### Table 1: Tra c intensity values that delineate the convex and concave regions of G( )

1992

"... In PAGE 8: ...heorem 2.2]. Having proved the various bounds on the value of (K), we will nd it instructive to numerically compute the values of (K) for sample bu er sizes. Table1 shows values for h(K) and (K) for di erent values of K. It can be immediately seen that the sample values conform to the earlier established bounds.... ..."

Cited by 2

### Table 1: Tra c intensity values that delineate the convex and concave regions of G( )

"... In PAGE 8: ...heorem 2.2]. Having proved the various bounds on the value of (K), we will nd it instructive to numerically compute the values of (K) for sample bu er sizes. Table1 shows values for h(K) and (K) for di erent values of K. It can be immediately seen that the sample values conform to the earlier established bounds.... ..."

### Table 4. Relative L2 and energy error norms for the patch test on meshes with concave elements

in Summary

"... In PAGE 30: ...igure 21. Shape functions in non-convex elements. (a), (b) Metric coordinate method;(c),(d)Meanvaluecoordinates a reference pentagon are shown, and the partitioning of the elements in the meshes shown in Figures 22a and 22d are illustrated in Figures 23b and 23c, respectively. The relative error norms obtained on meshes with concave elements are presented in Table4 . The mean value coordinates are used to evaluate the shape functions on convex and concave elements.... ..."

### Table 4: Characteristics of the Cutting Plane Method

"... In PAGE 15: ... Recall that the restricted master problems are solved with ACCPM [25] and subproblems are solved with HOPDM [23]. Table4 gives characteristics of the decomposition. For every problem, we report the dimension of space (the number of variables associated with the rst stage in Benders reformulation of the problem), the number of subproblems and some characteristics of the ACCPM runs: the number of outer iterations, the number of inner iterations required to restore approximate analytic center after adding new cuts and the total number of cuts added throughout the solution of the problem to the desired 6-digit optimality.... In PAGE 15: ... For every problem, we report the dimension of space (the number of variables associated with the rst stage in Benders reformulation of the problem), the number of subproblems and some characteristics of the ACCPM runs: the number of outer iterations, the number of inner iterations required to restore approximate analytic center after adding new cuts and the total number of cuts added throughout the solution of the problem to the desired 6-digit optimality. By analysing the results collected in Table4 , we conclude that ACCPM behaves well on these stochastic problems. The method is practically insensitive to the problem size and nds optimal solution after generating from 11 to 15 query points.... ..."

### Table 4: Characteristics of the Cutting Plane Method

1998

"... In PAGE 15: ... Recall that the restricted master problems are solved with ACCPM #5B25#5D and subproblems are solved with HOPDM #5B23#5D. Table4 gives characteristics of the decomposition. For every problem, we report the dimension of space #28the number of variables associated with the #0Crst stage in Benders reformulation of the problem#29, the number of subproblems and some characteristics of the ACCPM runs: the number of outer iterations, the number of inner iterations required to restore approximate analytic center after adding new cuts and the total number of cuts added throughout the solution of the problem to the desired 6-digit optimality.... In PAGE 15: ... For every problem, we report the dimension of space #28the number of variables associated with the #0Crst stage in Benders reformulation of the problem#29, the number of subproblems and some characteristics of the ACCPM runs: the number of outer iterations, the number of inner iterations required to restore approximate analytic center after adding new cuts and the total number of cuts added throughout the solution of the problem to the desired 6-digit optimality. By analysing the results collected in Table4 , we conclude that ACCPM behaves well on these stochastic problems. The method is practically insensitivetothe problem size and #0Cnds optimal solution after generating from 11 to 15 query points.... ..."

### Table 1: The computed values of AS and H for the individual catchments

"... In PAGE 5: ...e 3.105 and 0.410. The proposed procedure is employed to compute the values of AS and H for the remaining catchments ( Table1 ). It is observed in Figure 8 that the larger the average size of the convex and concave regions in the catchment, the larger is the average roughness of the catchment.... ..."

