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63 Chapter Eight RECOMMENDED COMPUTATIONAL PROCEDllRES: AWSC INTERSECTIONS The research results presented In this report form the foundation for the computational procedures for determining saturation headways, computing capacities and delay, and Betel rig level of senice for an AWSC intersection. This section documents the fourteen steps that make up the proposed computational procedures. These procedures wall form the basis for the AWSC mtersechon section of the new version of chapter ten of the HCM. An example calculation is given to illustrate the procedures. Figure 32 lists Me steps In He computational procedures. Step 1. Documentinitial Conditions Step 2. Adjust volumes and determine lane assignments Step 3. Determine geometric group Step 4. Determine base saturation headways Step 5. Compute starting value for departure headways Step 6. Compute degree of saturation Step 7. Compute actual value of departure headway Step 8. If departure headway values converge, continue to step 9; if not; return to step 6 Step 9. Make adjustment to departure headways Step 10. Compute service times Steps 1 1 and 12. Compute capacities Step 13. Compute delays Step 14. Compute level of service Figure 32. Recommended Computational Procedures INITIAL CONDITIONS AND ADJUSTMENTS Step 1. Input Conditions Five input parameters are required for this procedure. These are listed below. . number and configuration of lanes on each approach vol~es by fuming movement for each approach (v) percent heavy vehicles on each approach (THE) peak hour factor WHIT length of study period or length of oversaturated period, hours (T) Step 2. Volume Adjustments and Lane Assignment Step 2a. The volumes are converted to equivalent hourly flow rates using the peak hour factor. v= v PHF (36) Step 2b. The homey flow rates are allocated to each lane of each approach either as a result of direct observation or by estimation. Step 3. Geometric Group Determine the geometric group for each approach. The geometric group for the subject approach is based on the number of lanes on the opposing and conflicting approaches. The geometric groups are listed in Table 85. Table 85. Geometry Group . ~, 2 I: .............................. ;,. ................... ... .. ............. ... . ~.... it, .......... .......... .- . ~ ~.==~2'""'~22~"""""''~''''' 1': T 1 41egarT 1 1 2 41eg - T 1 1 3al4a 4 leg orT 1 2 3b T . 1 2 4b 4 kg 1 2 S 41egacT 2 1 or2 6 4 kg orT 3 _ 2 1 2 2 1 or2 3 Step 4. Base Saturation Headways The sa~ationheadwa~r for each lane for degree of conflict case ~ is determined from Table 86. The adjustments for turning movements and heavy vehicles are made using Table 87 and Equation 37.
64 h,,,~, = h, ~ hate Per ~ ho - par ~ ho - pin (3 where hubris the adjusunent to the case i base headway, hi is the base saturation headway for case i, h~T-dj is the headway adjusdnent for led turns (either 0.2 or 0.5, Table 86. Saturation Headway Values by Case and Geometry Group depending on geometry Casey, hRT.atj is tile headway adjustment for ritht~ns (either-0.6 or-0.7), hHV ,dj is the headway adjustment for heavy vehicles (~7), PAT iS the proportion of led-tarning vehicles on Me approach, PRT is the proportion of right-t~ning vehicles on the approach, and PHV is We proportion of heavy vehicles on the approach. .~ . ~t If ~ ~ 1 1 0 3.9 3.9 4.0 4.3 4.0 4.S4.S 4.S 1 2 1 >2=3 147 14.7 1 4.8 1 1 11 62 3 1 >~-3 15.8 1 58 1 59 1 6.2 1 5.9 1 44 1 6446 7.0 17.° 1 7.1 174 17.1 1~.6 17g 1 S 1 21~ 1 96 1 9.6 1 9~7 1 100 1 97 1 1~2 1 IT : ] Table 87. Saturation Headway Adjushnent Factors by Geometry Group ,.~ . ~ 1'"~' ' 'I ' :~ 1 . . . 1 ''''''I ' '''''"" '1"' ' 6~ 1''' ''my - .............................................. ....................... ....................... ................ , .,,,,,,,,.,,., .............................. . , l,,.,, ; ; , LT 1 0.2 1 0.2 1 0.2 1 0.2 1 0.2 1 0.2 1 0.5 RT -0.6 ~.6 ~.6 ~.6 ~.6 ~.7 HV 1.7 1.7 1.7 1.7 1.7 1.7 1.7 O.S .7 1.7 . , HEADWAY AND SERVICE TIME Step 5. Starting Value for Departure Headway The initial or starting value for the departure headway for each lane is established. The default value is 4 seconds. Step 6. Degree of Saturation Compute Me degree of saturation for each approach. The degree ofsaturation (x) Is the product of the flow rate and Me departure headway Ad. x = roll /3600 . ~,!'dt Step 7. Actual Value of the Departure Headway The actual departure headway for each lane, based on hectic flow on the opposing and conflicting approaches, is computed based on the probability of each lane having a vehicle waiting at the stop line. This probability is a combined probability based on each possible case of vehicles either being present or not present in each lane. Equation 39 gives the expected value of this distribution. h`= ~P[C]h~ (38) (39) where ha is He expand value of the headway distribution, P[C] is die probability of degree of conflict case i, and be
