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50 C h a p t e r 4 Overview As discussed in Chapter 3, the research team took an empiri- cal approach to the problem of reliability estimation. Before conducting the three main analyses (congestion by source, before-and-after studies of reliability improvements, and statistically based predictive relationships for reliability), exploratory analyses were conducted to (a) explore the basic characteristics of reliability and (b) establish basic parameters and principles for measuring and analyzing reliability. These analyses formed the basis for the more detailed analyses that followed, but they also offer valuable guidance on their own for others interested in measuring and studying reliability. recommended reliability Metrics for the research and General practice The research team concluded that all potentially useful reli- ability metrics communicate information about the size and shape of the underlying travel time distribution: that is, the history of travel times on a facility, corridor, or network. (The Phase 1 report more completely describes the wide range of possible reliability metrics.) As shown in Figure 4.1, travel times can be developed using a variety of methods, from direct measurement (top left) to purely synthetic means (top right). Although a wide variety of other performance metrics can be developed from travel times, is travel time the best primary metric to use? Travel times are not normalized and clearly will vary according to the length of the segment or trip being studied. The original candidate reliability measures were the ones in use throughout the United States. However, during the study, research in Europe suggested other potentially useful measures. To examine how these concepts related to those specified in the work plan, an analysis using 2006 freeway data from the Atlanta NaviGAtor system was conducted. The first concept tested was the notion that in a skewed distribu- tion, the median is a better descriptor of central tendency than the mean. Table 4.1 shows that for all the highway sec- tions studied, the mean and the median are very close. This is true for relatively uncongested sections (Travel Time Index [TTI] <1.1) and congested sections (TTI >1.4). Further confirmation that using the mean in the Buffer Index calculation provides the same information as using the width statistic is found in Figure 4.2. The strong positive rela- tionship indicates that both measures are closely related and can be used interchangeably. The team considered including the skew of the travel time distribution to be useful in the research. Use of this measure would largely be limited to researchers and technical person- nel as its communication to laypersons is problematic, but having a way of characterizing the travel time distributions of different facilities and time periods would be valuable. As a further empirical test of reliability performance mea- sures, an additional analysis using data from the Seattle area was conducted. The data for this research were obtained from the loop sensors maintained by WSDOT along SR 520, an urban limited-access freeway running from Seattle to Red- mond. The corridor was divided into westbound and east- bound segments and segments west of I-405 (Bellevue to Seattle) and east of I-405 (Redmond to Bellevue). This par- ticular data set was an excellent example for the study of reli- ability data because each of the four segments has a very different level and pattern of congestion. SR 520 westbound from Bellevue to Seattle experiences the highest level of con- gestion. Volumes are typically heavy throughout the day with congestion peaks in the a.m. and p.m. A 2-mile-long floating bridge with no shoulders on the western end of the corridor is highly susceptible to incident-induced congestion, adding to the existing volume saturationârelated delays. On the east- bound section of this roadway from Seattle to Bellevue, vol- umes are similar to those found in the westbound direction, but because the bridge bottleneck is located at the beginning Empirical Measurement of Reliability
51 Table 4.1. Travel Time Distribution Statistics: Atlanta Freeways, 2006 (4:00 to 7:00 p.m.) Section Section Length (mi) TTI Travel Time (min) Mean Median 95th Percentile I-75 northbound: south of Hudson Road to I-85 split 12.980 1.065 13.8 13.3 15.671 I-75 northbound: south of I-85 split to Brookwood Interchange 6.250 1.334 8.3 7.3 13.409 I-75 northbound: Brookwood Interchange to Wade Green Road 18.290 1.619 29.6 28.8 42.803 I-75 southbound: south of Hudson Road to I-85 split 12.610 1.560 19.7 18.5 30.418 I-75 southbound: south of I-85 split to Brookwood Interchange 6.570 1.665 10.9 10.7 14.089 I-75 southbound: north of Wade Green to Brookwood 16.760 1.056 17.7 17.1 20.140 I-85 northbound: Camp Creek Parkway to I-75 2.590 1.171 3.0 2.7 5.439 I-85 northbound: Brookwood Interchange to SR 316 17.430 1.570 27.4 27.0 36.305 I-85 southbound: I-75 to Camp Creek Parkway 2.670 1.055 2.8 2.7 3.291 I-85 southbound: SR 316 to Brookwood Interchange 18.690 1.248 23.3 23.0 28.537 I-285 eastbound: Cobb Parkway to Chamblee Tucker 13.400 1.673 22.4 21.9 32.365 I-285 westbound: Chamblee Tucker to Cobb Parkway 13.190 1.565 20.6 19.4 32.929 I-20 eastbound: I-285 Westside to I-75/I-85 3.680 1.036 3.8 3.7 4.496 I-20 westbound: I-75/I-85 to I-285 Westside 3.410 1.093 3.7 3.5 4.788 I-20 eastbound: I-75/I-85 to Wesley Chapel 8.590 1.345 11.6 11.3 16.234 I-20 westbound: Wesley Chapel to I-75âI-85 8.560 1.046 9.0 8.7 10.244 Figure 4.1. Travel time is the basis for defining mobility-based performance measures.
52 of the study corridor, the average travel times tend to be higher than those measured in the westbound direction. The eastbound traffic is frequently congested throughout the day, with substantial peaks in both a.m. and p.m. Table 4.2 shows the number of observations and minimum, maximum, mean, standard deviation, and skewness statistics for the travel time in the p.m. peak period (3:00 to 7:00 p.m.) for each section of SR 520. Using skewness and the standard error of skewness, a z-value can be calculated. If skewness divided by the standard error of skewness is greater than 1.96, then one can be 95% confident that the distribution is skewed. (The standard error of skewness is calculated as the square root of 6/n, where ânâ is the number of observations.) The standard error of skew- ness values for the four sections in Table 4.2 are all roughly 0.02, since the sample sizes (number of observations) are the same. The skewness ranges from 10 to 100 times the standard error of skewness, indicating that the distributions are skewed. Although a few extreme values affected the mean and the maximum, a few extreme values did not affect the 80th, 90th, and 95th percentile calculations, and therefore the difference between the mean and these percentiles was not as robust a measure as it would have been using the median. Because travel time data are by nature skewed, a travel time reliabilityâbased comparison to the median would be more appropriate (e.g., the Buffer Index). A test was performed in which all travel times affected by incidents and accidents were removed from the SR 520 data set for the western portion of the corridor from Bellevue to Seattle. This simulated the benefits that could be gained if vehicle improvements eliminated all vehicle accidents and breakdowns. Table 4.3 shows the statistics that reflect these two conditions. While improvements are seen in all direct measures of travel time, both indices report a worsening of reliability. This out- come is caused by the central condition having improved more than the extreme portions of the distribution. Thus the corri- dor is less reliable. But from both a motoristâs standpoint and a highway agencyâs standpoint, this outcome would be a signifi- cant improvement in performance. Because both the central tendency and the actual extreme travel times improved, the traveler would experience an improvement in the corridor operation. Consequently, the team was unconvinced that either of these indices effectively reported the changes illustrated by this experiment. Essentially the issue with choosing one number to explain a reliability distribution is that one number cannot explain the Table 4.2. Travel Time Statistics for P.M. Peak Period on SR 520 SR 520 Section Number Minimum Maximum Mean Standard Deviation Skewness Westbound Bellevue to Seattle 12,350 409 2,975 1,088.8 441.3 0.27 Eastbound Seattle to Bellevue 12,095 409 2,861 598.8 203.8 2.26 Westbound Redmond to Bellevue 12,385 330 2,365 492.4 364.6 2.58 Eastbound Bellevue to Redmond 12,371 330 3,354 604.9 264.2 3.13 Figure 4.2. Buffer Index versus width statistic on Atlanta freeways, 2006 (4:00 to 7:00 p.m.).