### Table 5-7: Summary for Offsets From Various offline Methods for State Route 26, Lafayette, Indiana (Cycle length = 120 seconds)

"... In PAGE 8: ...Figure Page 5-8 Comparison of offline offset design methods, Eastbound State Route 26 (Graph created with values from Table5 -7 through Table 5-11) .... In PAGE 8: ...Graph created with values from Table 5-7 through Table 5-11) ................90 5-9 Comparison of offline offset design methods, Eastbound State Route 26 (Graph created with values from Table5 -7 through Table 5-11) .... In PAGE 8: ...Graph created with values from Table 5-7 through Table 5-11) ................90 5-10 Comparison of offline offset design methods, Westbound State Route 26 (Graph created with values from Table5 -7 through Table 5-11).... In PAGE 8: ...Graph created with values from Table 5-7 through Table 5-11)..............91 5-11 Comparison of offline offset design methods, Westbound State Route 26 (Graph created with values from Table5 -7 through Table 5-11).... In PAGE 74: ... Subjective values are required for determining the arterial classification, as well as for the vehicle progression classifications provided in HCM Table 11-5. Table5 -1a and Table 5-1b show the HCM tables in which subjective values are required. Table 5-2 provides the HCM definitions for the progression adjustment factors (PF) for different arrival types.... In PAGE 74: ... Table 5-1a and Table 5-1b show the HCM tables in which subjective values are required. Table5 -2 provides the HCM definitions for the progression adjustment factors (PF) for different arrival types. These subjective requirements are explicitly acknowledged in the HCM, and the manual states that if knowledge of the intended signal timings and quality of progression are not available, no meaningful estimation of arterial level of service is possible, even on a planning level [NRC, 1997].... In PAGE 76: ... Table5 -1: Highway Capacity Manual Tables Requiring Subjective Values HCM TABLE 11-3. ARTERIAL CLASSIFICATION ACCORDING TO FUNCTIONAL AND DESIGN CATEGORIES FUNCTIONAL CATEGORY DESIGN CATEGORY PRINCIPAL ARTERIAL MINOR ARTERIAL High Speed design And control I Not Applicable Typical suburban Design and Control II II Intermediate Design II III or IV Typical urban Design III or IV IV (a) Arterial classification subjective values HCM TABLE 11-5.... In PAGE 77: ... Table5 -2: Highway Capacity Manual Definitions for Progression Adjustment Factors HIGHWAY CAPACITY MANUAL DESCRIPTIONS FOR PROGRESSION ADJUSTMENT FACTORS ARRIVAL TYPE DESCRIPTION FOR PROGRESSION ADJUSTMENT FACTOR 1 Dense platoon containing more than 80 percent of the lane group volume and arriving at the start of the red phase. This arrival type is representative of arterials that experience very poor progression quality as a result of conditions such as lack of overall network signal optimization.... In PAGE 78: ... However with advancements in traffic controller hardware functions to include actuated controls, the delay equation does not account for how variations in green splits affect the start of green times in modern coordinated-actuated controllers. Such variations in the start of green times directly impact the quality of progression (HCM PF Factors shown in Table5 -1) and the amount of delay experienced. However, the HCM has no procedure for estimating which PF Factors shall be used with design volumes or for the design of coordinated- actuated controller timings.... In PAGE 79: ...Furthermore, determining the quality of progression factor for the PF term of the HCM average intersection delay equation is a difficult task, even if observed in the field by an engineer. For existing arterial conditions, one analyst may conclude that current arterial signal timings are not facilitating progression and assign an arrival of type-2 ( Table5 -2). But, another analyst may conclude that because of platoon dispersion, vehicle progression for the exact same arterial resembles random arrivals and assign an arrival of type-3 (Table 5-2).... In PAGE 79: ... For existing arterial conditions, one analyst may conclude that current arterial signal timings are not facilitating progression and assign an arrival of type-2 (Table 5-2). But, another analyst may conclude that because of platoon dispersion, vehicle progression for the exact same arterial resembles random arrivals and assign an arrival of type-3 ( Table5 -2). Both of these arrival types are subjective values and are difficult to distinguish between one another in the field by technicians typically employed to do so.... In PAGE 80: ... An example of how slight discrepancies with both of the discussed issues impact an arterial level