University, 1515 West Wisconsin Avenue, Milwaukee, WI 53233. Current affiliation: Faculty of Civil Engineering, Damascus University, Damascus, Syria. [email protected]. which the event commenced, provides a more accurate representation of breakdown characteristics (6 ). Visual inspections of each event have been used elsewhere to detect the onset of a breakdown (7, 8). In most studies, the QDF was defined as the long-run average flow during the breakdown, although there were some minor differences, such as the deletion of the first 5-min interval (1). However, some differences were observed in the definition of the prebreakdown flow (PBDF). In Hall and Agyemang-Duah, the PBDF was based on periods of consecutive intervals, and the duration of the PBDF extended backward from the queue start point until the difference in the means of the flow rates for two successive periods became sig- nificant (1). In the Banks study, the prequeue flow was considered to begin at the last identifiable flow increase or decrease before the QDF period (3). Zhang and Levinson assumed that the prequeue period began when the flow at the bottleneck exceeded its long-run average QDF and ended when the flow dropped below the long-run average QDF (2). Other studies measured the PBDF over fixed time intervals, such as 1, 5, or 15 min immediately before a breakdown (4–6 ). Researchers have documented that the QDF is considerably lower than the flow observed just before a breakdown. Hall and Agyemang-Duah found a drop in flow of 5% to 6% at one freeway location in Mississauga, Ontario, Canada (1). Zhang and Levinson concluded that the drop in traffic flow attributable to queue formation ranged from 2% to 11% at two-, three-, and four-lane freeway sec- tions in the Twin Cities metropolitan area in Minnesota (2). Persaud et al. found that the QDF was 10% to 26% lower than the PBDF on three freeway locations in Toronto, Ontario, Canada (7 ). Yeon et al. examined four bottleneck flows at eight freeway sections in Philadelphia, Pennsylvania (4). The results of the study showed that the QDF was 0.5% to 6% less than the PBDF. Banks found that the drop in the PBDF ranged from 1.8% to 15.4% at 25 freeway bottlenecks in San Diego, California; Seattle, Washington; and Minneapolis–Saint Paul, Minnesota (3). Brilon et al. modeled capacity for three-lane freeway sections in Germany with a product limit estimate equation (9). The average drop in capacity after a breakdown was estimated to be 1,180 vehicles per hour (vph). Some studies have actually reported or discussed a potential increase in flow after a breakdown. Ringert and Urbanik noticed that some lanes experienced an increased flow rate after a breakdown (10). Sahin and Altun examined the behavioral theory in traffic at a hori- zontal curve bottleneck in Istanbul, Turkey (11). The study indi- cated that the flow rate increased in the shoulder lane and decreased in the median lane during fully congested conditions. Banks found that the bottleneck flow decreased at a breakdown in only two- thirds of the studied cases; therefore, the flow did not necessarily decrease for all breakdowns (12). The possibility of an increase in bottleneck flow for the entire section after a breakdown needs to be investigated. Additionally, although a loss of flow is predictable because of the traffic turbulence within the queue and the associated Breakdown Maturity Phenomenon at Wisconsin Freeway Bottlenecks Amjad Dehman This study aimed to evaluate the freeway breakdown mechanism and capacity inventory at four bottlenecks on the Milwaukee County, Wisconsin, freeway system. Bottleneck flow was considered for two capacity regimes: a free-flow capacity regime, defined by the pre- breakdown flow (PBDF), and a congested-flow capacity regime, defined by the queue discharge flow (QDF). More than 1,070 break- downs were used in the analysis. The study focused on the change in the traffic flow after a breakdown, not only across different sites but from one breakdown to another at the same site. The breakdown behavior of individual lanes was also considered. Furthermore, the correlation between the QDF and the PBDF was also investigated. Some breakdowns resulted in a bottleneck flow increase for the entire section, rather than a flow drop. Therefore, breakdowns were catego- rized into two types: mature breakdowns and immature breakdowns. The concepts of the flow increase phenomenon, breakdown maturity, and capacity inventory were introduced and discussed. The recent trend in the definition of freeway capacity considers two capacities under two regimes: the free-flow regime (before a break- down) and the congested-flow regime (after a breakdown). How- ever, differences have been noticed when the onset of breakdowns is determined and, therefore, when each capacity regime is defined. Hall and Agyemang-Duah used an occupancy-to-flow ratio of 1.1 as the criterion to identify the start of a queue; the queue discharge flow (QDF) period ended when the ratio fell below 1.1 (1). For breakdown identification, Zhang and Levinson used two occupancy thresholds: larger than 25%, which indicated congested conditions, and less than 20%, which indicated uncongested conditions (2). The two occupancy thresholds were set after a comparison with the visual inspection results. Banks defined periods of QDF as beginning with an abrupt decrease in speed at or just upstream of the bottle- neck; the QDF ended when the speed had shifted back to the free- flow speed (3). Many researchers have used a fixed speed threshold to define the start of a breakdown. For example, Yeon et al. used a speed threshold of 50 mph to define a breakdown (4), and Lorenz and Elefteriadou used a threshold of 56 mph (5). However, the funda- mental speed–flow diagram is well known for its scatter and ran- domness. Therefore, the Shawky and Nakamura approach, which examines each breakdown individually and identifies the speed at
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Transportation Research Record: Journal of the Transportation Research Board, No. 2395, Transportation Research Board of the National Academies, Washington, D.C., 2013, pp. 1–11.DOI: 10.3141/2395-01
Department of Civil, Construction, and Environmental Engineering, Marquette University, 1515 West Wisconsin Avenue, Milwaukee, WI 53233. Current affiliation: Faculty of Civil Engineering, Damascus University, Damascus, Syria. [email protected].