53 entire distribution. Rather than relying on only one percentile calculation or one index, several must be documented to effec- tively track travel times. By noting the 80th, 90th, and 95th per- centile values in comparison to the median (50th percentile) value, the range in travel time changes can be demonstrated from year to year. Each statistic can illustrate the change in a particular problem. An example of the use of these statistics is given in Figure 4.3, which shows the westbound segment of SR 520 from Bellevue to Seattle. The gray lines are weekday travel times in the p.m. peak period from 3:00 to 8:00 p.m. The black lines are the weekday travel times during the same time period, except that travel times during incident or accident conditions have been removed; that is, the black lines represent the travel time percentiles if no incidents or accidents occurred. This case is an excellent example of the shifting of the travel time percentile lines. The median travel time improves from 1,500 to 1,300 sec- onds at 5:30 p.m., the peak 5-minute time period. The shift in the 95th percentile is more pronounced at the onset of the peak period congestion from 3:00 to 4:00 p.m. The 50th, 80th, and 95th percentile travel times all have noticeable improvement over the before condition. At the same time, on this badly oversaturated roadway, it is quickly apparent that although incidents and accidents make travel both worse and more unreliable, they are by no means the primary cause of either congestion, nor are they the only cause of unreliable travel. It was concluded from this analysis that a few additions to the list of reliability metrics originally developed in Phase 1 Table 4.3. Effect on Travel Times of Removing All Incidents and Accidents on SR 520, Bellevue to Seattle, P.M. Peak Period (3:00 to 7:00 p.m.) Travel Times for Weekdays (s) Travel Times for Days with No Incident Effects (s) Difference (s) Mean 1,089 1,026 63 Median 1,063 1,006 57 80th Percentile 1,560 1,467 93 90th Percentile 1,687 1,651 36 95th Percentile 1,780 1,748 32 Misery Index 0.59 0.66 -0.07 Unreliability skew 1.08 1.2 -0.12 Figure 4.3. Travel time distributions on SR 520.
54 were in order. Based on the skewness of the travel time distri- butions, the median is a better central tendency statistic to use as a base value for travel time for indices. Therefore, the following adjustments were made: ⢠The two Buffer Indices were defined using both the mean and median as the reference value (note that the skew sta- tistic already uses the median as its reference value); ⢠The 80th percentile travel time was added as a reliability metric; ⢠The skew statistic was added; and ⢠Some on-time measures were defined by using the median rather than the mean. The final set of reliability metrics appears in Table 4.4. Note that TTI rather than pure travel time is used as the primary measurement for the percentiles of the distribution. As a unitless index, TTI is normalized for distance so that sections of different lengths can be compared. An alternative would have been to use the travel rate (minutes per mile, the inverse of space mean speed). All the reliability measures used in this report were derived from the distribution of TTIs rather than raw travel time. travel time Distributions and reliability performance Metrics The Introduction presents several perspectives for defining reliability. For the purpose of the L03 research, reliability was defined as the variability of travel times on an extended high- way section over the course of 6 months to 1 year for different time slices of the day. This definition allowed direct measure- ment with the available data and is consistent with the current state of the practice in performance measurement and eco- nomic analyses. A simple way to visualize reliability is to develop travel time distributions and superimpose reliability metrics on them. Figures 4.4 through 4.8 show an example of this pro- cess for a 5.19-mile section in Atlanta during 2007 for mul- tiple time slices: peak hour, peak period, midday, weekday (all hours), and weekend and holiday (all hours). Throughout the analysis, holidays were defined as the major federal holidays: New Yearâs Day, Martin Luther King Day, Presidentâs Day, Independence Day, Labor Day, Veteranâs Day, Thanksgiving, and Christmas Day. This is a highly congested section in peak periods, with an average TTI over 2.0, which means that trips take over twice as long as they would under free-flow condi- tions. During the course of the research the team found that several observations on these plots can be generalized to other locations: ⢠The shape of the travel time distribution for congested peak times (nonholiday weekdays) is much broader than the sharp spike evident in uncongested conditions. The breadth of this broad shoulder of travel times decreases as con- gestion levels decrease; ⢠Similarly, the tails of the distributions (to the right) appear more exaggerated for the uncongested time slices. How- ever, note that the highest travel times occur during the peaks; and ⢠Despite the fact that peaks have been defined, there are still a number of trips that occur at close to free flow; there are more of these trips in the peak period than in the peak hour. This is probably because peak times actually shift slightly from day to day, as traffic demand can be shifted by events. Also, there are probably some days when overall demand is lower than other days. Table 4.4. Final Set of Reliability Metrics Used in the Research Reliability Performance Metric Definition Units Buffer Index Difference between 95th percentile TTI and average TTI, normalized by average TTI. Difference between 95th percentile TTI and median TTI, normalized by median TTI. % Failure and on-time measures Percentage of trips with travel times <1.1 median travel time (MTT) and <1.25 MTT. Percentage of trips with space mean speed less than 50, 45, and 30 mph. % Planning Time Index 95th percentile TTI. None 80th percentile TTI Self-explanatory. None Skew statistic (90th percentile TTI - median)/(median - 10th percentile TTI). None Misery Index (modified) Average of highest 5% of travel times divided by free-flow travel time. None
55 Figure 4.4. Peak hour travel time distribution, Atlanta, I-75 northbound, I-285 to SR 120 (2007). Figure 4.5. Peak period travel time distribution, Atlanta, I-75 northbound, I-285 to SR 120 (2007). Figure 4.6. Midday travel time distribution, Atlanta, I-75 northbound, I-285 to SR 120 (2007).
56 Data requirements for establishing reliability To allow sufficient time for the occurrence of the myriad of events (e.g., incidents, bad weather) that can affect travel times, reliability requires a fairly long history of travel times. The question is, how much data are needed to make a reasonable estimate of a sectionâs reliability? The study team worked with the assumption that a yearâs worth of data was desirable. The research team conducted tests with urban freeway (detector-based) data from Atlanta and the San Francisco Bay Area. These tests were conducted by selecting multiple samples from several time durations, computing the TTI and Buffer Index for the samples, comparing them with the annual value, and noting the error. Table 4.5 shows the results of using 2007 freeway data from Atlanta for the peak period on each sec- tion. It is apparent from these results that a monthâs worth of data provides reasonable estimates of average travel time, but it is insufficient to establish reliability. Longer time periods also were tested; the results for the Buf- fer Index appear in Figure 4.9. For this analysis, all possible month combinations for each sampling rate were tested. With 6 months of data, the error rate for the Buffer Index was about the same as it was with 1 month of data for estimating TTI. Incidents are relatively infrequent in terms of the num- ber of minutes each year that they are present on a facility. Figure 4.7. Weekday travel time distribution, Atlanta, I-75 northbound, I-285 to SR 120 (2007). Figure 4.8. Weekend and holiday travel time distribution, Atlanta, I-75 northbound, I-285 to SR 120 (2007).