of service is provided. Table5 -3 and Table 5-4 show the quantitative calculations used to compute an arterial level of service for a hypothetical 0.2 mile suburban arterial section with slightly different values assigned to the g/c ratios and the quality of progression factors.... In PAGE 81: ...developed for accurately modeling the multitude of coordinated-actuated control parameters now in use on most modern traffic signal systems. Table5 -3: HCM Calculations for Average Control Delay per Vehicle on Arterial Approach SUMMARY OF ARTERIAL INTERSECTION DELAY ESTIMATES Arterial Description: 4 lane suburban arterial, 0.2 mile section, volume = 1500 vph Adjusted Saturation flow rate = 3000 vph, Unit extension of 2.... In PAGE 81: ...or X = 0.833 and X = 0.714 respectively. Table5 -4: HCM Calculations for Arterial Level of Service COMPUTATION OF ARTERIAL LOS WORKSHEET Arterial Description: 4 lane suburban arterial, 0.2 mile section, Volume = 1500 vph, Adjusted Saturation flow rate = 3000 vph, Unit extension of 2.... In PAGE 84: ...then tabulated to calculate the arterial cumulative delay and travel times with respect to intersection locations. See Table5 -5 for an example of arterial cumulative value calculations. Plots of these cumulative delay and travel times can provide insight on the performance of the system.... In PAGE 85: ... Additionally, although the graphic procedure discussed is limited to cumulative delay and travel times, similar graphic procedures can be expanded to include the number of stops or emission estimates for HC, CO, and NOX. Table5 -5: Cumulative Delay and Travel Times used to Construct Figure 5-4 and Figure 5-5 MID-DAY TRAFFIC S.R.... In PAGE 87: ... STEP 2: Data Calculations Individual link values are then used to compute the cumulative values for link lengths, travel times, and delay times at each of the node locations on the arterial. After these cumulative data are compiled, the averages ( Table5 -5, cols. 7 amp; 8), and standard deviations (Table 5-5, cols.... In PAGE 87: ... After these cumulative data are compiled, the averages (Table 5-5, cols. 7 amp; 8), and standard deviations ( Table5 -5, cols. 9 amp; 10) for the cumulative arterial measures of effectiveness (MOEs) are computed.... In PAGE 88: ... In contrast to current methods, this proposed performance evaluation procedure can provide a graphic comparison of different system plans to validate new proposed signal timings. As shown in Figure 5-6, Figure 5-7, and Table5 -6 ,a proposed arterial timing plan can be compared with an existing arterial timing plan through graphical and tabular analysis procedures to quantitatively illustrate that the proposed timing plan accomplishes the design objective of reducing delay and travel times. This comparison of alternate signal timing plans provides the designer a tool that illustrates the improvement of the proposed arterial signal timing plan over the existing arterial signal timing plan.... In PAGE 90: ... Table5 -6: Lane Group Comparison of Delay per Vehicle at Individual Intersection; State Route 26, Node 1 Lane Group Movements Existing Delay (sec/veh) Proposed Delay (sec/veh) Existing Level of Service Proposed Level of Service 41.4 38.... In PAGE 94: ... All offset setting methodologies were used with the intent to replicate how practicing engineers typically specify offsets for coordinated-actuated systems. Table5 -7 summarizes the offsets determined with each method and what offset setting technique was used within that package. Table 5-7: Summary for Offsets From Various offline Methods for State Route 26, Lafayette, Indiana (Cycle length = 120 seconds)... In PAGE 95: ...Cumulative results for measures of effectiveness consisting of travel time (sec/veh) and delay (per-min) for the arterial through movement for each timing strategy are provided in Table5 -8 through Table 5-12. Graphical performance summaries comparing the alternate offset timing strategies are shown in Figure 5-8 through Figure 5-11.... In PAGE 96: ... Table5 -8: Existing Offset Results LINK START END CUMM TRAVEL TIME (sec) STDEV CUMM TRAVEL TIME (sec) CUMM DELAY TIME (per-min) STDEV CUMM DELAY TIME (per-min) 101 1 32.6 1.... In PAGE 97: ... Table5 -9: Fine-Tuned Offset Results LINK START END CUMM TRAVEL TIME (sec) STDEV CUMM TRAVEL TIME (sec) CUMM DELAY TIME (per-min) STDEV CUMM DELAY TIME (per-min) 101 1 32.2 1.... In PAGE 98: ... Table5 -10: PASSER II-90 Offset Results LINK START END CUMM TRAVEL TIME (sec) STDEV CUMM TRAVEL TIME (sec) CUMM DELAY TIME (per-min) STDEV CUMM DELAY TIME (per-min) 101 1 32.1 0.... In PAGE 99: ... Table5 -11: SYNCHRO Offset Results LINK START END CUMM TRAVEL TIME (sec) STDEV