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Study of freeway traffic near an off-ramp
Transportation Research Part A 36 (2002) 563–572 www.elsevier.com/locate/tra
Study of freeway traffic near an off-ramp Michael J. Cassidy *, Shadi B. Anani, John M. Haigwood Department of Civil and Environmental Engineering, Institute of Transportation Studies, University of California, 109 McLaughlin Hall, Berkeley, CA 94720, USA Received 3 July 2000; received in revised form 3 January 2001; accepted 5 January 2001
Abstract A bottleneck with a diminished capacity is shown to have arisen on a freeway segment whenever queues from the segment’s off-ramp spilled-over and occupied its mandatory exit lane. Although the ramp’s queues were confined to the right-most exit lane, non-exiting drivers reduced their speeds upon seeing these queues and this diminished flows in all lanes. It is also shown that the lengths of these exit queues were negatively correlated with the discharge flows in the freeway segment’s adjacent lanes; i.e., longer exit queues from the over-saturated off-ramp were accompanied by lower discharge rates for the non-exiting vehicles. Whenever the off-ramp queues were prevented from spilling-over to the exit lane (by changing the logic of a nearby traffic signal), much higher flows were sustained on the freeway segment and a bottleneck did not arise there. These observations underscore the value of control strategies that enable diverging vehicles to exit a freeway unimpeded. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Freeway traffic control; Off-ramps; Bottlenecks
1. Introduction It is shown that a very disruptive freeway bottleneck was averted by keeping an off-ramp from becoming over-saturated. This demonstration relies upon traffic data visually extracted from videotapes combined with observations taken in a floating car and, very importantly, visual analyses of cumulative curves of vehicle counts and occupancies that were plotted in special ways. The latter were measured by inductive loop detectors and obtaining these data proved a challenge because some detectors were not always functioning. Certain details concerning these detectors are thus relegated to footnotes so that they do not detract from what is otherwise a simple narrative. *
Corresponding author. Tel.: +1-510-642-7702; fax: +1-510-643-8919. E-mail address: [email protected] (M.J. Cassidy).
0965-8564/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 5 - 8 5 6 4 ( 0 1 ) 0 0 0 1 6 - 7
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Fig. 1. Southbound Interstate 5, Orange County, California.
In the following section, the freeway site used for the study is described. Observations of traffic flowing through the bottleneck (i.e., in the presence of the over-saturated off-ramp) are presented in Section 3. Section 4 serves to document the improved freeway conditions that resulted from keeping this ramp under-saturated. 1 Some implications of these findings are provided in Section 5. 2. Study site Fig. 1 is a sketch of the study site, a segment of southbound Interstate 5 in Orange County, California. The loop detectors, shown along with their respective mile post (MP) locations, measured the vehicle counts and occupancies in each lane over 30-s intervals. Analyses of traffic in the high-occupancy vehicle (HOV) lane are not described here, since HOV operation seemed to have little impact on the regular-use lanes. Both on-ramps were metered and their inflows were nearly the same each observation day. The site was ‘‘observed’’ (i.e., data were jointly collected from video, floating car runs and loop detectors) during the afternoon rush hours on four separate days. On two of these days (March 30 and May 30, 2000), the La Paz Road off-ramp became over-saturated and queues spilled-over to the freeway’s exit lane. On the other two observation days (May 31 and June 1, 2000), the traffic signal at the downstream end of this off-ramp was made to allocate sufficient capacity to keep it under-saturated. 3. The bottleneck and its cause This section begins with a description of the cumulative curves of vehicle count, N, and occupancy, T, used for locating the freeway bottleneck. To this end, Fig. 2(a) presents curves 1
The strategy promoting under-saturated ramp operation was not deployed at the behest of the research team. Rather, one of the ramp’s loop detectors, which was used to activate a traffic signal immediately downstream, functioned intermittently; i.e., there were long periods when it functioned and long periods when it did not. During periods marked by the former, the traffic signal served ramp queues in their entirety, while during the latter, off-ramp queues grew and spilled onto the freeway’s exit lane. The research team merely collected observations both when the detector was functioning and when it was not (and both cases were easily distinguished by the data).
