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TABLE XIII EFFECT OF THE TOPOLOGY ON NETWORK OPTIMIZATION
Table 1: Wedge Shock Comparison Results From the M ops count, for these problems DRSB is just under seven times times faster than RSB on average and up to ten times faster. The DRSB M ops counts which are below average arose from the rst iteration failing and the code having to expand the working graph. This is particularly noticeable for the 7th mesh (M ops count of 1.4) where the rst iteration failed in two of the bisection problems, one of these being at the second recursive level. In mitigation however, the 7th mesh had changed fairly dramatically from the 6th (725 ! 899 triangles) with much re nement around the shock and de-re nement away from it. At only one stage did the code revert to the full sub-graph (for the 3rd mesh) and since this was at the third recursive level it did not add greatly to the cost. 12
TABLE I TOPOLOGICAL CHARACTERISTICS OF EMPIRICAL POWER NETWORKS
Table 1. Summary of odd parity and TC results using: (a) node transfer crossover and node description crossover with relative probability 3 and 1, respectively; (b) layered sub-graph crossover and node description crossover with relative probability 3 and 1, respectively; (c) linear sub-graph crossover and node description crossover with relative probability 3 and 1, respectively; (d) one-point crossover and node description crossover with relative probability 3 and 1, respectively.
"... In PAGE 9: ... Apparently, node transfer crossover (Table 1a) gives the best results in terms of e ort and per- centage of solutions. However, The results ob- tained with layered subgraph crossover (Table 1b) are really very close to those in Table1 a, with the exception of the computational e ort of the 5-parity problem. We believe that this result is a statistical artifact, and that the two crossover operators are essentially equivalent.... In PAGE 9: ...ith those found in the literature, e.g. in terms of number of generations to achieve solutions of equivalent complexity.1 The scalability of the method can be assessed by the e ort shown in Table1 a. E orts for the odd 3, 4 and 5-parity problems are comparable to those reported using other methods.... ..."
Table 1. Summary of odd parity and TC results using: (a) node transfer crossover and node description crossover with relative probability 3 and 1, respectively; (b) layered sub-graph crossover and node description crossover with relative probability 3 and 1, respectively; (c) linear sub-graph crossover and node description crossover with relative probability 3 and 1, respectively; (d) one-point crossover and node description crossover with relative probability 3 and 1, respectively.
"... In PAGE 9: ... Apparently, node transfer crossover (Table 1a) gives the best results in terms of e ort and per- centage of solutions. However, the results ob- tained with layered subgraph crossover (Table 1b) are really very close to those in Table1 a, with the exception of the computational e ort of the 5-parity problem. We believe that this result is a statistical artifact, and that the two crossover operators are essentially equivalent.... In PAGE 9: ...ith those found in the literature, e.g. in terms of number of generations to achieve solutions of equivalent complexity.1 The scalability of the method can be assessed by the e ort shown in Table1 a. E orts for the odd 3, 4 and 5-parity problems are comparable to those reported using other methods.... ..."
Table 5: Comparison of solution times for different network topologies
2000
"... In PAGE 8: ...We investigated time complexity of CCO-BAVP and GA- BAVP algorithms for 3, 4, 5, 6 and 7 node network topologies. Ignoring the trivial solution of the 2 OD pairs, Table5 compares the % increase (over the previous problem formulation solution) of CCO-BAVP and EP-BAVP. It is clearly demonstrated that as the problem complexity increases, from 12 OD pairs to 42 OD pairs, the time complexity of the GA based algorithm does not increase as fast as the CCO solution.... In PAGE 8: ... The two algorithms achieve comparable results (within a few % difference from each other), with some topologies and link capacities favoured by the CCO-BAVP and others by GA-BAVP. Also, as the problem complexity increases, from 12 OD pairs to 42 OD pairs, the time complexity of the GA based algorithm does not increase as fast as the CCO solution (see Table5 ). GA- BAVP outperforms CCO-BAVP in the initial convergence period, but after that CCO-BAVP exhibits faster convergence towards optimum.... ..."
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Table 1 Characteristics of network topology. Network (NW) Number
"... In PAGE 13: ....1.1. Network Models: We got two real world networks from a telecom. Their main charac- teristics are described in the first lines of Table1 . The samples NW1 and NW2 were drawn following a breadth-first search, i.... In PAGE 14: ... (2002) in this study. Table1 also provides the clustering coefficients and the average path lengths for different networks. In addition to the real world networks we generated scale-free networks NW5 - NW7 with different power-law coefficients (2.... ..."
Table 4. Shared Backup Path Protection Problem Performance Parameters
"... In PAGE 14: ...# Variables Test ID # Paths SBPP PR 32LM 135 302 1,405 45LM 178 401 2,046 32HM 286 604 2,976 45HM 368 781 4,076 32LS 122 276 950 45LS 169 383 1,840 32HS 239 510 1,699 45HS 319 364 683 2,921 Table 3. Problem Characteristics for SBPP and PR Table4 illustrates that the majority of SBPP problems were not solved to optimality by either GDS or CPLEX within the 12 hour algorithm testing time limit. The star topologies appeared easier to solve.... ..."
Table 4 Characteristics of networks used in simulation
"... In PAGE 10: ...ts predominant traffic (see Sect. 6). The parameters of the BFWC appear in Table 7. The simulations were performed over three real ISP topologies with real link delays (see Table4 ). The infec- tion is started by a random host within the network.... ..."
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.... ..."
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