CUMM TRAVEL TIME (sec) CUMM DELAY TIME (per-min) STDEV CUMM DELAY TIME (per-min) 101 1 32.1 1.... In PAGE 100: ... Table5 -12: TRANSYT-7F Offset Results LINK START END CUMM TRAVEL TIME (sec) STDEV CUMM TRAVEL TIME (sec) CUMM DELAY TIME (per-min) STDEV CUMM DELAY TIME (per-min) 101 1 31.4 0.... In PAGE 101: ...Cumulative Travel Time (State Route 26 (Eastbound)) (Earl Avenue to Creasy Lane) 0 50 100 150 200 250 0 1000 2000 3000 4000 5000 6000 7000 Linear Distance Along Corridor (ft) Time (s) Signal Location Fine-tuned Existing PASSER2 Offsets SYNCHRO TRANSYT 7F Posted Speed Limit Figure 5-8: Comparison of offline offset design methods, Eastbound State Route 26 (Graph created with values from Table5 -8 through Table 5-12) Cumulative Delay (State Route 26 (Eastbound)) (Earl Avenue to Creasy Lane) 0 100 200 300 400 500 600 700 800 900 1000 0 1000 2000 3000 4000 5000 6000 7000 Linear Distance Along Corridor (ft) Delay (person-min) Signal Location Fine-tuned Existing PASSER2 SYNCHRO TRANSYT 7F Figure 5-9: Comparison of offline offset design methods, Eastbound State Route... In PAGE 101: ...Cumulative Travel Time (State Route 26 (Eastbound)) (Earl Avenue to Creasy Lane) 0 50 100 150 200 250 0 1000 2000 3000 4000 5000 6000 7000 Linear Distance Along Corridor (ft) Time (s) Signal Location Fine-tuned Existing PASSER2 Offsets SYNCHRO TRANSYT 7F Posted Speed Limit Figure 5-8: Comparison of offline offset design methods, Eastbound State Route 26 (Graph created with values from Table 5-8 through Table 5-12) Cumulative Delay (State Route 26 (Eastbound)) (Earl Avenue to Creasy Lane) 0 100 200 300 400 500 600 700 800 900 1000 0 1000 2000 3000 4000 5000 6000 7000 Linear Distance Along Corridor (ft) Delay (person-min) Signal Location Fine-tuned Existing PASSER2 SYNCHRO TRANSYT 7F Figure 5-9: Comparison of offline offset design methods, Eastbound State Route 26 (Graph created with values from Table5... In PAGE 102: ...Cumulative Travel Time (State Route 26 (Westbound)) (Creasy Lane to Earl Avenue) 0 50 100 150 200 250 300 0 1000 2000 3000 4000 5000 6000 7000 Linear Distance Along Corridor (ft) Time (s) Signal Location Fine-tuned Existing PASSER2 SYNCHRO TRANSYT 7F Posted Speed Limit Figure 5-10: Comparison of offline offset design methods, Westbound State Route 26 (Graph created with values from Table5 -8 through Table 5-12) Cumulative Delay (State Route 26 (Westbound)) (Creasy Lane to Earl Avenue) 0 200 400 600 800 1000 1200 1400 1600 0 1000 2000 3000 4000 5000 6000 7000 Linear Distance Along Corridor (ft) Delay (person-min) Signal Location Fine-tuned Existing PASSER2 SYNCHRO TRANSYT 7F Figure 5-11: Comparison of offline offset design methods, Westbound State... In PAGE 102: ...Cumulative Travel Time (State Route 26 (Westbound)) (Creasy Lane to Earl Avenue) 0 50 100 150 200 250 300 0 1000 2000 3000 4000 5000 6000 7000 Linear Distance Along Corridor (ft) Time (s) Signal Location Fine-tuned Existing PASSER2 SYNCHRO TRANSYT 7F Posted Speed Limit Figure 5-10: Comparison of offline offset design methods, Westbound State Route 26 (Graph created with values from Table 5-8 through Table 5-12) Cumulative Delay (State Route 26 (Westbound)) (Creasy Lane to Earl Avenue) 0 200 400 600 800 1000 1200 1400 1600 0 1000 2000 3000 4000 5000 6000 7000 Linear Distance Along Corridor (ft) Delay (person-min) Signal Location Fine-tuned Existing PASSER2 SYNCHRO TRANSYT 7F Figure 5-11: Comparison of offline offset design methods, Westbound State Route 26 (Graph created with values from Table5... In PAGE 103: ... To accommodate left turning vehicles from upstream intersections, an online algorithm should attempt to keep the average start of green as low as possible in relation to downstream intersections while also accounting for downstream queues that may impede progression. Table5 -13 through Table 5-15 provide statistical significance summaries comparing the fine-tuning offset... In PAGE 104: ... Table5 -13: State Route 26 statistical significance summary; Fine-tuned offsets versus PASSER-II 90 offsets Measure of Effectiveness FINE TUNED PASSER II-90 Percent Reduction Calculated t-statistic Test statistic for 95% C.I.... In PAGE 104: ...078 -1.688 (#) Standard deviation; n1 = n2 = 20 replications Table5 -14: State Route 26 statistical significance summary; Fine-tuned offsets versus SYNCHRO offsets Measure of Effectiveness FINE TUNED SYNCHRO Percent Reduction Calculated t-statistic Test statistic for 95% C.I.... In PAGE 105: ... Table5 -15: State Route 26 statistical significance summary; Fine-tuned offsets versus TRANSYT-7F Measure of Effectiveness FINE TUNED PASSER II-90 Percent Reduction Calculated t-statistic Test statistic for 95% C.I.... ..."