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Fig. 2. (a) Oblique N- and T-curves, MP 17.3 (May 30, 2000). (b) Oblique N- and T-curves, MP 16.6 (May 30, 2000).
measured by the detectors at MP 17.3 on May 30, 2000. The N-curve, shown in this figure as the thick line, came from the counts summed across all five lanes at this MP. It was constructed by
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taking linear interpolations through these 30-s counts so that its slopes are the flows past the MP in each (30 s) measurement interval. But instead of plotting N versus time t, an oblique coordinate system was used to plot N qo ðt to Þ versus t for the curve’s starting time, to , and some choice of qo . The value of qo was chosen so that the range of N qo ðt to Þ over the observation period was small compared with the N itself. In this way, the vertical scale was magnified along with the curve’s features, such as sustained changes in its slopes and its wiggles. (The choice of qo is a matter of judgement; i.e., one must judge the level of magnification needed to distinguish curve features ‘‘by eye’’.) This method of plotting the curves is identical to what was described in Cassidy and Windover (1995), but it was Munoz and Daganzo (2000) who first recognized that this is an oblique plot. In similar fashion, the thin line in Fig. 2(a) is the T-curve at MP 17.3, where cumulative occupancy, T, is measured in units of total time spent by vehicles atop the detectors to time t (Lin and Daganzo, 1997). As before, the curve describes the measurements across all five travel lanes. It was drawn using piece-wise linear interpolations so that its slopes are the occupancy rates and it is shown using oblique coordinates (i.e., the T was reduced by a chosen rate bo ) so that changing slopes are clearly visible. The curves in Fig. 2(a) reveal that backward-moving congestion (from downstream) arrived at MP 17.3 by time 17:10; as labeled in the figure, this was the time when a reduction in N was accompanied by a sharp rise in T, a clear indication of a queue’s arrival. Beyond time 17:10, changes in the N and T occurred in ‘‘opposite directions’’, revealing the passages of backwardmoving acceleration waves (i.e., increases in N accompanied by reductions in T) and backwardmoving deceleration waves (reductions in N with increases in T) that are characteristic of congested traffic. Dotted line segments have been added to Fig. 2(a) to highlight these changing patterns; i.e., the dots emphasize that a convex (concave) trend in the N-curve was accompanied by a concave (convex) one in the T. Prior to time 17:10, changes in the N and T occurred in the ‘‘same directions’’; i.e., use of a straightedge will confirm that, until this time, the N-curve in Fig. 2(a) exhibits several timedependent increases in its slopes and that these are accompanied by increases in T. (Our selection of qo and bo for Fig. 2(a) caused the initial portion of the N-curve to exhibit a general upward trend while the T-curve slopes downward. However, our diagnostic is concerned with changes in the curves’ slopes and not with their general trends.) These patterns in the Fig. 2(a) curves reveal that, before time 17:10, changes in traffic conditions emanated from upstream, as is characteristic of uncongested traffic. Fig. 2(b) presents oblique N- and T-curves measured in the four regular-use lanes at MP 16.6 (and 16.4 ). 2 Each was constructed as previously described. They reveal that changes in the slopes of both curves occurred in the same directions and piece-wise linear approximations are shown as
2
Prior to this day of data collection, the loop detectors in the left-most regular-use lanes at MP 16.6, and in the rightmost regular lanes at MP 16.4, were disabled. The curves in Fig. 2(b) were therefore constructed by supplementing the data from MP 16.6 with data from MP 16.4; i.e., they were constructed using data from the four functioning detectors (collectively measuring conditions in all four travel lanes) at both MPs 16.6 and 16.4 (see Fig. 1). Finagling the data in this fashion did not affect the findings, since video showed very little lane changing between these two closely-spaced MPs. Except where otherwise noted, the data euphemistically described as having been measured at MP 16.6 (only) were actually agglomerated measurements at both MPs 16.6 and 16.4.