which the event commenced, provides a more accurate representation of breakdown characteristics (6). Visual inspections of each event have been used elsewhere to detect the onset of a breakdown (7, 8).
In most studies, the QDF was defined as the long-run average flow during the breakdown, although there were some minor differences, such as the deletion of the first 5-min interval (1). However, some differences were observed in the definition of the prebreakdown flow (PBDF). In Hall and Agyemang-Duah, the PBDF was based on periods of consecutive intervals, and the duration of the PBDF extended backward from the queue start point until the difference in the means of the flow rates for two successive periods became sig-nificant (1). In the Banks study, the prequeue flow was considered to begin at the last identifiable flow increase or decrease before the QDF period (3). Zhang and Levinson assumed that the prequeue period began when the flow at the bottleneck exceeded its long-run average QDF and ended when the flow dropped below the long-run average QDF (2). Other studies measured the PBDF over fixed time intervals, such as 1, 5, or 15 min immediately before a breakdown (4–6).
Researchers have documented that the QDF is considerably lower than the flow observed just before a breakdown. Hall and Agyemang-Duah found a drop in flow of 5% to 6% at one freeway location in Mississauga, Ontario, Canada (1). Zhang and Levinson concluded that the drop in traffic flow attributable to queue formation ranged from 2% to 11% at two-, three-, and four-lane freeway sec-tions in the Twin Cities metropolitan area in Minnesota (2). Persaud et al. found that the QDF was 10% to 26% lower than the PBDF on three freeway locations in Toronto, Ontario, Canada (7). Yeon et al. examined four bottleneck flows at eight freeway sections in Philadelphia, Pennsylvania (4). The results of the study showed that the QDF was 0.5% to 6% less than the PBDF. Banks found that the drop in the PBDF ranged from 1.8% to 15.4% at 25 freeway bottlenecks in San Diego, California; Seattle, Washington; and Minneapolis–Saint Paul, Minnesota (3). Brilon et al. modeled capacity for three-lane freeway sections in Germany with a product limit estimate equation (9). The average drop in capacity after a breakdown was estimated to be 1,180 vehicles per hour (vph). Some studies have actually reported or discussed a potential increase in flow after a breakdown. Ringert and Urbanik noticed that some lanes experienced an increased flow rate after a breakdown (10). Sahin and Altun examined the behavioral theory in traffic at a hori-zontal curve bottleneck in Istanbul, Turkey (11). The study indi-cated that the flow rate increased in the shoulder lane and decreased in the median lane during fully congested conditions. Banks found that the bottleneck flow decreased at a breakdown in only two-thirds of the studied cases; therefore, the flow did not necessarily decrease for all breakdowns (12). The possibility of an increase in bottleneck flow for the entire section after a breakdown needs to be investigated. Additionally, although a loss of flow is predictable because of the traffic turbulence within the queue and the associated
Breakdown Maturity Phenomenon at Wisconsin Freeway Bottlenecks
Amjad Dehman
This study aimed to evaluate the freeway breakdown mechanism and capacity inventory at four bottlenecks on the Milwaukee County, Wisconsin, freeway system. Bottleneck flow was considered for two capacity regimes: a free-flow capacity regime, defined by the pre-breakdown flow (PBDF), and a congested-flow capacity regime, defined by the queue discharge flow (QDF). More than 1,070 break-downs were used in the analysis. The study focused on the change in the traffic flow after a breakdown, not only across different sites but from one breakdown to another at the same site. The breakdown behavior of individual lanes was also considered. Furthermore, the correlation between the QDF and the PBDF was also investigated. Some breakdowns resulted in a bottleneck flow increase for the entire section, rather than a flow drop. Therefore, breakdowns were catego-rized into two types: mature breakdowns and immature breakdowns. The concepts of the flow increase phenomenon, breakdown maturity, and capacity inventory were introduced and discussed.