### Table 1. Learning results for sensor features. #rules #given #derived #correctly der. correct/given correct/derived

1996

"... In PAGE 19: ... For four di erent goal concepts (namely s line, s jump, s convex, s concave) we used the di erent training sets for learning resulting in dif- ferent sets of rules. In Table1 , we have summarized the results of learning rules for single sensors. It shows for each basic feature set the average number of learned rules, counted for the di erent goal concepts separately.... In PAGE 20: ... For this test, we have taken the best basic feature set, Set 2, and a grammar corresponding to grdt apos;s one. Table1 summarizes the results, which clearly indicate that for our domain, a learner that just covers the goal concept learns too few rules, that are unlikely to be applicable in future scenes.9 5.... ..."

Cited by 33

### Table 1. Learning results for sensor features. #rules #given #derived #correctly der. correct/given correct/derived

1996

"... In PAGE 19: ... For four di erent goal concepts (namely s line, s jump, s convex, s concave) we used the di erent training sets for learning resulting in dif- ferent sets of rules. In Table1 , we have summarized the results of learning rules for single sensors. It shows for each basic feature set the average number of learned rules, counted for the di erent goal concepts separately.... In PAGE 20: ... For this test, we have taken the best basic feature set, Set 2, and a grammar corresponding to grdt apos;s one. Table1 summarizes the results, which clearly indicate that for our domain, a learner that just covers the goal concept learns too few rules, that are unlikely to be applicable in future scenes.9 5.... ..."

Cited by 33