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dashed lines in Fig. 2(b) to emphasize this. As such, changes in flow and occupancy rate at MP 16.6 were forward-moving and emanated from upstream; i.e., traffic was uncongested. The backward-moving waves at MP 17.3, combined with forward-moving changes in traffic at MP 16.6, indicate that a bottleneck activated somewhere between. The sudden slope reductions in the curves of Fig. 2(b) show that this activation occurred at about time 17:00. The deleterious effects of this bottleneck on freeway flow are thus evident from the flow reduction labeled in Fig. 2(b); i.e., the flow (from time 16:30 to 17:00) of 2085 vehicles per hour per lane (vphpl) dropped to 1900 vphpl and remained at this rate until time 17:50. The bottleneck’s activation on this day therefore reduced flow through the segment by nearly 10%. Observations on additional days showed that reductions of this magnitude, and sometimes much greater, were the norm. On one particular day (when video observations were not available), for example, the bottleneck’s activation reduced flow on the freeway by 40% (Anani et al., 2000). Not surprisingly, data from upstream detectors (accompanied by observations from a floating car) showed that this bottleneck created extensive freeway congestion each day. Study of videotapes taken from the Alicia Parkway over-crossing revealed that this bottleneck arose whenever long queues from the La Paz Road off-ramp spilled-over and created stop-and-go conditions in the freeway segment’s mandatory exit lane (see Fig. 1). To demonstrate this, Fig. 3 presents the numbers of vehicles to have occupied the exit lane during the rush (on May 30); these were counted directly from video. The figure shows that the bottleneck’s activation (at time 17:00) coincided with a sharp increase in these counts. 3 Fig. 3 also shows that large numbers of vehicles (and thus long queues) continued to occupy the exit lane until time 17:50. Beyond this time, the counts in the exit lane began to diminish and by time 18:05, the numbers dropped to about 15 and remained steady; i.e., the exit queues had dissipated by time 18:05. This dissipation favorably influenced the freeway flows passing MP 16.6. The oblique N-curve in Fig. 4 shows that the flows at this location rose appreciably to 2020 vphpl just after time 18:05. Further analyses of video showed that exiting vehicles rarely entrapped traffic with destinations further downstream. Such an impediment to flow might have occurred had diverging motorists decelerated before forcing themselves into the exit queues (see Munoz and Daganzo, 2000). But study of the videos indicated that exiting drivers were disciplined (or courteous) in that they tended to move into the mandatory exit lane upstream of its queues and thereby did not impede non-exiting vehicles. Even when these queues extended nearly all the way back to MP 17.3, the observed rates of vehicles squeezing into them never exceeded 1 or 2 per minute and this seldom seemed to affect through-moving traffic. Despite this, floating car observations indicated that, in the presence of these exit queues, vehicle speeds were slow in all freeway lanes up to the off-ramp gore at MP 16.7. In fact, non-exiting vehicles traveled at speeds as low as 25 km per hour until reaching this gore, at which point, they accelerated. Apparently, non-exiting drivers in the adjacent lanes reduced their speeds in response to seeing exit queues. As demonstrated in the following section, the bottleneck was completely eliminated by preventing long exit queues from forming.
3
It was also at this time that the La Paz off-ramp’s middle detector began to malfunction and counts (taken from video) indicated that the downstream traffic signal’s ability to serve exiting flows dropped from 1200 vph to only 820 vph.
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Fig. 3. Numbers of vehicles in the mandatory exit lane (May 30, 2000).
4. Eliminating the freeway bottleneck During another observation day, May 31, 2000, the La Paz off-ramp remained under-saturated throughout the rush; the traffic signal immediately downstream provided right-of-way so as to prevent the formation of queues in the exit lanes 4 and this was verified from video. Consequently, the freeway segment sustained very high flows and no bottleneck even arose there. These desirable outcomes are demonstrated in Figs. 5(a) and (b), oblique N- and T-curves at MPs 17.3 and 16.6, respectively. The coincident changes in the N and T displayed in Fig. 5(a) mean that on this day, changes in traffic conditions measured at MP 17.3 were forward-moving and thus emanated from upstream. In short, congestion no longer spilled-over to this location. Study of Fig. 5(b) reveals that from time 17:20 to 17:30, a small reduction in N was accompanied by a (nearly undetectable) rise in T. Apparently on this day, congestion from a less restrictive bottleneck downstream temporarily impeded flow past MP 16.6 (without propagating back to MP 17.3). But even with this short-term impedance, the flows at MP 16.6 were relatively high. As annotated on Fig. 5(b), the average rate from time 16:45 to 17:45 was over 2100 vphpl and two shorter periods were marked by flows of 2200 vphpl. These were appreciably higher than the average discharge flow (of 1900 vphpl) measured in the presence of exit queues on the previous day.
4
During this day, the off-ramp’s middle detector functioned throughout the rush and the traffic signal accommodated exit demands sometimes exceeding 1250 vph.
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Fig. 4. Oblique N-curve, MP 16.6 (May 30, 2000).
Traffic on an additional observation day (June 1, 2000) likewise did not encounter any exit queues from the La Paz off-ramp. The resulting freeway flows were again very high and no bottleneck arose in the segment between MPs 17.3 and 16.6.