The recent trend in the definition of freeway capacity considers two capacities under two regimes: the free-flow regime (before a break-down) and the congested-flow regime (after a breakdown). How-ever, differences have been noticed when the onset of breakdowns is determined and, therefore, when each capacity regime is defined. Hall and Agyemang-Duah used an occupancy-to-flow ratio of 1.1 as the criterion to identify the start of a queue; the queue discharge flow (QDF) period ended when the ratio fell below 1.1 (1). For breakdown identification, Zhang and Levinson used two occupancy thresholds: larger than 25%, which indicated congested conditions, and less than 20%, which indicated uncongested conditions (2). The two occupancy thresholds were set after a comparison with the visual inspection results. Banks defined periods of QDF as beginning with an abrupt decrease in speed at or just upstream of the bottle-neck; the QDF ended when the speed had shifted back to the free-flow speed (3). Many researchers have used a fixed speed threshold to define the start of a breakdown. For example, Yeon et al. used a speed threshold of 50 mph to define a breakdown (4), and Lorenz and Elefteriadou used a threshold of 56 mph (5). However, the funda-mental speed–flow diagram is well known for its scatter and ran-domness. Therefore, the Shawky and Nakamura approach, which examines each breakdown individually and identifies the speed at
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speed reduction, additional research is needed into the factors that create the wide range of flow drops after breakdowns, as reported by many studies at many sites. The focus of this paper is to examine the change in freeway bottleneck flow after a breakdown and the phenomena associated with this change.
Data ColleCtion anD StuDy SiteS
All the data used in this study were retrieved from the WisTransPortal project webpage. This website, supported by the Wisconsin Depart-ment of Transportation and maintained by the Traffic Operations and Safety Laboratory of the University of Wisconsin–Madison, provided detailed basic traffic stream characteristics (5-min occu-pancy, volume, and speed) at locations of interest on the Milwaukee, Wisconsin, freeway system. Because of the nature of this study, and to ensure its accuracy, bottlenecks were selected that yielded many breakdowns.
Four bottleneck sites were selected. The location of each site, the number of breakdowns, and other information are given below. The detailed site geometry and the location of the detectors are illustrated in Figure 1.
Sites 1 and 2. I-894 (US-45) northbound at Belton Rail Road:– Activation period: January 2004 to April 2008;– Peak time: evening for Site 1, morning for Site 2; and– Number of breakdowns: 229 for Site 1, 332 for Site 2;
Site 3. I-43 southbound at Locust Street:– Activation period: November 2006 to April 2008;– Peak time: morning; and– Number of breakdowns: 111; and
Site 4. I-894 (US-45) southbound at Belton Rail Road:– Activation period: June 2004 to December 2007;– Peak time: evening; and– Number of breakdowns: 385.
Only breakdowns under dry and clear weather conditions were used in the analysis. Sites 1 and 2 belong to the same freeway segment but were considered as separate sites, one correspond-ing to the morning peak, and one corresponding to the evening peak. This treatment was recommended because the visibility, the light conditions, the driving habits, the lane–flow distribution, the vehicle mix, and the characteristics of the driver population can all vary depending on the time of day, even at the same freeway location.
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FIGURE 1 Study sites summary and detector deployment: (a) Sites 1 and 2, (b) Site 3, and (c) Site 4 (distances not scaled; north is to right).
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The four sites fulfilled all the bottleneck boundary requirements. In Figure 1, the detector stations marked “B” are the bottleneck loca-tions at which the flows were measured. The detector stations marked “D” were used to confirm that the downstream operations and off-ramps represented free-flow conditions. The detector stations marked “U” were used to confirm the queue formation and congestion spill-age upstream of the bottleneck. The queue discharge speed is usually highly variable within a bottleneck. The queue discharge speed was also measured at the stations marked “B,” and the speed was higher at the downstream stations and lower at the upstream stations.
Freeway BreakDown DeFinition anD CharaCteriStiCS
Freeway capacity flow is usually introduced as an equivalent flow rate, which is aggregated and averaged across all section lanes and given in vph per lane (vphpl). All the sites examined in this study
were three-lane freeway sections. A weighted average by volume was used to compute the average section speed, because the vol-umes were different across the lanes. Similarly to definitions found in the literature, a breakdown was defined as occurring when the traffic speed dropped below a critical free-flow speed for at least 15 min while the speed at the downstream detector station remained at or above this critical speed level.