65 is the saturation headway for case i. The probability, PUCE, for each degree-of-conflict case is computed based on Me degree of saturation on each approach. For We opposing approach, the conflichug approach from the left, and the convicting approach from the right, the ratios are given by xO, X<:L, and x,, lively. For single lane approaches, Me probabilities are computed using Me foDow~ng equations. P[C1] = (1 - xo) (1 - Xci) (1 - FOR) (40) PtC2] = (Xo) (] - x=) (1 - x=) they P[C3] = (1 - xo) (ice) (1 - PER) + (1 - xo) (1 - ACE) (XCR) (42) P[C~ = (Jo) (1 - x~ (x=) + (xo) (XCZ) (} - X=) + (1 - xo) (X=) (X=) (43) PtCS] = (Xo) (ACE) (Xa~) (44) For muld-lane approaches, the departure headway is given by Equation 45. 12 ho = EP[Cd ho (4~ ~1 Step S. Convergence If the expected value of Me departure headway has changed less than some value (say 0.01 seconds) on each approach, the analyst can proceed to step 9. If Me expected values are stiff changing, the analyst should return to step 6 to compute a new value of the degree of saturation. Step 9. Adjustment to Departure Headway An adjustment to the converged value of departure headway is made to account for the interdependence between the degree of conflict cases. This adjustment is computed using Equation 46. P,,,t,fil] = P[.~1 + a~ - ~ - 1] t4o where Padj~i,k] is Me probability of degree of conflict case i given case k and ~ is a constant. Step 10. Service Time The service time is computed using Equation 47 and the depar~eheadway~computed from step 9 and Me move- up time, m. A move-up time of 2.0 seconds is used for sites from Groups ~ through 4 and 2.3 seconds for sites from Groups 5 and 6. s = hi - m (471 CAPACITY Two values of capacity are computed, each based on a different concept of capacity. Step Il. Capacity Based on Concept ~ The capacitor of each approach is computed assuming that Me Bows on the opposing and conflicting approaches are held constant. The Even flow rate on the subject lane is increased and the departure headways are computed for each approach using steps 5 Trough 9 of this computational procedure until the degree of saturation for any lane reaches one. The current value of the subject approach How rate is the maximum possible throughput or capacity of this lane. Step 12. Capacity Based on Concept 2 The capacitor of each approach is computed assuming that the g~ven~ow rates oneach~ntersection approach are held In constant proportion to each over. All flow rates are increased incrementally and the departure headways are computed for each approach using steps 5 through 9 of this computational procedure until the degree of saturation for any lane reaches one. The current value of flow on each lane is He maximum possible throughput or capacity of that lane. DELAY AND LEVEL OF SERVICE Step 13. Delay Average stopped delay per vehicle is computed for each lane and each approach using Equation 48. [ ~ 450T]] (48)
66 where d is the average stopped delay per vehicle, s is the service time, x is the lane or approach degree of saturation, and T is the length of the measurement interval or congested period. The intersection delay is the weighted average of the delay on each of the approaches. Step 14. Level of Sernce The level of service for each approach and for the intersection is determined using Table SS and Me computed values of stopped delay. Table 88. Level of Service Ranges , ; .... , . ,: ,.,,,.~.,,,,,~,.a. ~,.~.,~, ': ' ~ A O-S B S - 10 C 10 -20 D 20 -30 E 30 -4S F >4S , SAMPLE CALCULATION A sample calculation is presented here to illustrate We proposed computational procedure. The example intersection has one lane on each approach wad flow rates and We percentage of heavy vehicles shown In Table 89. Table 89. Traffic Volumes for Sample Calculation .,.~ Nor&bound LT SO S TH ". . 