5. Conclusions The site studied here became an active bottleneck whenever its mandatory exit lane was occupied by stop-and-go queues. This conclusion follows from having observed that the bottleneck (1) arose with the onset of queueing in the exit lane; (2) disappeared with the dissipation of the exit lane’s queues; and (3) never activated on days when the off-ramp remained under-saturated. Apparently, the exit queues caused non-exiting drivers in adjacent lanes to reduce their speeds. This conclusion is based upon (1) observations in floating cars that showed speeds in the non-exit lanes remained low until vehicles passed the (over-saturated) off-ramp; and yet (2) the video tapes seldom showed any evidence of diverging vehicles directly entrapping traffic with destinations further downstream (i.e., rather than forcing themselves into the exit queues, the former usually joined the rear of the queues). The bottleneck was eventually averted by keeping the off-ramp under-saturated. In the present case, the exit queues were completely eliminated in a simple way and the required signal logic did this without having much impact on surface street traffic nearby. But, more generally, in those
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Fig. 5. (a) Oblique N- and T-curves, MP 17.3 (May 31, 2000). (b) Oblique N- and T-curves, MP 16.6 (May 31, 2000).
instances when the complete elimination of exit queues is not feasible, the present observations suggest that at least some improvement in freeway conditions can be realized by keeping the exit queues as small as possible. As evidence of this, Figs. 6(a) and (b) present data from an earlier observation day, March 30, 2000. Fig. 6(a) shows some counts of vehicles occupying the segment’s mandatory exit lane. These were sampled (from video) at the discrete times designated by the figure’s vertical bars. The figure
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Fig. 6. (a) Numbers of vehicles in the mandatory exit lane (March 30, 2000). (b) Oblique N-curve at MP 16.6 and numbers of vehicles in the exit lane (March 30, 2000).
is provided here merely to demonstrate that, on this day, the numbers in the exit lane were smaller than the largest values measured on May 30 (and previously shown in Fig. 3). The corresponding oblique N-curve measured at MP 16.6 (on March 30) is provided in Fig. 6(b). 5 As annotated on this figure, the discharge flows began at about time 7:04. Notably, these discharge rates were well above the average rate of 1900 vphpl; recall that this latter rate had been measured in the presence of larger numbers of vehicles occupying the exit lane on May 30.
5
This curve was actually measured by the four detectors at MP 16.6 and Footnote 2 does not apply here.
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Also shown in Fig. 6(b) are counts of accumulated vehicles that were actually part of the exit queues on March 30; i.e., these are the counts of vehicles in the exit lane that were either stopped or very slow-moving. To simplify the figure’s presentation, these counts were partitioned into categories of zero (or nearly zero) in queue; short queues of 5–10 vehicles; moderate and long queues of approximately 15 and 20 vehicles, respectively; and very long queues of about 25 or more. When presented in this way, it is apparent that the lengths of the exit queues affected the freeway discharge rates, with smaller values of the former giving rise to larger values of the latter. A description of this is provided below. Referring to Fig. 6(b), the onset of discharge (i.e., the bottleneck’s activation) coincided with the initial appearance of exit queues. Soon after the latter’s short-term disappearance, the discharge recovered to a rate of 2090 vphpl; it was temporarily suppressed when exit queues became very long at time 17:22; it increased to the very high rate of 2190 vphpl when queues diminished 5 min later; and it was again suppressed at about time 17:42 when queue lengths sharply increased. Although the findings reported here are not surprising, the manuscript’s contribution is clear: it serves to document some severe traffic problems caused by driver reactions to queues occupying an adjacent exit lane and it demonstrates the effectiveness of one simple solution to these problems. As such, the findings underscore the value of control strategies that expedite freeway exiting. The findings also highlight the importance of studying bottlenecks using methods like those presented here. Notably, the diagnoses in this study were not the result of conjecture relating to the site’s geometry. For example, Fig. 1 shows that the bottleneck occurred within a so-called weaving area, but the freeway congestion was shown to have been neither a result of weaving nor any other immediately obvious geometric feature. The cause of congestion was identified through direct and careful study of the site’s traffic features.
Acknowledgements This research was funded by Partners for Advanced Transit and Highways, PATH, University of California. The authors are indebted to a number of persons at the California Department of Transportation for their assistance in data acquisition, most notably V. Avedissian, H. Benouar and D. Pishdadian.
References Anani, S., Cassidy, M.J., De Alba, M., Haigwood, J., 2000. Examining how ATMIS can increase freeway bottleneck capacity. Draft report to the California PATH Program, University of California, USA. Cassidy, M.J., Windover, J.R., 1995. Methodology for assessing dynamics of freeway traffic flow. Transportation Research Record 1484, 73–79. Lin, W.F., Daganzo, C.F., 1997. A simple detection scheme for delay inducing incidents. Transportation Research 31A, 141–155. Munoz, J.C., Daganzo, C.F., 2000. Experimental characterization of multi-lane freeway traffic upstream of an off-ramp bottleneck. Draft report to the California PATH Program, University of California, USA.