57 Table 4.6 shows annual incident minutes on an 11-mile stretch of U.S. 101 southbound in California. All incidents of any type were present only 17% of the time on U.S. 101 southbound. One must, therefore, simulate a relatively long time to hope to be able to capture a single incident. The exploratory research found that the travel time vari- ance and the mean travel time for any facility are highly cor- related. Figure 4.10 shows how the standard deviation of the travel time rate for U.S. 101 southbound varies according to the mean travel time rate. As the Atlanta data above also show, many fewer samples are required to estimate the mean travel time than to estimate its variance (or standard deviation). The research team concluded from these analyses that a minimum of 6 months of data is required to estimate travel time reliability. In areas where snow and ice are frequent events, this requirement would be expected to increase to a full year. It may be possible in winter weatherâaffected loca- tions to use 6 months of data if the data represent every other month. However, the team proceeded with the idea that a yearâs worth of data would provide more sound results and strove to achieve the 1-year minimum. trends in reliability An examination of congestion and reliability trends from 2006 to 2008 on the 10 Atlanta study sections was under- taken. Anecdotal information suggested that congestion had decreased in 2008 after a midyear spike in gas prices and the economic downturn. Table 4.7 presents the results for the peak period. Note that the peak period was fixed and was deter- mined using the procedure given in this chapter using 2006 data. On all 10 sections, TTI increased between 2006 and 2007 and decreased between 2007 and 2008. In nine cases, the 2008 TTIs were below those of 2006. Note that eight of the 10 sections had ramp meters installed in 2008. On seven of the 10 study sections, the Buffer Index actually increased in 2008 over 2007 levels, yet overall congestion was better (i.e., TTI went down). The two components of the Buf- fer Index (95th percentile and mean travel time) decreased in all cases. However, when the Buffer Index increased, it can be seen that the drop in the 95th percentile was proportionately lower than the drop in the mean travel time, leading to a higher index value. The 80th percentile travel time decreased in 2008 on all sections, and the skew statistic exhibited a similar pattern as the Buffer Index. The Planning Time Index (not shown in Table 4.5. Error Rates for Using 1 Month of Data to Estimate Annual Average Travel Time and Reliability During Peak Periods in Atlanta (2006) Section Mean Absolute Error Travel Time Buffer Index I-285 eastbound from GA 400 to I-75 8.1% 25.4% I-285 eastbound from GA 400 to I-85 7.0% 24.9% I-285 westbound from GA 400 to I-75 5.8% 26.9% I-285 westbound from GA 400 to I-85 5.1% 26.4% I-75 northbound from I-20 to Brookwood 4.0% 46.2% I-75 northbound from I-285 to Roswell Road 7.1% 26.1% I-75 northbound from Roswell Road to Barrett Parkway 4.3% 42.1% I-75 southbound from I-20 to Brookwood 6.0% 33.5% I-75 southbound from I-285 to Roswell Road 5.2% 25.0% I-75 southbound from Roswell Road to Barrett Parkway 8.2% 19.3% Overall 6.1% 23.1% Figure 4.9. Error rates for samples to estimate TTI and Buffer Index in study sections during peak periods in Atlanta (2008).
58 Table 4.7) exhibited the same characteristics as the 95th per- centile since its base is free-flow speed, which does not change. Figures 4.11 and 4.12 show the travel time distributions for two sections where the Buffer Index and skew statistic increased: ⢠The I-75 section had ramp meters turned on in mid-October 2008 and saw a decrease in demand of 5.5% from 2007 to 2008; and ⢠The I-285 section had ramp meters turned on by July 1, 2008, and saw a decrease in demand of 1.8%. Note that for the same fixed peak period, there was more free- flow travel in 2008 on both sections. On the I-75 section the increase in free-flow travel was due primarily to the decrease in demand, but on the I-85 section the improved flow was probably due to a combination of reduced demand and ramp meters. Both the Buffer Index and the skew statistic indicate there was more spread in the distribution, but the worst travel times (the 80th and 95th percentiles) were decreased. What can be concluded from these seemingly conflicting results on the seven segments about reliability trends? In other words, does reliability get better or worse at these locations? Table 4.6. Annual Incident Minutes on U.S. 101 Southbound in Marin County Incident Type Logged Incidents Estimated Logged (%) Estimated Number of Incidents Duration (min) Total Incident Minutes Annual ProbabilityMean Standard Deviation Accident, injury 19 100% 19 42.8 40.3 813 0.87% Accident, noninjury 84 99% 85 22.6 22.2 1,915 2.05% Accident, other 76 99% 77 19.7 17.0 1,513 1.62% Breakdown 88 60% 147 17.9 19.8 2,620 2.80% Other 15 60% 25 32.5 73.4 812 0.87% Traffic hazard 274 60% 457 19.0 14.9 8,662 9.25% Subtotal incidents 556 69% 809 20.2 22.2 16,335 17.45% Nonincidents NA NA NA NA NA 77,265 82.55% Total year NA NA NA NA NA 93,600 100.00% Note: Estimated Logged accounts for the typical underreporting of less severe incidents. NA = not applicable. Figure 4.10. Standard deviation of travel time rates for U.S. 101 Southbound.
59 Year 2006 2007 2008 Section I-75 NB from I-285 to Roswell Roada TTI 2.046 2.026 1.665 Average TTI 11.271 11.162 9.177 95th Percentile TTI 16.934 17.507 14.800 Buffer Index 0.502 0.568 0.613 80th Percentile TTI 13.974 14.191 11.458 Skew statistic 0.942 1.087 1.514 Daily VMTb 691,399 689,628 N/A Section I-75 SB from I-285 to Roswell Roada TTI 1.312 1.369 1.293 Average TTI 7.665 7.994 7.552 95th Percentile TTI 10.139 10.517 9.868 Buffer Index 0.323 0.316 0.307 80th Percentile TTI 8.353 8.719 8.306 Skew statistic 1.524 1.515 1.461 Daily VMT 691,399 689,628 N/A Section I-75 NB from I-20 to Brookwood TTI 1.350 1.542 1.339 Average TTI 6.710 7.664 6.656 95th Percentile TTI 8.120 10.755 8.031 Buffer Index 0.210 0.403 0.207 80th Percentile TTI 7.097 8.112 7.015 Skew statistic 1.283 1.923 0.771 Daily VMT 616,038 620,959 595,034 Section I-75 SB from I-20 to Brookwood TTI 2.052 2.171 2.067 Average TTI 9.336 9.877 9.404 95th Percentile TTI 13.110 14.270 12.389 Buffer Index 0.404 0.445 0.317 80th Percentile TTI 10.805 11.416 11.042 Skew statistic 1.324 1.120 0.956 Daily VMT 616,038 620,959 595,034 Section I-285 EB from GA 400 to I-75c TTI 1.359 1.481 1.380 Average TTI 9.322 10.162 9.469 95th Percentile TTI 12.548 13.150 12.493 Buffer Index 0.346 0.294 0.319 80th Percentile TTI 10.505 11.382 10.849 Skew statistic 1.148 0.996 1.070 Daily VMT 584,487 588,442 572,211 Table 4.7. Trends in Reliability, Atlanta Freeways (2006â2008) Year 2006 2007 2008 Section I-285 WB from GA 400 to I-75c TTI 1.826 1.893 1.672 Average TTI 12.564 13.026 11.504 95th Percentile TTI 19.053 19.754 19.543 Buffer Index 0.517 0.516 0.699 80th Percentile TTI 15.632 16.140 14.699 Skew statistic 1.202 1.043 1.779 Daily VMT 584,487 588,442 572,211 Section I-285 EB from GA 400 to I-85c TTI 2.247 2.314 1.797 Average TTI 14.495 14.926 11.593 95th Percentile TTI 23.353 24.724 21.084 Buffer Index 0.611 0.656 0.819 80th Percentile TTI 19.336 19.945 15.256 Skew statistic 1.285 1.248 2.347 Daily VMT 588,597 580,629 567,497 Section I-285 WB from GA 400 to I-85c TTI 1.621 1.681 1.511 Average TTI 10.424 10.809 9.713 95th Percentile TTI 13.740 13.707 12.612 Buffer Index 0.318 0.268 0.299 80th Percentile TTI 11.622 11.957 11.082 Skew statistic 0.790 0.763 0.656 Daily VMT 588,597 580,629 567,497 Section I-75 NB from Roswell Road to Barrett Parkwaya TTI 1.579 1.652 1.514 Average TTI 8.762 9.170 8.405 95th Percentile TTI 11.827 12.823 12.357 Buffer Index 0.350 0.398 0.470 80th Percentile TTI 10.206 10.560 9.656 Skew statistic 1.513 1.348 1.586 Daily VMT 669,568 675,274 N/A Section I-75 SB from Roswell Road to Barrett Parkwaya TTI 1.809 1.872 1.614 Average TTI 9.785 10.129 8.730 95th Percentile TTI 13.835 14.301 12.791 Buffer Index 0.414 0.412 0.465 80th Percentile TTI 11.208 11.575 10.529 Skew statistic 0.849 0.920 0.945 Daily VMT 669,568 675,274 N/A (continued on next page)