The critical free-flow speed was identified through the fundamen-tal speed–flow diagram. The speed–flow diagram consists of two regimes: an uncongested regime, illustrated by a progressive relation-ship, and a congested regime, illustrated by a regressive relationship; these regimes are illustrated in Figure 2. The critical free-flow speed was identified as the speed observed at the end of the uncongested regime (the end of the progressive branch). The average critical free-flow speeds for the examined sites are provided in Table 1. The fundamental speed–flow diagram is well known for its scatter and randomness. Consequently, the use of a fixed critical speed threshold can be misleading because the actual critical free-flow speed point
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FIGURE 2 Breakdown speed–flow relationships at Site 2: (a) mature breakdown with sharp speed drop, (b) mature breakdown with smooth speed transition, and (c) immature breakdown with sharp speed transition.
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TABLE 1 Breakdown Characteristics at Each Site and in Each Lane
Lane Type Site 1 Site 2 Site 3 Site 4
Average 15-min PBDF (vphpl)
Median lane 2,165 2,397 2,058 2,350
Middle lane 1,836 2,003 4,240a 2,086
Shoulder lane 1,486 1,627 Ramp merge area 2,311
All lanes 1,829 2,009 2,099 2,249
Average QDF (vphpl)
Median lane 2,006 2,121 2,024 2,259
Middle lane 1,760 1,843 4,035a 1,895
Shoulder lane 1,644 1,703 Ramp merge area 2,169
All lanes 1,803 1,889 2,020 2,108
Average Bottleneck Flow Change (%)b
Median lane −7.3 −11.5 −1.7 −3.9
Middle lane −4.1 −8.0 −5.7a −9.2
Shoulder lane +10.6 +4.7 Ramp merge area −6.1
All lanes −1.4 −6.0 −3.8 −6.3
Average 15-min Prebreakdown Free-Flow Speed (mph)
Median lane 55.8 54.2 54.9 57.8
Middle lane 52.9 51.4 53.4 51.9
Shoulder lane 54.5 53.8 51.3 47.8
All lanesc 54.5 53.2 53.2 52.6
Average Queue Discharge Speed (mph)
Median lane 40.1 39.8 41.6 45.4
Middle lane 39.4 38.6 39.1 39.1
Shoulder lane 43.9 43.6 34.9 34.9
All lanesc 41.0 40.7 38.5 39.9
Average Speed Drop (%)d
Median lane −28.1 −26.6 −24.2 −21.5
Middle lane −25.5 −24.9 −26.8 −24.7
Shoulder lane −19.4 −19.0 −32.0 −27.0
All lanes −24.8 −23.5 −27.6 −24.1
Note: Breakdown characteristics included in this table were recorded on dry and clear days. Average breakdown durations for Sites 1, 2, 3, and 4 are 67, 107, 62, and 47 min, respectively.aThe detector station used at Site 3 was located upstream of the ramp entrance; therefore, the exact lane flow distribution downstream of the ramp was not obtainable. The traffic flow was estimated for the entire merge influence area (i.e., ramp flow + shoulder lane flow + middle lane flow).bAverage flow change after breakdown = (average QDF − average 15-min PBDF)/average 15-min PBDF.cThe speed of each lane was weighted by the volume of that lane when the average speed of the entire section (all lanes) was computed. The all-lanes weighted average speed was computed over all breakdowns.dAverage speed drop = (average QDF speed − average PBDF speed)/average PBDF speed.
may be shifted mistakenly in the congested regime in some circum-stances, especially when the speed drops gradually without a clear, sharp decrease. In this study, each breakdown was analyzed sepa-rately to determine the critical free-flow speed. The breakdown was determined to have ended when the speed went back to the critical free-flow speed level for a sustained amount of time (at least 5 min). The time between the beginning and the end of a breakdown was referred to as the breakdown duration. The complete mechanism of the breakdown shown in Figure 2a is further illustrated in Figure 3.
The PBDF was defined as the 15-min hourly equivalent volume observed just before the beginning of a breakdown. The average
QDF was defined as the hourly equivalent volume averaged over all 5-min intervals during the entire breakdown. The QDF was not based on a consistent time interval because breakdown durations vary from day to day. The basic breakdown characteristics for each site and for each lane are summarized in Table 1.
all-laneS BreakDown analySiS
Table 1 indicates that the average drop in flow at the four sites ranged from −1.4% to −6.3% when computed for the entire section. This range is compatible with findings from previous studies. Although all the sites experienced a cumulative drop in flow after a breakdown (on average), further analysis revealed that some individual breakdowns might result in a total flow increase for the entire section.
Figure 4 plots the QDF versus the 15-min PBDF at each of the study sites. Each point in Figure 4 represents one breakdown, and the flows are aggregated across all lanes in vphpl. The plots illustrate a posi-tive relationship between the QDF and the 15-min PBDF: the QDF generally increased as the 15-min PBDF increased. Figure 5 plots the change in flow after a breakdown versus the observed 15-min PBDF. These plots illustrate a negative relationship between the change in flow after a breakdown and the 15-min PBDF: the value of the change in flow decreased algebraically as the 15-min PBDF increased.