Study of freeway traffic near an off-ramp Michael J. Cassidy *, Shadi B. Anani, John M. Haigwood Department of Civil and Environmental Engineering, Institute of Transportation Studies, University of California, 109 McLaughlin Hall, Berkeley, CA 94720, USA Received 3 July 2000; received in revised form 3 January 2001; accepted 5 January 2001
Abstract A bottleneck with a diminished capacity is shown to have arisen on a freeway segment whenever queues from the segment’s off-ramp spilled-over and occupied its mandatory exit lane. Although the ramp’s queues were confined to the right-most exit lane, non-exiting drivers reduced their speeds upon seeing these queues and this diminished flows in all lanes. It is also shown that the lengths of these exit queues were negatively correlated with the discharge flows in the freeway segment’s adjacent lanes; i.e., longer exit queues from the over-saturated off-ramp were accompanied by lower discharge rates for the non-exiting vehicles. Whenever the off-ramp queues were prevented from spilling-over to the exit lane (by changing the logic of a nearby traffic signal), much higher flows were sustained on the freeway segment and a bottleneck did not arise there. These observations underscore the value of control strategies that enable diverging vehicles to exit a freeway unimpeded. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Freeway traffic control; Off-ramps; Bottlenecks
1. Introduction It is shown that a very disruptive freeway bottleneck was averted by keeping an off-ramp from becoming over-saturated. This demonstration relies upon traffic data visually extracted from videotapes combined with observations taken in a floating car and, very importantly, visual analyses of cumulative curves of vehicle counts and occupancies that were plotted in special ways. The latter were measured by inductive loop detectors and obtaining these data proved a challenge because some detectors were not always functioning. Certain details concerning these detectors are thus relegated to footnotes so that they do not detract from what is otherwise a simple narrative. *
Corresponding author. Tel.: +1-510-642-7702; fax: +1-510-643-8919. E-mail address: [email protected] (M.J. Cassidy).
0965-8564/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 5 - 8 5 6 4 ( 0 1 ) 0 0 0 1 6 - 7
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Fig. 1. Southbound Interstate 5, Orange County, California.
In the following section, the freeway site used for the study is described. Observations of traffic flowing through the bottleneck (i.e., in the presence of the over-saturated off-ramp) are presented in Section 3. Section 4 serves to document the improved freeway conditions that resulted from keeping this ramp under-saturated. 1 Some implications of these findings are provided in Section 5. 2. Study site Fig. 1 is a sketch of the study site, a segment of southbound Interstate 5 in Orange County, California. The loop detectors, shown along with their respective mile post (MP) locations, measured the vehicle counts and occupancies in each lane over 30-s intervals. Analyses of traffic in the high-occupancy vehicle (HOV) lane are not described here, since HOV operation seemed to have little impact on the regular-use lanes. Both on-ramps were metered and their inflows were nearly the same each observation day. The site was ‘‘observed’’ (i.e., data were jointly collected from video, floating car runs and loop detectors) during the afternoon rush hours on four separate days. On two of these days (March 30 and May 30, 2000), the La Paz Road off-ramp became over-saturated and queues spilled-over to the freeway’s exit lane. On the other two observation days (May 31 and June 1, 2000), the traffic signal at the downstream end of this off-ramp was made to allocate sufficient capacity to keep it under-saturated. 3. The bottleneck and its cause This section begins with a description of the cumulative curves of vehicle count, N, and occupancy, T, used for locating the freeway bottleneck. To this end, Fig. 2(a) presents curves 1
The strategy promoting under-saturated ramp operation was not deployed at the behest of the research team. Rather, one of the ramp’s loop detectors, which was used to activate a traffic signal immediately downstream, functioned intermittently; i.e., there were long periods when it functioned and long periods when it did not. During periods marked by the former, the traffic signal served ramp queues in their entirety, while during the latter, off-ramp queues grew and spilled onto the freeway’s exit lane. The research team merely collected observations both when the detector was functioning and when it was not (and both cases were easily distinguished by the data).