60 Figure 4.12. I-75 northbound, I-285 to Roswell Road, peak period. Table 4.7. Trends in Reliability, Atlanta Freeways (2006â2008) (continued) Year 2006 2007 2008 All Sections TTI 1.720 1.800 1.585 Average travel time 10.033 10.492 9.220 95th Percentile TTI 14.266 15.151 13.597 Buffer Index 0.399 0.428 0.451 Year 2006 2007 2008 80th Percentile TTI 11.874 12.400 10.989 Skew statistic 1.186 1.196 1.308 Daily VMT 3,150,088 3,154,932 2,878,074 Daily VMT without I-75 (I-285 to Barrett Pkwy) 1,789,122 1,790,030 1,734,742 a Ramp meters were turned on mid-October 2008. b VMT (vehicle miles traveled) was calculated for both directions combined, then divided by two for each directional section. c Ramp meters were turned on July 1, 2008. Note: NB = northbound; SB = southbound; EB = eastbound; WB = westbound. Figure 4.11. I-285 eastbound, GA 400 to I-85, peak period.
61 Both the Buffer Index and the skew statistic indicate there was more spread in the distribution, but the worst travel times (the 80th and 95th percentiles) were decreased. That the drop in the 95th percentile was not as great as the drop in the mean indicates that although base (typical) conditions improved, the variation around the new base was higher (as indicated by the Buffer Index and skew statistic). So, for a traveler in 2008, the worst days are better than they were in 2007, but compared with a typical trip, the worst days are proportion- ately worse. Whether reliability got better or worse depends on whether the traveler perceives the extra time in absolute or relative terms. In absolute terms, the buffer time (95th per- centile minus the mean) improved in 2008. Assume for the moment that the decreases in the metrics are due solely to the decreased demand in 2008, which would have reduced the base (recurring) congestion. Also assume that the worst travel times are influenced by roadway events such as incidents. The decreases in the 80th and 95th percen- tiles in 2008 are another indication of the interaction between base congestion and events; that is, assuming event character- istics are equivalent, less base congestion leads to lower event- related congestion. However, the lessened impact is somewhat marginal: the drop in the worst travel times was not as big as for base congestion. There are two implications of these results for future research and existing practice. First, the Buffer Index may not be the most appropriate metric for tracking trends. In the Atlanta analysis, it can be seen that the mean travel times had a proportionately higher decrease than the 95th percentile. Presumably, this trend occurred because the major factor was decreased demand, which would tend to decrease all travel times, and not primarily affect the extremes as some opera- tional treatments do. So, because of the way the Buffer Index is normalized by the mean, it can produce a counterintui- tive result; that is, it can produce worsened reliability and decreased average congestion. Although this nuance means that the Buffer Index might not be the best metric for mea- suring trends, it still gives useful information about condi- tions. In the new reality of 2008, the size of the buffer did indeed increase, even if the increase was primarily the result of a large decrease in the mean travel time. The second implication is that demand can have a signifi- cant effect on both average congestion level and reliability. As shown in Figure 2.2 (Chapter 2), conceptually, demand and base capacity interact with events to produce total congestion patterns. Overall, analysis shows just how important volume is to congestion and reliability when capacity is improved. Defining peak hour and peak period The length of peak times for conducting congestion and reli- ability analyses can be defined by either (a) determining fixed times for all locations, based on subjective local knowledge; or (b) determining the start and end times empirically. The research team decided on the latter method and defined peak hour and peak period as follows: ⢠Peak hour is the continuous 60-minute period during which the space mean speed is less than 45 mph. As this period can be much longer than an hour, the selection of the actual peak hour within this period is based on exam- ining alternative 60-minute periods based on three criteria: ââ Low space mean speed, ââ High vehicle hours of travel, and ââ High vehicle miles of travel. The analyst must decide which 60-minute period is the actual peak hour based on comparing this information with local knowledge. Note that for routinely congested sections, the highest VMT will occur either right before the actual peak (high flow right before breakdown conditions) or after the peak (high flow during queue release); and ⢠Peak period is a continuous time period of at least 75 min- utes during which the space mean speed is less than 45 mph. The peaks for the urban freeway study sections are shown in Table 4.8. estimating Demand in Oversaturated Conditions on Freeways When traffic flow breaks down on freeways, the observed vol- ume of vehicles moving past a point drops due to slower speeds and the onset of queuing. Roadway detectors count only volume (the number of vehicles that pass a given point), not demand (the number of vehicles that want to pass the point). The simultaneous volumeâspeed plots in Figures 4.13 and 4.14 are typical of congested freeways everywhere. This loss in capacity after flow breakdown is often referred to as lost productivity or lost efficiency because it means that under such conditions, throughput is actually lost. The actual demand that wants to pass a given point is stored upstream in the queue. The applications that are likely to use the L03 results (e.g., the Highway Capacity Manual [HCM], travel forecasting and simulation models) need to know that demand in order to predict traffic conditions. To address this need, the research team developed a procedure for allocating queued demand to the time period when that demand is try- ing to use a section of highway. The steps are as follows: 1. A congestion threshold speed of 35 to 45 mph is set by the analyst (40 mph is used in the examples presented here). For each 5-minute observation a. If the mean observed speed is â¥40 mph, then the ob- served volume is equal to the demand.