The dashed lines in Figures 4 and 5 represent the points (or theo-retical breakdowns) at which the QDF is exactly the same as the 15-min PBDF. The points to the top of those dashed lines represent breakdowns with a QDF larger than the 15-min PBDF; the points to the bottom of the dashed lines illustrate breakdowns with a QDF lower than the 15-min PBDF. There were many breakdowns for which the bottleneck flow increased after the breakdown, as indi-cated by the points above the dashed lines. Flow increases were observed more often at low PBDF rates. Positive changes in flow were more apparent at Sites 1 and 2 than at Sites 3 and 4. However, in all cases, negative changes (reductions in flow) were more frequent and of larger magnitude than positive changes (increases in flow); this finding explains why the average change in flow computed in Table 1 was negative overall for all sites.
Given that freeway capacity is a stochastic phenomenon that is influenced by many factors, the Pearson’s correlation coefficients in Figure 4 indicate a reasonably moderate positive correlation between the QDF and the PBDF. The QDF is expected to be higher at higher PBDFs. The change in flow after a breakdown (as a percentage) had a stronger but negative correlation with the PBDF, as demonstrated in Figure 5. Therefore, higher PBDF values resulted in sharper flow reductions after the breakdown (flow drop inflation). Although an increased PBDF involved a sharper flow reduction after the break-down, the continuous positive correlation between the PBDF and the QDF indicates that the QDF still increased even with the flow drop inflation. This finding means that an increasing PBDF overwhelmed the resulting flow drop inflation, and the net flow after the breakdown (the QDF) was still expected to be higher at higher PBDFs.
interpretationS oF Change in BottleneCk Flow
negative Changes in Bottleneck Flow after Breakdown
Congestion not only reduces traffic speed but also affects traffic adversely in several ways. Drivers who travel under a congested
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FIGURE 3 Mechanism of breakdown, based on Figure 2a (15-min PBDF = average of three 5-min observations).
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FIGURE 4 QDF versus 15-min PBDF: (a) Site 1, (b) Site 2, (c) Site 3, and (d) Site 4. Direction of arrows refers to rise in breakdown maturity level. Each point represents a breakdown. Flows are aggregated across lanes. Average correlation coefficient across all sites is .478.
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regime may be required in some instances to come to a complete stop. Those stops propagate upstream in the form of successive shock waves that impede traffic movement. The shock waves, in turn, cause a blockage for approaching traffic and a temporal starvation for the downstream section. The blockages and starvations impede the full utilization of freeway capacity. The traffic flow under congestion is very sensitive to vehicle acceleration and deceleration, which vary widely depending on the vehicle’s classification, length, weight, and manufacturer specifications. In summary, speed reduction, shock waves, blockage and starvation in the queue, maneuverability con-cerns, and vehicle acceleration–deceleration capabilities all adversely affect the full utilization of the freeway facility, and the final result is a significant reduction in traffic flow. Obviously and intuitively,
an increase in the PBDF or in the utilization of the freeway leads to intensified competition in the traffic stream after the breakdown, and the result is a sharper drop in flow, as demonstrated by Figure 5. Breakdowns that yield a total drop in flow across the entire freeway section are referred to here as mature breakdowns.
positive Changes in Bottleneck Flow after Breakdown
Traffic volume is not usually distributed equally across lanes, and differences between lanes sometimes become substantial. Conse-quently, at the onset of congestion, some lanes may be fully utilized
Dehman 7
and transfer maturely to the congestion regime. Other lanes may be underutilized and transfer immaturely to the congestion regime because of their proximity to the fully utilized lanes. Drivers who travel on the underutilized lanes reduce their speed if they see con-gestion on the adjacent utilized lanes, even though the flow rate in those drivers’ lanes is not high enough to cause congestion or activate the breakdown. This behavior is a result of drivers being worried about nearby vehicles and being affected by surrounding conditions; therefore, driver discomfort and anxiety can transfer easily from one lane to another. At the onset of congestion, drivers within the queue, as well as upstream approaching drivers, real-ize that there is unused capacity in the underutilized lanes. Con-sequently, drivers may decide to diverge into the underutilized lanes, which have less turbulence, higher speed, and extra spaces. Therefore, the underutilized lanes can suffer from a sudden moder-ate decrease in the speed after the breakdown but with a possibility of a flow increase.
Although congestion turbulence in the fully utilized lanes results in a flow reduction, as explained earlier, demand increase and lane changing into the underutilized lanes result in a sudden increase in flow in these lanes. In some extreme cases, in which one or some lanes are utilized very poorly before the breakdown, the flow gain in the underutilized lanes may create a significant flow increase that can weigh or even exceed the flow reduction observed in the fully utilized lanes. This situation yields a total increase in section flow after the breakdown. The flow increase after a breakdown is not only caused by the shift in lane usage but also by an increase in the approaching flow that arrives at the section from upstream. Breakdowns that yield a total flow increase across the entire freeway section are referred to here as immature breakdowns.