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Fig. 2. (a) Oblique N- and T-curves, MP 17.3 (May 30, 2000). (b) Oblique N- and T-curves, MP 16.6 (May 30, 2000).
measured by the detectors at MP 17.3 on May 30, 2000. The N-curve, shown in this figure as the thick line, came from the counts summed across all five lanes at this MP. It was constructed by
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taking linear interpolations through these 30-s counts so that its slopes are the flows past the MP in each (30 s) measurement interval. But instead of plotting N versus time t, an oblique coordinate system was used to plot N qo ðt to Þ versus t for the curve’s starting time, to , and some choice of qo . The value of qo was chosen so that the range of N qo ðt to Þ over the observation period was small compared with the N itself. In this way, the vertical scale was magnified along with the curve’s features, such as sustained changes in its slopes and its wiggles. (The choice of qo is a matter of judgement; i.e., one must judge the level of magnification needed to distinguish curve features ‘‘by eye’’.) This method of plotting the curves is identical to what was described in Cassidy and Windover (1995), but it was Munoz and Daganzo (2000) who first recognized that this is an oblique plot. In similar fashion, the thin line in Fig. 2(a) is the T-curve at MP 17.3, where cumulative occupancy, T, is measured in units of total time spent by vehicles atop the detectors to time t (Lin and Daganzo, 1997). As before, the curve describes the measurements across all five travel lanes. It was drawn using piece-wise linear interpolations so that its slopes are the occupancy rates and it is shown using oblique coordinates (i.e., the T was reduced by a chosen rate bo ) so that changing slopes are clearly visible. The curves in Fig. 2(a) reveal that backward-moving congestion (from downstream) arrived at MP 17.3 by time 17:10; as labeled in the figure, this was the time when a reduction in N was accompanied by a sharp rise in T, a clear indication of a queue’s arrival. Beyond time 17:10, changes in the N and T occurred in ‘‘opposite directions’’, revealing the passages of backwardmoving acceleration waves (i.e., increases in N accompanied by reductions in T) and backwardmoving deceleration waves (reductions in N with increases in T) that are characteristic of congested traffic. Dotted line segments have been added to Fig. 2(a) to highlight these changing patterns; i.e., the dots emphasize that a convex (concave) trend in the N-curve was accompanied by a concave (convex) one in the T. Prior to time 17:10, changes in the N and T occurred in the ‘‘same directions’’; i.e., use of a straightedge will confirm that, until this time, the N-curve in Fig. 2(a) exhibits several timedependent increases in its slopes and that these are accompanied by increases in T. (Our selection of qo and bo for Fig. 2(a) caused the initial portion of the N-curve to exhibit a general upward trend while the T-curve slopes downward. However, our diagnostic is concerned with changes in the curves’ slopes and not with their general trends.) These patterns in the Fig. 2(a) curves reveal that, before time 17:10, changes in traffic conditions emanated from upstream, as is characteristic of uncongested traffic. Fig. 2(b) presents oblique N- and T-curves measured in the four regular-use lanes at MP 16.6 (and 16.4 ). 2 Each was constructed as previously described. They reveal that changes in the slopes of both curves occurred in the same directions and piece-wise linear approximations are shown as
2
Prior to this day of data collection, the loop detectors in the left-most regular-use lanes at MP 16.6, and in the rightmost regular lanes at MP 16.4, were disabled. The curves in Fig. 2(b) were therefore constructed by supplementing the data from MP 16.6 with data from MP 16.4; i.e., they were constructed using data from the four functioning detectors (collectively measuring conditions in all four travel lanes) at both MPs 16.6 and 16.4 (see Fig. 1). Finagling the data in this fashion did not affect the findings, since video showed very little lane changing between these two closely-spaced MPs. Except where otherwise noted, the data euphemistically described as having been measured at MP 16.6 (only) were actually agglomerated measurements at both MPs 16.6 and 16.4.