62 Table 4.8. Peak Hour and Peak Period Definitions for L03 Study Sections Peak Hour Peak Period City Section Start Start End Length (h) Houston 1 6:20 6:00 8:15 2:15 2 6:35 6:15 8:40 2:25 3 7:35 6:40 9:20 2:40 4 16:40 15:15 18:55 3:40 5 16:50 16:20 19:10 2:50 6 16:50 16:20 19:10 2:50 7 6:05 6:15 7:50 1:35 8 6:45 6:15 9:10 2:55 9 6:45 6:15 9:10 2:55 10 7:00 7:20 8:55 1:35 11 16:35 16:15 18:30 2:15 12 16:50 16:40 18:30 1:50 13 16:55 16:45 19:00 2:15 Minneapolisâ St. Paul 14 7:00 6:25 8:55 2:30 15 15:19 15:10 17:35 2:25 16 16:35 15:10 18:05 2:55 17 16:20 16:20 18:10 1:50 18 16:05 15:05 18:25 3:20 19 16:15 16:15 18:20 2:05 20 7:55 7:55 9:25 1:30 21 16:15 16:15 17:55 1:40 22 16:10 14:45 17:55 3:10 23 7:00 7:00 8:35 1:35 24 16:20 16:10 18:20 2:10 25 6:55 6:55 8:55 2:00 26 16:00 15:25 17:55 2:30 27 16:15 16:15 18:05 1:50 28 7:05 7:05 8:55 1:50 29 16:20 16:20 18:15 1:55 Peak Hour Peak Period City Section Start Start End Length (h) Los Angeles 30 7:10 6:45 9:30 2:45 31 7:15 6:35 9:00 2:25 32 16:45 16:50 19:00 2:10 San Francisco Bay Area 35 16:25 15:45 18:50 3:05 San Diego 37 15:45 15:25 18:40 3:15 38 16:55 16:55 18:30 1:35 39 6:45 6:45 8:20 1:35 40 16:40 15:00 19:05 4:05 41 16:25 15:45 18:25 2:40 42 6:30 6:25 8:55 2:30 Atlanta 43 17:00 16:30 18:30 2:00 44 7:45 7:15 8:30 1:15 45 17:15 7:15 9:00 1:45 46 17:00 15:30 18:30 3:00 47 7:15 7:15 8:45 1:30 48 17:15 16:30 18:30 2:00 49 17:00 16:00 18:30 2:30 50 7:45 7:15 9:00 1:45 51 17:00 16:30 18:30 2:00 52 7:30 7:15 9:00 1:45 Jacksonville 74 7:30 7:15 8:40 1:25 75 17:00 16:45 18:10 1:25 76 7:25 7:10 8:30 1:20 77 17:00 16:45 18:10 1:25 78 17:00 16:45 18:10 1:25 79 7:20 7:10 8:35 1:25 80 17:00 16:45 18:10 1:25 81 16:45 16:35 17:55 1:20 Note: Sections are keyed to Table 3.2. b. If the mean speed is <40 mph, then the observed vol- ume is not equal to demand, and a demand estimate is required. 2. The congested period is then the set of consecutive 5-min- ute observations with speeds <40 mph. If a single 5-minute period is uncongested, but it is surrounded by congested 5-minute observations, then this single 5-minute observa- tion is considered to be congested, as well. 3. The congested period is split into two halves. The queue is assumed to be building during the first half of the con- gested period and dissipating during the second half. 4. The cumulative demand is computed for about half an hour before the onset of congestion and for half an hour after the termination of congestion. a. During the first half of the congested period, the demand rate (vehicles per 5-minute period) is assumed to be equal
63 congested period should not be sharply higher than the estimated demand rate for the second half of the con- gested period. It is sometimes necessary to smooth out the transition by assuming the congested period extends an additional 5-minute period. Figure 4.15 illustrates the application of this approach to a congested period for U.S. 101 in Marin County, California. reliability Breakpoints on Freeways After reviewing the urban freeway data, it became apparent to the research team that the data could be used in creative ways to answer basic questions about reliability and to provide insight into the complex statistical modeling ahead. One of these questions was, at what volume (demand) levels does reliability radically change? The issue this question addresses is similar to establishing basic capacity values for when flow breakdown occurs, except that here the concern is with the volume level that causes reliability to rapidly deteriorate. A to the average of the demand rates observed in the last two 5-minute periods just before the onset of congestion. This demand rate is assumed to be fixed for the first half of the congested period, and it is used to compute the cumulative demand for this half of the congested period. b. Once the cumulative demand at the midpoint of the con- gested period is computed, then the analyst calculates a second demand rate to be used during the second half of the congested period. This second demand rate is set so that the cumulative demand will equal the cumulative observed volume by the end of the congested period. c. The second-half demand rate then is added to the cumulative demand at the midpoint of the congested period until the end of the congested period is reached, at which point the estimated demand should be equal to the observed cumulative volume. d. The two 5-minute periods after the termination of the congested period are checked to see if the estimated demand curve smoothly fits to the observed cumula- tive volume curve. The observed 5-minute volume for the first 5-minute period following the end of the Figure 4.13. Volume drop after onset of congestion: Example 1. Figure 4.14. Volume drop after onset of congestion: Example 2.
64 of congestion on the freeway, is quite a bit lower than the theoretical 2,000 vphpl capacity of the freeway (after convert- ing from passenger car capacity to mixed-flow capacity). But note that the volumes in Figure 4.16 are the average across the peak period. Peak 15-minute demands within the peak period may be significantly higher than the average volume across the entire peak period. Figure 4.17 shows similar computations and results for the five detectors in the westbound direction of I-580. Both the mean and the standard deviation in the travel time rate for each peak period tended to rise almost vertically in the range of 1,600 to 1,700 vphpl averaged across the peak period. The breakpoint volumes for freeway reliability varied by detector location, even for the same facility. Figures 4.18 and 4.19 show the volumeâreliability relation- ships for one yearâs worth of peak and off-peak time periods for a single detector in each direction on I-580. The breakpoint vol- ume for this detector was in the 1,200 to 1,300 vphpl range for the eastbound direction and 1,100 to 1,200 vphpl westbound. For the eastbound direction, the relationship appeared to be precisely vertical once the breakpoint volume was reached for the peak period. The westbound direction appeared to have a few nonrecurrent incidents that caused some reliability prob- lems before the breakpoint volume was reached. Figure 4.20, computed from a yearâs worth of loop detector data for U.S. 101 southbound, shows that a similar flat rela- tionship between mean volume and standard deviation of travel time existed on this freeway until the breakpoint vol- ume of between 1,050 and 1,150 vphpl was reached. After this point, both the mean and the standard deviation of the travel time rate increased steeply, but not precisely vertically. The analysis above shows that travel time reliability on a freeway is not a function of counted traffic volumes until a breakpoint volume is reached. At that breakpoint, travel time complete description of this effort is provided in the Phase 2 report; a summary is provided below. Various measures of travel time reliability were investigated, and the standard deviation of the measured travel time rate per mile was selected as an appropriate indicator of travel time reli- ability for the purpose of establishing reliability breakpoints. The team chose the standard deviation in order to examine both sides of the mean volume that lead to breakdown. Two methods for measuring the standard deviation of the travel time rate were evaluated. Loop detectors provide excellent temporal coverage for limited geographic locations, and vehicle probes provide excellent geographic coverage of a facility for limited time periods. A method was developed for calibrating loop detector estimates of travel time reliability to probe vehicle measurements of travel time reliability so that the annual travel time reliability for the freeway could be estimated. A yearâs worth of loop detector station data for four sta- tions (located on two freeways in the San Francisco Bay Area) was evaluated to determine how traffic volumes and inci- dents affected the observed travel time reliability on a freeway for the morning peak, afternoon peak, and off-peak periods over the course of a year. Three weeks of travel time rate data were evaluated from 13 loop detector stations on eastbound I-580. The mean and standard deviation of the travel time rate (minutes per mile) were computed for each of three time periods (a.m. peak, p.m. peak, off-peak) for each day of the week. As shown in Figure 4.16, both the mean travel time rate and the standard deviation were relatively constant until the counted mean volume (across all detectors) for a peak period reached between 1,250 and 1,350 vehicles per hour per lane (vphpl). Somewhere in this range, the mean and standard deviation of the travel time rate starts to soar almost verti- cally. This breaking point, when there are strong indications Figure 4.15. Example of demand estimation during oversaturated conditions.
65 Figure 4.16. Volume and reliability on I-580 eastbound at multiple detectors. Figure 4.17. Volume and reliability on I-580 westbound at multiple detectors.