This discussion explains the observed immature breakdowns (flow increases) in Figures 4 and 5. The maturity phenomenon also explains why a flow increase is usually observed at the lowest aggregated (sec-tion) flow rates (as shown in Figure 5). Low aggregated flow rates occur when capacity utilization and lane flow distribution before the breakdown are very poor. The percentages of the observed immature breakdowns were 35.4%, 16.3%, 14.4%, and 8.8% of all breakdowns observed at Sites 1, 2, 3, and 4, respectively. The lower frequency of immature breakdowns at Sites 3 and 4 is attributed to better lane flow distribution and more adequate utilization across all lanes at these sites.
The measuring of the QDF immediately after the breakdown may also magnify the increase in bottleneck flow after a breakdown. The use of the 15-min or 5-min QDF immediately after the breakdown resulted in more observations of flow increases. For example, of the 332 breakdowns at Site 2, there were 54 observations of increased bottleneck flow (16.3%) when the typical long-run average QDF was compared with the 15-min PBDF. This number of observa-tions increased to 130 (39.2%) and 149 (44.9%) when the imme-diate 15-min QDF and the immediate 5-min QDF, respectively, were used. This finding reveals the instantaneous and the imme-diate response of drivers who diverge to the underutilized lanes after a breakdown and indicates that the turbulence then infects and spreads over all lanes more equally.
per lane BreakDown analySiS
Figure 6 illustrates the speed–flow relationships at Site 2 for immature breakdowns and mature breakdowns. The relationships are given for each lane individually and for the whole section
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FIGURE 6 Speed–flow relationships at Site 2 when freeway broke down immaturely: (a) median lane, (b) middle lane, (c) shoulder lane, and (d) all lanes. Parts (a) to (c) are based on Part (d ).
(continued on next page)
8 Transportation Research Record 2395
and are based on 10 breakdowns. When the whole section broke down immaturely, the median lane appeared mainly to break down maturely (Figure 6a), as indicated by the left-shifted congested regime that shows a flow decrease after the breakdown. The middle lane tentatively broke down maturely and immaturely (Figure 6b). The shoulder lane appeared to break down immaturely, as indicated by the right-shifted congested regime that shows a flow increase after the breakdown (Figure 6c). Because the flow increase in the immature lane (or lanes) exceeded the drop in flow in the mature lane (or lanes), the whole section broke down immaturely and experienced a total increase in flow associated with a right-shifted congested regime (Figure 6d). During mature breakdowns, the median and middle lanes appeared mainly to break down maturely, and the shoulder lane tenta-tively broke down maturely and immaturely. In this case, the decrease in flow in the mature lane (or lanes) exceeded the increase in flow in the immature lane (or lanes), if any, and the whole section broke down maturely and experienced a total decrease in flow associated with a left-shifted congested regime (Figure 6h).
The same mechanism explained in Figure 6 was observed at Site 1. However, at Sites 3 and 4, the shoulder lane was heavily utilized and was competing with the on-ramp flow; this situation resulted in an area of turbulence on the right-hand side of the freeway. Therefore, the shoulder and middle lanes mainly broke down maturely, with sharp drops in both speed and flow. The median lane broke down immaturely on some occasions; this situation resulted in some obser-vations of increased flow. The flow increase in the under utilized lane (or lanes) sometimes overweighed the flow decrease in the fully uti-lized lane (or lanes) and resulted in occasional immature breakdown observations for the whole section.
Sites 1 and 2 include a crest vertical curve alignment: an overpass above a railroad line. To quickly and confidently traverse the verti-
cal curve, drivers are inclined to merge to the fastest lanes and shy away from the shoulder lane and its disturbing ramp junctions. The flow concentration in the fastest lanes generates a left-sided turbu-lence, which activates the breakdown. The breakdown mechanism is different at Sites 3 and 4, at which the ramp traffic merges into a heavily utilized shoulder lane and causes undesirable turbulence in the merge influence area. In this case, the right-sided turbulence stimulates the congestion. At all sites, the movement of vehicles away from the turbulence area moderates the observed reductions in both speed and flow. From the data in Table 1 and on the basis of the Site 2 averages, the median and middle lanes generally experienced a substantial drop in speed (−26.6% and −24.9% for each lane, respectively) with a significant reduction in flow after the breakdown (−11.5% and −8.0% for each lane, respectively). Additionally, the underutilized shoulder lane experienced a milder speed reduction (−19.0%), although the flow increased significantly (+4.70%). The Site 1 averages also showed similar trends for all three lanes. At Sites 3 and 4, the shoulder and middle lanes experienced a substantial drop in speed, with a significant reduction in flow after the breakdown. How-ever, the median lane, because it was not directly impacted by the ramp traffic friction, experienced a milder reduction in speed, with an insignificant reduction in flow.