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dashed lines in Fig. 2(b) to emphasize this. As such, changes in flow and occupancy rate at MP 16.6 were forward-moving and emanated from upstream; i.e., traffic was uncongested. The backward-moving waves at MP 17.3, combined with forward-moving changes in traffic at MP 16.6, indicate that a bottleneck activated somewhere between. The sudden slope reductions in the curves of Fig. 2(b) show that this activation occurred at about time 17:00. The deleterious effects of this bottleneck on freeway flow are thus evident from the flow reduction labeled in Fig. 2(b); i.e., the flow (from time 16:30 to 17:00) of 2085 vehicles per hour per lane (vphpl) dropped to 1900 vphpl and remained at this rate until time 17:50. The bottleneck’s activation on this day therefore reduced flow through the segment by nearly 10%. Observations on additional days showed that reductions of this magnitude, and sometimes much greater, were the norm. On one particular day (when video observations were not available), for example, the bottleneck’s activation reduced flow on the freeway by 40% (Anani et al., 2000). Not surprisingly, data from upstream detectors (accompanied by observations from a floating car) showed that this bottleneck created extensive freeway congestion each day. Study of videotapes taken from the Alicia Parkway over-crossing revealed that this bottleneck arose whenever long queues from the La Paz Road off-ramp spilled-over and created stop-and-go conditions in the freeway segment’s mandatory exit lane (see Fig. 1). To demonstrate this, Fig. 3 presents the numbers of vehicles to have occupied the exit lane during the rush (on May 30); these were counted directly from video. The figure shows that the bottleneck’s activation (at time 17:00) coincided with a sharp increase in these counts. 3 Fig. 3 also shows that large numbers of vehicles (and thus long queues) continued to occupy the exit lane until time 17:50. Beyond this time, the counts in the exit lane began to diminish and by time 18:05, the numbers dropped to about 15 and remained steady; i.e., the exit queues had dissipated by time 18:05. This dissipation favorably influenced the freeway flows passing MP 16.6. The oblique N-curve in Fig. 4 shows that the flows at this location rose appreciably to 2020 vphpl just after time 18:05. Further analyses of video showed that exiting vehicles rarely entrapped traffic with destinations further downstream. Such an impediment to flow might have occurred had diverging motorists decelerated before forcing themselves into the exit queues (see Munoz and Daganzo, 2000). But study of the videos indicated that exiting drivers were disciplined (or courteous) in that they tended to move into the mandatory exit lane upstream of its queues and thereby did not impede non-exiting vehicles. Even when these queues extended nearly all the way back to MP 17.3, the observed rates of vehicles squeezing into them never exceeded 1 or 2 per minute and this seldom seemed to affect through-moving traffic. Despite this, floating car observations indicated that, in the presence of these exit queues, vehicle speeds were slow in all freeway lanes up to the off-ramp gore at MP 16.7. In fact, non-exiting vehicles traveled at speeds as low as 25 km per hour until reaching this gore, at which point, they accelerated. Apparently, non-exiting drivers in the adjacent lanes reduced their speeds in response to seeing exit queues. As demonstrated in the following section, the bottleneck was completely eliminated by preventing long exit queues from forming.
3
It was also at this time that the La Paz off-ramp’s middle detector began to malfunction and counts (taken from video) indicated that the downstream traffic signal’s ability to serve exiting flows dropped from 1200 vph to only 820 vph.
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Fig. 3. Numbers of vehicles in the mandatory exit lane (May 30, 2000).
4. Eliminating the freeway bottleneck During another observation day, May 31, 2000, the La Paz off-ramp remained under-saturated throughout the rush; the traffic signal immediately downstream provided right-of-way so as to prevent the formation of queues in the exit lanes 4 and this was verified from video. Consequently, the freeway segment sustained very high flows and no bottleneck even arose there. These desirable outcomes are demonstrated in Figs. 5(a) and (b), oblique N- and T-curves at MPs 17.3 and 16.6, respectively. The coincident changes in the N and T displayed in Fig. 5(a) mean that on this day, changes in traffic conditions measured at MP 17.3 were forward-moving and thus emanated from upstream. In short, congestion no longer spilled-over to this location. Study of Fig. 5(b) reveals that from time 17:20 to 17:30, a small reduction in N was accompanied by a (nearly undetectable) rise in T. Apparently on this day, congestion from a less restrictive bottleneck downstream temporarily impeded flow past MP 16.6 (without propagating back to MP 17.3). But even with this short-term impedance, the flows at MP 16.6 were relatively high. As annotated on Fig. 5(b), the average rate from time 16:45 to 17:45 was over 2100 vphpl and two shorter periods were marked by flows of 2200 vphpl. These were appreciably higher than the average discharge flow (of 1900 vphpl) measured in the presence of exit queues on the previous day.
4
During this day, the off-ramp’s middle detector functioned throughout the rush and the traffic signal accommodated exit demands sometimes exceeding 1250 vph.
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Fig. 4. Oblique N-curve, MP 16.6 (May 30, 2000).
Traffic on an additional observation day (June 1, 2000) likewise did not encounter any exit queues from the La Paz off-ramp. The resulting freeway flows were again very high and no bottleneck arose in the segment between MPs 17.3 and 16.6.