66 same freeway facility. In other words, the breakpoint volume does not appear to be a fixed ratio of the theoretical capacity of the subject section of the facility. The breakpoint in reliability generally occurs at a counted volume significantly lower than the theoretical capacity of the facility computed according to HCM procedures. This differ- ence is partly because the breakpoint volume computed in reliability decreases abruptly. Once the breakpoint volume is exceeded, the decrease in travel time reliability (increase in variance) is extreme and so abrupt as to suggest it is asymp- totic, with a nonsingular relationship to further volume increases. The breakpoint volume varies significantly between facili- ties and even (by location and direction of travel) within the Figure 4.18. Volume and reliability for a single detector on I-580 eastbound. Figure 4.19. Volume and reliability for a single detector on I-580 westbound.
67 An analysis was undertaken using data from the study sec- tions in Seattle and Atlanta. For comparison with HCM ter- minology, the team defined SSR in terms of vehicles per hour per lane: ⢠Data were available at 5-minute intervals in the two loca- tions, so the first step was to aggregate the data to 15-min- ute time intervals; ⢠For each 15-minute interval, an estimate of the corre- sponding vehicles per hour per lane value was made by multiplying the 15-minute volume by four and applying a peak hour factor of 0.95 (a more sophisticated version of this method would compute the peak hour factor directly from the data); and ⢠The data for a detector location were scanned in time sequence, looking for points when flow broke down (i.e., when congestion or queuing began). Speeds less than 45 mph was used in this analysis. When two consecutive 15-minute periods registered speeds less than the threshold, the flow that occurred immediately before breakdown was assigned as the SSR. The results are shown in Table 4.9. The results are in vehicles per hour per lane, which includes both automobiles and trucks. One way to look at the results is that they represent how capacity varies over the course of a year. The theoretical maximum capacity is probably somewhere close to the 99th percentile, allowing for the fact the actual maximum SSR may be an outlier. this analysis is the average hourly volume counted over a peak period as opposed to the peak 15-minute demand used in the HCM capacity computation. But this peaking effect does not entirely explain the differ- ence in volumes. Part of the reason that the breakpoint vol- ume is significantly lower than the theoretical capacity is that most sections of freeway are upstream of a bottleneck; thus, they are affected by downstream congestion backing up into the subject section long before the subject sectionâs HCM capacity is reached. Further, traffic-influencing events, espe- cially incidents, effectively lower capacity when they occur, and over time they degrade reliability. This effect manifests itself in lower breakpoint volumes than for capacity (vol- umes) related strictly to physical features. Finally, even for bottlenecks, the data suggest that the reliability breakpoint occurs long before the theoretical HCM capacity of the bot- tleneck is reached. Sustainable Service rates on Freeways The concepts presented in the previous section can be extended to the idea of a sustained service rate (SSR), which is defined as the highest flow rate that can be sustained over a peak demand period with a low probability of breakdown. Brilon et al. proposed calling this broader capacity the whole- year capacity of the facility (1). They focused on capacity just before breakdown, but the L03 team sought to quantify the probability of breakdown for different flow rates. Figure 4.20. Volume and reliability on U.S. 101 southbound.
68 Table 4.9. Distribution of SSR at Selected Locations (2007) SSR (vphpl) Route Station Mean Standard Deviation Maximum P99 P95 P90 P75 Median P10 P5 P1 Atlanta I-75 northbound, Northside 10068 1,390 482 1,975 1,921 1,848 1,739 1,663 1,560 543 132 87 I-75 northbound, Northside 10070 1,922 288 2,407 2,386 2,236 2,125 2,050 1,967 1,750 1,430 621 I-75 northbound, Northside 750510 1,825 264 2,561 2,449 2,295 2,157 1,954 1,809 1,579 1,357 985 I-75 northbound, downtown connector 10026 1,631 357 2,169 2,169 2,082 2,036 1,900 1,654 1,205 929 316 I-75 northbound, downtown connector 10033 1,597 475 2,245 2,240 2,170 2,121 1,944 1,686 915 684 174 I-75 northbound, downtown connector 10037 1,581 366 2,553 2,199 2,016 1,936 1,806 1,682 1,152 840 287 I-75 northbound, downtown connector 10038 1,567 367 2,412 2,153 1,961 1,879 1,804 1,696 1,058 892 272 I-75 southbound, downtown connector 10130 1,270 306 2,110 1,776 1,658 1,599 1,493 1,295 902 575 291 I-75 southbound, downtown connector 10131 1,666 334 2,381 2,181 2,017 1,955 1,853 1,733 1,321 1,031 305 I-285 eastbound, North Arc 2850010 1,675 328 2,091 2,082 1,984 1,950 1,889 1,789 1,174 966 536 I-285 eastbound, North Arc 2850014 1,843 457 2,444 2,434 2,360 2,305 2,206 1,933 1,248 838 448 I-285 eastbound, North Arc 2850017 1,347 495 2,175 2,130 1,905 1,852 1,721 1,419 507 209 42 I-285 westbound, North Arc 2851033 1,634 307 2,230 2,126 1,917 1,849 1,797 1,728 1,306 911 527 Seattle I-405 614DN 1,668 202 1,991 1,953 1,904 1,851 1,782 1,708 1,463 1,326 817 I-405 614DS 1,766 233 2,212 2,082 2,018 1,976 1,896 1,809 1,562 1,265 680 I-405 672DN 1,749 348 2,101 2,094 2,041 2,018 1,953 1,854 1,250 775 486 I-405 677DN 2,145 358 2,595 2,557 2,493 2,462 2,371 2,219 1,790 1,649 574 I-405 678DN 1,839 315 2,265 2,253 2,151 2,105 2,044 1,910 1,497 1,117 650 I-405 678DS 1,554 268 1,976 1,961 1,881 1,839 1,725 1,596 1,250 1,072 547 I-405 681RS 2,027 266 2,398 2,356 2,291 2,240 2,170 2,081 1,826 1,687 635 I-405 684DN 1,687 169 2,094 2,044 1,896 1,862 1,782 1,706 1,505 1,429 1,197 I-405 684DS 1,616 198 1,961 1,896 1,828 1,775 1,725 1,659 1,433 1,303 673 I-405 687RN 1,531 200 1,961 1,832 1,775 1,729 1,649 1,558 1,341 1,227 597 I-405 689RS 1,516 173 1,961 1,786 1,718 1,664 1,611 1,543 1,334 1,224 836 (continued on next page)