CapaCity inventory
Figure 7a illustrates how the QDF changes according to the PBDF for the shoulder lane at Sites 2 and 4. The same figure also plots, in vph, the gain (or the loss) in the flow after the breakdown. PBDFs were grouped into successive bins, and the QDF and the flow gains or losses were averaged over all values within each PBDF
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FIGURE 6 (continued) Speed–flow relationships at Site 2 when freeway broke down maturely: (e) median lane, (f) middle lane, (g) shoulder lane, and (h) all lanes. Parts (e) to (g) are based on Part (h).
Dehman 9
bin. Although the flow gain diminished and the flow loss expanded as the PBDF increased, the QDF increased continuously at both sites. When the PBDF was in the range of 1,250 to 1,450 vph at Site 2, the shoulder lane gained around 300 to 190 vph, which is a significant addition and led to a QDF in the range of 1,550 to 1,640 vph (“Points A” in the figure). However, even with this significant addition, the QDF at Points A is significantly lower than the respective QDF at Points B (1,750 to 1,770 vph); these QDF values are associated with the highest PBDF values (1,850 to 2,000 vph) and the sharpest loss in flow (90 to 230 vph). Addition-ally, the shoulder overall average QDF at Site 2 (1,703 vph) is sig-nificantly larger than the QDF associated with Points A. Therefore,
the large addition or gain of flow after a breakdown was not capable of recapturing the capacity. Once a breakdown occurred, the speed dropped sharply, and shock waves impeded the traffic stream from completely reutilizing the wasted capacity. In conclusion, the late utilization of capacity (after a breakdown) was critically and sub-stantially less efficient than an early utilization of capacity (before a breakdown). Even at Site 4, the largest shoulder QDFs were associ-ated with the sharpest loss in flow at Points B. Therefore, the opti-mization of bottleneck capacity requires a breakdown at high flow rates even though this situation can be associated with magnified flow drops and no chance of flow gain after the breakdown. The trend demonstrated in Figure 7a was also generally apparent in the
FIGURE 7 Comparison of bottleneck flows at Sites 2 and 4: (a) shoulder lane (all plotted flows are for shoulder lane in vph) and (b) entire section. Zone A and Points A refer to QDFs below long-run average QDF; Zone B and Points B refer to QDFs above long-run average QDF (ave = average).
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shoulder, middle, and median lanes of all the sites (i.e., an increased PBDF magnified the drop in capacity but increased the QDF).
The long-run average QDF may be considered as the average bottleneck capacity at a particular site. Accordingly, the Zone A area in Figure 7a reflects the waste in capacity, and Zone B reflects the optimal utilization. The difference between the QDF in Zone A and that in Zone B is considerable at Sites 2 and 4. Traffic manage-ment schemes at a particular site should try to increase the number of optimal breakdowns and reduce the waste in capacity or the Zone A area.
The capacity of the shoulder lane at Site 2 appeared critically wasted in comparison to the Site 4 shoulder capacity. The shoulder lane reached a QDF of about 1,600 vph at Points A in Site 2, compared with 2,300 vph at Points B in Site 4. Zone B in the shoulder lane at Site 2 is associated with substantially lower QDFs when compared with Zone B at Site 4. Even the optimal Zone B at Site 2 is inefficient compared with the imperfect Zone A at Site 4. The early utilization and optimiza-tion of capacity in the shoulder lane at Site 4 generated this enormous capacity difference. This difference is magnified when Site 1 is com-pared with Site 4. This discussion reveals that unused capacity before a breakdown is not completely retrievable or recoverable.
Figure 7b compares Site 2 and Site 4 on the basis of the QDF aggregated over all lanes. Site 4 has a substantially higher capac-ity than Site 2. The average QDF at Site 4 is more than 200 vphpl greater than at Site 2 and represents significant capacity (600 vph per section). The optimal Zone B at Site 2 is inefficient compared to the imperfect Zone A at Site 4. Even at the overlapped PBDF values, Site 4 generates QDFs that are significantly higher than those at Site 2. According to the PBDF averages shown in Table 1, Site 4 has a proper lane flow distribution, which allows capacity to be early and adequately utilized across all lanes, including the shoulder. Site 2 has an improper lane flow distribution and a low utilization of the shoulder lane; this lane will be reutilized later during con-gestion but inefficiently. Therefore, the capacity utilization during congestion can be degraded if the PBDF is distributed improperly across lanes.