5. Conclusions The site studied here became an active bottleneck whenever its mandatory exit lane was occupied by stop-and-go queues. This conclusion follows from having observed that the bottleneck (1) arose with the onset of queueing in the exit lane; (2) disappeared with the dissipation of the exit lane’s queues; and (3) never activated on days when the off-ramp remained under-saturated. Apparently, the exit queues caused non-exiting drivers in adjacent lanes to reduce their speeds. This conclusion is based upon (1) observations in floating cars that showed speeds in the non-exit lanes remained low until vehicles passed the (over-saturated) off-ramp; and yet (2) the video tapes seldom showed any evidence of diverging vehicles directly entrapping traffic with destinations further downstream (i.e., rather than forcing themselves into the exit queues, the former usually joined the rear of the queues). The bottleneck was eventually averted by keeping the off-ramp under-saturated. In the present case, the exit queues were completely eliminated in a simple way and the required signal logic did this without having much impact on surface street traffic nearby. But, more generally, in those
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Fig. 5. (a) Oblique N- and T-curves, MP 17.3 (May 31, 2000). (b) Oblique N- and T-curves, MP 16.6 (May 31, 2000).
instances when the complete elimination of exit queues is not feasible, the present observations suggest that at least some improvement in freeway conditions can be realized by keeping the exit queues as small as possible. As evidence of this, Figs. 6(a) and (b) present data from an earlier observation day, March 30, 2000. Fig. 6(a) shows some counts of vehicles occupying the segment’s mandatory exit lane. These were sampled (from video) at the discrete times designated by the figure’s vertical bars. The figure
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Fig. 6. (a) Numbers of vehicles in the mandatory exit lane (March 30, 2000). (b) Oblique N-curve at MP 16.6 and numbers of vehicles in the exit lane (March 30, 2000).
is provided here merely to demonstrate that, on this day, the numbers in the exit lane were smaller than the largest values measured on May 30 (and previously shown in Fig. 3). The corresponding oblique N-curve measured at MP 16.6 (on March 30) is provided in Fig. 6(b). 5 As annotated on this figure, the discharge flows began at about time 7:04. Notably, these discharge rates were well above the average rate of 1900 vphpl; recall that this latter rate had been measured in the presence of larger numbers of vehicles occupying the exit lane on May 30.
5
This curve was actually measured by the four detectors at MP 16.6 and Footnote 2 does not apply here.
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Also shown in Fig. 6(b) are counts of accumulated vehicles that were actually part of the exit queues on March 30; i.e., these are the counts of vehicles in the exit lane that were either stopped or very slow-moving. To simplify the figure’s presentation, these counts were partitioned into categories of zero (or nearly zero) in queue; short queues of 5–10 vehicles; moderate and long queues of approximately 15 and 20 vehicles, respectively; and very long queues of about 25 or more. When presented in this way, it is apparent that the lengths of the exit queues affected the freeway discharge rates, with smaller values of the former giving rise to larger values of the latter. A description of this is provided below. Referring to Fig. 6(b), the onset of discharge (i.e., the bottleneck’s activation) coincided with the initial appearance of exit queues. Soon after the latter’s short-term disappearance, the discharge recovered to a rate of 2090 vphpl; it was temporarily suppressed when exit queues became very long at time 17:22; it increased to the very high rate of 2190 vphpl when queues diminished 5 min later; and it was again suppressed at about time 17:42 when queue lengths sharply increased. Although the findings reported here are not surprising, the manuscript’s contribution is clear: it serves to document some severe traffic problems caused by driver reactions to queues occupying an adjacent exit lane and it demonstrates the effectiveness of one simple solution to these problems. As such, the findings underscore the value of control strategies that expedite freeway exiting. The findings also highlight the importance of studying bottlenecks using methods like those presented here. Notably, the diagnoses in this study were not the result of conjecture relating to the site’s geometry. For example, Fig. 1 shows that the bottleneck occurred within a so-called weaving area, but the freeway congestion was shown to have been neither a result of weaving nor any other immediately obvious geometric feature. The cause of congestion was identified through direct and careful study of the site’s traffic features.
Acknowledgements This research was funded by Partners for Advanced Transit and Highways, PATH, University of California. The authors are indebted to a number of persons at the California Department of Transportation for their assistance in data acquisition, most notably V. Avedissian, H. Benouar and D. Pishdadian.
References Anani, S., Cassidy, M.J., De Alba, M., Haigwood, J., 2000. Examining how ATMIS can increase freeway bottleneck capacity. Draft report to the California PATH Program, University of California, USA. Cassidy, M.J., Windover, J.R., 1995. Methodology for assessing dynamics of freeway traffic flow. Transportation Research Record 1484, 73–79. Lin, W.F., Daganzo, C.F., 1997. A simple detection scheme for delay inducing incidents. Transportation Research 31A, 141–155. Munoz, J.C., Daganzo, C.F., 2000. Experimental characterization of multi-lane freeway traffic upstream of an off-ramp bottleneck. Draft report to the California PATH Program, University of California, USA.