69 I-405 693RN 1,599 167 1,961 1,851 1,794 1,767 1,702 1,630 1,417 1,349 992 I-405 694RN 1,574 178 1,961 1,889 1,820 1,763 1,687 1,596 1,368 1,296 961 I-405 696DN 1,927 48 1,961 1,961 1,961 1,961 1,961 1,927 1,892 1,892 1,892 I-405 696DS 1,615 221 1,961 1,953 1,866 1,835 1,769 1,674 1,349 1,186 920 I-405 698DN 1,586 151 1,961 1,961 1,805 1,771 1,693 1,571 1,414 1,349 1,091 I-405 698DS 1,607 185 1,999 1,938 1,866 1,813 1,721 1,630 1,383 1,292 1,087 I-405 704DN 2,032 276 2,398 2,383 2,337 2,272 2,204 2,105 1,714 1,497 992 I-405 706DN 1,615 541 1,961 1,961 1,961 1,961 1,961 1,892 992 992 992 I-405 708DN 1,811 175 2,124 2,105 2,010 1,995 1,919 1,843 1,630 1,467 1,201 I-405 708DS 1,788 222 2,117 2,094 2,048 2,003 1,934 1,839 1,528 1,440 954 I-405 709DN 1,930 222 2,322 2,208 2,158 2,139 2,060 1,961 1,740 1,550 866 I-405 709DS 1,933 293 2,379 2,364 2,223 2,174 2,117 1,995 1,588 1,307 783 I-405 710RN 1,778 229 2,132 2,086 1,999 1,961 1,904 1,824 1,592 1,292 714 I-405 710RS 1,926 239 2,318 2,288 2,177 2,124 2,056 1,951 1,786 1,600 673 I-405 711RN 1,776 179 2,060 1,999 1,959 1,934 1,877 1,820 1,617 1,427 946 I-405 711RS 1,877 427 2,504 2,402 2,310 2,250 2,174 2,048 1,205 920 688 I-405 716RN 1,891 256 2,291 2,227 2,139 2,098 2,041 1,930 1,661 1,349 817 I-405 716RS 1,979 291 2,409 2,345 2,280 2,200 2,128 2,025 1,775 1,455 509 I-405 717RN 1,830 246 2,284 2,124 2,067 2,041 1,972 1,877 1,581 1,330 692 I-405 717RS 1,940 215 2,333 2,307 2,236 2,147 2,060 1,959 1,754 1,653 1,068 I-405 720DS 1,498 272 1,961 1,923 1,820 1,775 1,695 1,554 1,180 984 540 I-405 722DS 1,512 209 1,961 1,892 1,744 1,710 1,642 1,539 1,296 1,060 817 I-405 726RS 1,629 334 2,333 2,291 2,128 2,029 1,900 1,585 1,345 1,007 638 I-405 730RN 1,572 313 2,044 2,044 1,961 1,923 1,843 1,568 1,243 882 585 I-405 730RS 1,641 218 1,961 1,961 1,892 1,851 1,744 1,661 1,490 1,258 570 I-405 731RN 1,564 309 1,972 1,972 1,921 1,870 1,816 1,695 1,094 1,056 654 I-405 731RS 1,459 220 1,961 1,961 1,824 1,718 1,623 1,482 1,224 1,140 654 (continued on next page) Table 4.9. Distribution of SSR at Selected Locations (2007) (continued) SSR (vphpl) Route Station Mean Standard Deviation Maximum P99 P95 P90 P75 Median P10 P5 P1
70Table 4.9. Distribution of SSR at Selected Locations (2007) (continued) SSR (vphpl) Route Station Mean Standard Deviation Maximum P99 P95 P90 P75 Median P10 P5 P1 Seattle I-405 734DN 1,781 251 2,200 2,200 2,071 2,006 1,921 1,832 1,493 1,224 654 I-405 734DS 1,736 281 2,170 2,170 2,105 2,067 1,955 1,721 1,493 1,391 570 I-405 736DN 1,951 248 2,470 2,345 2,253 2,181 2,092 1,982 1,752 1,391 897 I-405 736DS 1,942 285 2,424 2,333 2,242 2,212 2,117 2,006 1,634 1,455 654 I-405 738DN 1,888 255 2,223 2,200 2,139 2,094 2,014 1,934 1,733 1,486 665 I-405 738DS 1,894 265 2,409 2,265 2,200 2,155 2,056 1,946 1,596 1,509 752 I-405 739DN 1,816 240 2,147 2,120 2,037 2,003 1,946 1,858 1,661 1,277 718 I-405 739DS 1,790 238 2,272 2,196 2,120 2,048 1,915 1,813 1,566 1,440 654 I-405 740RN 1,772 251 2,101 2,075 2,014 1,987 1,927 1,835 1,471 1,307 673 I-405 740RS 1,846 227 2,379 2,307 2,139 2,075 2,003 1,866 1,611 1,497 1,037 I-405 741RN 1,624 386 2,082 2,044 1,984 1,946 1,873 1,790 950 756 498 I-405 741RS 1,795 214 2,307 2,212 2,143 2,014 1,904 1,801 1,626 1,566 965 I-405 742DN 1,783 281 2,120 2,098 2,044 2,016 1,949 1,877 1,429 1,144 661 I-405 742DS 1,606 556 1,961 1,961 1,961 1,961 1,961 1,892 965 965 965 I-405 763DS 1,644 226 2,044 2,003 1,927 1,873 1,794 1,695 1,372 1,262 806 I-405 764DS 1,927 48 1,961 1,961 1,961 1,961 1,961 1,927 1,892 1,892 1,892 Note: P99, P95, P90, P75, P10, P5, and P1 = 99th, 95th, 90th, 75th, 10th, 5th, and 1st percentile, respectively.
71 there is more excess capacity to buffer their effect, which is shown by the long tail to the left but no second peak for non- recurring events. Sites with a bimodal distribution may also be upstream of a bottleneck. Thus, flow will be observed to break down under low-volume conditions when actually it is queue spill- back from the downstream bottleneck. reliability of Signalized arterials Data from the Orlando signalized arterial study sections were analyzed after undergoing the quality control checks dis- cussed in Chapter 3. Figures 4.24 through 4.29 show the travel time distributions and selected performance measures. (These are the first continuous travel time distributions for signalized arterials that the team has seen.) As with urban freeway travel time distributions, the distribution is skewed to the right (toward higher travel times), but the extent of the skew does not appear to be as great, possibly because Further examination of the shape of the SSR distribu- tions revealed some interesting results. Two distinct patterns emerged: a unimodal and a bimodal distribution. The uni- modal SSR distribution is exhibited in Figures 4.21 and 4.22. As with travel times, the distribution is skewed, but to the left as opposed to the right. A typical bimodal distribution is shown in Figure 4.23. A crude analysis of congestion levels indicates that the uni- modal distribution is most common on slightly to moder- ately congested sites, but the bimodal distribution is more characteristic of highly congested locations. A possible explanation for the occurrence of two distribu- tion types is that the bimodal distribution shows both a recurring (close to 2,000 vphpl) and a nonrecurring (around 1,000 vphpl) SSR. Locations with high base congestion are more vulnerable to traffic-influencing events such as incidents, and this sensitivity may be reflected in the SSRs. These loca- tions also may be more prone to lane-blocking incidents because of higher incident rates or lack of shoulders, or both. Incidents in less congested locations have less effect because Figure 4.21. Distribution of SSR on I-405 in Seattle at Station 651DN. Figure 4.22. Distribution of SSR on I-405 in Seattle at Station 708DS.
72 Figure 4.23. Distribution of SSR on I-405 in Seattle at Station 612DN. Figure 4.24. Orlando, Section 3, a.m. peak. Figure 4.25. Orlando, Section 3, p.m. peak.
73 Figure 4.26. Orlando, Section 4, a.m. peak. Figure 4.27. Orlando, Section 4, p.m. peak. Figure 4.28. Orlando, Section 5, a.m. peak.
74 reliability of rural Freeway trips Figures 4.30 through 4.33 show the reliability of trips on the two study sections for 2006 and 2007 combined. The plots show the distribution of the actual travel times. However, in calculating TTI and associated statistics, travel times faster than the free-flow travel time were set to the free-flow travel time to be consistent with how these statistics were calculated on urban freeways. Vulnerability to Flow Breakdown An alternative way to view travel time reliability is in terms of a facilityâs vulnerability or susceptibility to disruptions that lead to congestion. That is, in the absence of recurring incidents on arterials do not have the same effect as on free- ways. Since midblock flows of signalized arterials are largely controlled by the metering of upstream signals, the flows are well below what the midblock capacity would be with- out the signals. This excess capacity absorbs the effect of single-lane or shoulder blockages at midblock locations. Some midblock incidents have little or no effect and do not produce the extreme travel times observed on freeways. However, if an incident occurs at the signal, where capacity already is restricted, there will be a major impact on traffic flow. The morning distributions appear to be more compact and peaked than the afternoon distributions, which tend to be broader. This difference may be a function of higher con- gestion levels in the afternoon; the team noticed a similar pat- tern on congested urban freeways. Figure 4.29. Orlando, Section 5, p.m. peak. Figure 4.30. I-45 northbound, Texas (length = 61.4 miles).