200 S RT ' - 7S S . . Southbound LT SO S TH 100 S RT 50 S Eastbound LT SO S TH 300 S RT SO S Westbound LT IS S TH 400 S RT 2S S . Step 1. Input Conditions Five~ut parameters are required for this procedure. The values of these parameters are documented. There is one lane on each approach. The flow rates and percentage of heavy vehicles are shown in Table 89. The peak hour factor is one. T is assumed to be 0.25 hours. Step 2. Volume Adjustments and Lane Assignment The hourly flow rates are converted to equivalent hourly flow rates using the peak hour factor. Since the peak hour factor is one, He equivalent hourly flow rates are the same as the given input flow rates. There is one lane on each approach so all of the flows will be on the same lane on each approach. Step 3. Geometric Group This intersection is Group ~ since there is one lane on each approach. No geometric adjus~nent in the saturation headway is required. Step 4. Base Saturation Headways The base saturation headways are computed starting with the values given In Table 86. Left turn and right turn adjustments are applied using the factors Even in Table 87. The results for each approach are given in Table 90. Table 90. Base Saturation Headways ................................... .................... ...................... .................... .................... D.~c Am . ~ ................................ ....... ........... , ........... . ~ ...................................... .................................... .................................. .. 1 3.8 3.9 3.9 4.0 2 4.7 4.7 4.7 4.8 3 S.8 S.S S.S S.9 4 7.0 7.0 7.0 7.1 S 9.6 9.6 9.6 9.7 . ~. i. Step 5. Starting Value of Departure Headway The initial or starting value of departure headway for each lane is established. The default value is 4 seconds. Steps 6 and 7. Degree of Saturation and Actual Value of the Departure Headway The final values for the degree of saturation and departure headway for each approach are given in Table 91.
67 Table 91. Degree of Saturation and Deparh~re Headway '2 '. ~. _ . Dcgrec of Sanction 0.69 0.4S 0.81 0.90 Departed Headway 7.6 8.1 7.3 7.2 . l Step 8. Convergence The calculations converged after four iterations. Step 9. Adjustment to Departure Headway The departure headways are adjusted to account for senal correlation. A value of a of 0.01 was used. The final values of degree of saturation and departure headway are given in Table 92. Table 92. Degree of Saturation and Deparhlre Headway ~-,,.~5,,,,,,51 Degree of Sanction 0.64 0.42 0.76 0.84 Departure Headway 7.1 7.6 6.8 6.8 _ Step 10. Service Time For Group ~ sites, the move-up time is 2.0 seconds. This value is used to compute the senice time, given the departure headway for each approach. The values are shown in Table 93. Table 93. Semce Time Service Time 1 S.1 S.6 4.8 4.8 , . Capacity Calculations Two values of capacity are computed, each based on a different concept of capacitor. The results from both capacity calculations are given in Table 94. Table 94. Capacity Calculations Concept 1 AM lotion Concept 2 App~ Moon 463 lS13 342 1481 414 lS89 217 1481 S03 1478 434 1481 S18 1442 488 8 Step 11. Capacity Based on Concept 1 The capacity of each approach is computed assuming that the flows on the opposing and conflicting approaches are held constant. The given flow rate on the subject lane is increased and the departure headways are computed for each approach using steps 5 through 9 of this communions procedure until the degree of saturation for any lane reaches one. Step 12. Concept Based on Concept 2 The capacity of each approach is computed assuming that He given flow rates on each intersection approach are held in constant proportion to each other. AD flow rates are increased incrementally and He departure headways are computed for each approach using steps 5 through 9 of this complexional procure until the degree of saturation for any lane reaches one. The current value of flow on each lane is the maximum possible throughput or capacity of that lane. Step 13. Delay Average stopped delay per vehicle is computed for each lane and each approach using equation 48. Step 14. I,eve} of Service The level of service for each approach and for the intersection is determined using Table 88 and the computed values of stopped delay. The results are shown in Table 95. Table 95. Delay and Level of Service Calculations . , 0 : . ............................................... . , ... .. . ~ , . , ..... ; |Delay ILevel of Service 17.0 C 11.1 C 23.8 D 33.3 E
68 , . ~ .