BreakDown Maturity in praCtiCe
The use of breakdown maturity in practice is now considered. Drivers usually behave spontaneously or according to their convenience. They are not advised of the bottleneck in advance and therefore do not avoid traversing a potential area of turbulence. This situation opens the scope for the initiation of new traffic management techniques that help redistribute traffic flow across lanes by reducing the wasteful or inefficient spontaneous behavior of upstream drivers or merging traffic.
For example, in the case of an on-ramp bottleneck (right-side tur-bulence), an overhead variable message sign could advise upstream drivers to switch to the fastest lanes (i.e., the middle and the median). This technique could result in better utilization of the median and middle lanes and leave capacity in the shoulder lane for ramp traffic. The message sent by the sign should moderately discourage drivers from traveling in the shoulder lane. Excessive divergence into the outer or faster lanes could generate another source of congestion. Therefore, the message could merely be “the shoulder lane is con-gested” or “the shoulder lane is expected to become congested,” and shoulder drivers should be left to decide whether to diverge into the other lanes. Another milder message could be “the left lanes are not congested.” Additionally, the whole system should be actu-
ated by predetermined thresholds of traffic characteristics, so the sign would turn off after a desired flow distribution was achieved. The sign could also adopt a cycling scheme, so that the sign would alternate between two phases: phase one (the message) and phase two (blank). The length of each phase should adapt to real-time traffic conditions. For example, if the shoulder lane occupancy exceeded a critical value, the system would lengthen the first phase. If the median occupancy approached a critical threshold, the system would prolong the second phase. Several detector stations before and throughout the bottlenecks would be needed to make such systems efficient.
In the case of congested middle and median lanes (left-side tur-bulence), the same system described above could be deployed but with different messages, such as “the left lanes are congested” or “the shoulder lane is not congested.” Additionally, ramp metering systems could perform another function and advise drivers who are merging into the mainline to stay in the shoulder lane to avoid the potential turbulence on the fastest lanes. A sign attached to the metering signal could say “merge and stay in the shoulder lane.”
From a geometric design perspective, an ideal flow distribution could also be enhanced by some rules, such as the avoidance of many successive ramps of the same type (on- or off-ramps), an increase in the distance between ramp junctions, and the flattening of vertical curves. The success of the previously mentioned potential applica-tions critically depends on the capabilities of intelligent transpor-tation systems and the complexity of their algorithms. In addition, such applications would involve many challenges in terms of driver adherence and safety.
ConCluSionS anD reCoMMenDationS
This study examined the change in bottleneck flow after break-downs at different sites and in different lanes within the same site, as well as from one breakdown to another. The Pearson correlation coefficient between the QDF and the 15-min PBDF at the same site ranged from .364 to .588, with an average of .478; the correlation between the change in bottleneck flow (%) and the 15-min PBDF ranged from −0.389 to −0.771, with an average of −0.606. On aver-age, the bottleneck flow after breakdowns at one site (Site 2) was −6.0% (a drop). However, through 332 breakdowns, the change in flow after breakdowns at the same site ranged from +14% to −20%; these figures show completely different behavior. Accord-ingly, freeway breakdowns were classified into two types: mature and immature. Mature breakdowns occurred when the available lanes were heavily or reasonably utilized before a breakdown, so the entire section experienced a flow reduction after the breakdown because there was insignificant unused capacity in all of the section lanes after the breakdown. Immature breakdowns occurred when some lanes were poorly utilized before a breakdown, so the entire section experi-enced a flow increase after the breakdown because extra capacity was still available for significant utilization after a breakdown.
Mature breakdowns can be characterized by different maturity lev-els. The maturity level of the breakdown is raised if early utilization of freeway capacity before the breakdown allows for a higher PBDF and therefore a higher QDF. An increase in breakdown maturity increases the QDF, although this magnifies the drop (%) in the PBDF.
The late utilization of capacity after a breakdown is critically incapable of recapturing the normal or average capacity. Free-way capacity is not completely retrievable after a breakdown, and the waste in capacity inventory can be substantial. The Highway Capacity Manual may address this influential subject through a new
Dehman 11
capacity adjustment factor that adjusts freeway capacity for lane utilization. An understanding of the concepts of breakdown matu-rity and capacity inventory is important because highway expansion projects usually take time and are limited by budget and right-of-way constraints.
This study proposed some traffic management techniques to deploy breakdown maturity concepts in practice. It is recommended that those techniques be evaluated. It is expected that rebalancing the traffic flow across lanes will have three major outcomes. First, the probability of a breakdown would be reduced by reducing the chance of an excessive traffic flow being concentrated on either side of the freeway. Second, if the traffic demand is excessively large and breakdown is inevitable, the ideal flow distribution would at least delay or retard the onset of the breakdown. Third, the maturity level of breakdowns would be raised, and so the PBDF and the QDF would both be increased.
reFerenCeS
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The Highway Capacity and Quality of Service Committee peer-reviewed this paper.