75 Figure 4.31. I-45 southbound, Texas (length = 60.0 miles). Figure 4.32. I-95 northbound, South Carolina (length = 33.1 miles). Figure 4.33. I-95 southbound, South Carolina (length = 33.1 miles).
76 facility began to be highly vulnerable to breakdown. On aver- age days, there is little noticeable congestion, but on the worst days, congestion builds rapidly. This period between TTI divergence and the uptick in average congestion is therefore extremely important from a traffic management standpoint. Figure 4.35 shows the corresponding probability of con- gestion (when speeds are less than 50 mph, identified in the HCM as the approximate point of breakdown flow) for the entire afternoon time period for the same location shown in Figure 4.34. Figure 4.36 shows two characteristics of conges- tion at point locations. First, there appears to be a nonlinear relationship between average TTI and 95th percentile TTI, as seen in the steeper growth of the curves up to the peak. Sec- ond, average volume peaked early (around 4:10 p.m.) and stayed relatively flat throughout the peak, indicating that congestion, there is a likelihood that a disruption (e.g., an incident) may cause congestion to form. Whether conges- tion will materialize is a function of how severe the disrup- tion is and how much traffic volume is present. An analysis was undertaken to understand this effect using data from Atlanta. Figure 4.34 shows volumes and TTIs for individual stations (detectors in all lanes at a roadway loca- tion) measured at 5-minute intervals for nonholiday week- days. The transition from uncongested midday conditions to prepeak conditions can be seen around 2:50 p.m. Volumes started to increase quickly at about this time, and the 95th percentile TTI increased even more sharply. However, aver- age TTI stayed almost unchanged until after 3:15 p.m. The point at which the 95th percentile and average TTIs diverged (i.e., 2:50 p.m.) can be thought of as the point at which the Figure 4.34. Beginning of weekday peak on I-75 in Atlanta at Station 750502 (2008). 2: 30 2: 40 2: 50 3: 00 3: 10 3: 20 3: 30 3: 40 3: 50 4: 00 4: 10 4: 20 4: 30 4: 40 4: 50 5: 00 5: 10 5: 20 5: 30 5: 40 5: 50 6: 00 6: 10 7: 10 6: 20 6: 30 6: 40 6: 50 7: 00 Time of Day Probability of Congestion 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Figure 4.35. I-75 in Atlanta at Station 750502 (2008).
77 ⢠I-285 Northern Arc, from I-75 to I-85 (10.37 miles) â4 36 links eastbound, and â4 34 links westbound. The number of links is different for the directions because of station placement. For each directional section, morning and afternoon peak times were considered. The analysis pro- ceeded as follows. First, reliability metrics for the individual links were calcu- lated for each direction and time slice. After this, reliability for the entire trip was calculated. A simple method of com- bining the link reliability metrics was then used: all the met- rics for the links were averaged to see if the resulting average was correlated with the trip metrics. Figures 4.37 through 4.39 demonstrate that the metrics are very highly correlated. Sim- ple nonlinear functions were then fit to the data. All coeffi- cients were significant at an alpha level of 0.001 (most at an alpha level of 0.0001). Root mean squared error (RMSE) was used as a measure of goodness of fit when no intercept term was specified in the regression analyses. 95 3 2 41 0 8014th percentile TTI RMSEtrip = =( )X . . % ( . )1 80 1 8 42 0 8702th percentile TTI RMSEtrip = =( )X . . % ( . )2 MeanTTI RMSEtrip = =( )X30 9020 0 1 4 3. . % ( . ) MedianTTI RMSEtrip = =( )X41 0600 2 6 4 4. . % ( . ) StandardDeviation RMSE trip = = 0 6195 1 5 1 1163. . X 3 3 976 4 52. %, . ( . )R =( ) congestion suppressed volumes, as discussed earlier in this chapter under âEstimating Demand in Oversaturated Condi- tions on Freeways.â reliability of Urban trips Based on reliability of Links The approach taken in this research for urban conditions was to define travel time reliability over a section of highway, typi- cally 4 to 5 miles in length, with relatively homogenous geo- metric and traffic conditions. In many transportation modeling applications, it is desirable to know the travel time of entire trips, and by extension, the reliability of trips. The data sources used in this study precluded studying entire trips (from origin to destination) because they were collected at the roadway level. However, an experiment was conducted with urban free- way data from Atlanta in an attempt to develop trip-based reliability. Specifically, the team was interested in seeing if the reliability of a trip could be predicted from the reliability of the individual links comprising the trip. Here trip means travel occurring solely on the freeway, as data for access to and egress from the freeway were not available. The term links refers to stations (detectors for all lanes at a specific location). From the Atlanta section data, extended sections were devel- oped by combining two adjacent sections. These combinations resulted in four one-way trips (one in each direction): ⢠I-75 North, from I-285 to Barrett Parkway (12.53 miles) â4 25 links northbound, and â4 20 links southbound; and 2: 30 2: 45 3: 00 3: 15 3: 30 3: 45 4: 00 4: 15 4: 30 4: 45 5: 00 5: 15 5: 30 5: 45 6: 00 6: 15 6: 30 6: 45 7: 00 7: 15 7: 30 7: 45 8: 00 Time of Day Index 3.500 3.000 2.500 2.000 1.500 1.000 Volume 850Average TTI 95th Percentile TTI Average Volume 750 600 500 800 700 650 550 450 400 Figure 4.36. Complete weekday peak, I-75 in Atlanta at Station 750502 (2008).
78 Figure 4.37. Trip versus link reliability: mean TTI. Figure 4.38. Trip versus link reliability: standard deviation. Figure 4.39. Trip versus link reliability: 95th percentile TTI.
79 their reliability metrics treated in the same way; that is, the reliability statistics of the nonfreeway links could be com- bined with the freeway linksâ reliability statistics. Finally, the trips used here were relatively short, even for urban condi- tions. Longer trips may run into the same time dependency noted for long-distance trips in this chapterâs discussion of the Reliability of Rural Freeway Trips. reference 1. Brilon, W., J. Geistefeldt, and H. Zurlinden. Implementing the Concept of Reliability for Highway Capacity Analysis. In Transpor- tation Research Record: Journal of the Transportation Research Board, No. 2027, Transportation Research Board of the National Academies, Washington, D.C., 2007, pp. 1â8. http://trb.metapress.com/content/ u700713ur834410r/fulltext.pdf. where X1 = average of 95th percentile TTIs for all the links in the trip, X2 = average of 80th percentile TTIs for all the links in the trip, X3 = average of mean TTIs for all the links in the trip, X4 = average of median TTIs for all the links in the trip, and X5 = average of standard deviations of TTIs for all the links in the trip. It should be pointed out that the strong correlation is prob- ably due to the trip-based measures using travel times from individual links. However, in travel demand forecasting mod- els, trip travel times are calculated this way. Although the analysis was restricted to freeway sections, the team does not see why nonfreeway links could not be added to the trip, and
