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s Chapter Two PREVIOUS WORK This chapter summarizes the work of Free researchers or groups that constitute the major body of research conducted onAWSC'nt~sectionsto date. lacquesHebert published a study of Free Intersections in Chicago that became the basis for the capacity guidelines of the 1985 HCM. Anthony Richardson developed a queuing mode} usage headway data measured by Hebert. Researchers at the University of Idaho developed emp~cally-based models for capacity and delay that were published In Transportation Research Circular (TRC) 373 and In the 1994 HCM update. HEBERT AND THE 1985 HCM Jacques Hebert (1963) proposed a capacity model for AWSC intersections based on saturation headway values for two cases, one In which the driver faced another vehicle on the opposing or conflicting approaches and one In which He driver faced no over vehicles. He measured values of 4.0 seconds and 7.6 seconds for these two cases, based on a study of three sites in Chicago conducted during periods of continuous queuing. Saturation headway values for these Ho cases are He basis for He 1985 HCM capacity procedures. Hebert presented equations to forecast He capacity of an approach based on the volume split between the two intersecting sheets and He number of lanes on each street. Equation ~ gives He capacity equation four an intersection with one lane on each approach. 3600 c = - 10.15 - up (1) where vp is the proportion of He intersection volume on the higher volume street. The 1985 HCM summanzed Hebert's work into capacity guidelines that can be used to assess He performance of an AWSC Intersection based on demand split for 2-lane by 2-lane (i.e., one lane in each direction), 2-lane by 4-lane, and 4-lane by 4-lane intersections. Tables ~ and 2 show the intersection cap acid by demand split for a 2 by 2 Intersection and by intersection type for a 50/50 demand split. Table ~ shows that He intersection capac~h,r is maximum when the flow is evenly split among all approaches; He approach cap recite under this split is 425 vph. Table 2 shows that simultaneous movement from a two-lane approach can occur, increasing the capacitor of the approach. Table 1. Intersection Capacibr as a Function of Volume Split ............... :~. ~i ,.,.,.~. .,. ~, SO/SO 1,900 SS/4S 1,800 60/40 1,700 6S/3S 1,600 70/30 1,SOO Note: Demand Split is Me proportional split of Traffic between the ~n~g~ Table 2. Intersection Capacity as a Function of Intersection Type . ~........... ................. , .. ........ ,.; ....................................................................................................................... ......................................................................................................................... 2-lane by 2-lane 1,900 2-lane by 4-lane 2,800 I Plane by 4-lane 3,600 Note: Caries are based on SO/50 demand Split RICHARDSON MODEL Anthony Richardson (1987) proposed a method of computing He capacity of an approach of an AWSC intersection by iteratively computing the service time of each approach based on the likelihood of vehicles being present on the opposing and conflichug approaches. His iterative method assumed two states, no vehicles on the opposing or conflicting approaches and one or more vehicles on the conflicting approaches. The computational method converges quickly and is easily implemented using computer software. While the basic method is valid, the major 1imitadon of the Richardson mode} is He small number of sates Hat are considered. Richardson proposed an MIG/l queueing model to estimate delay, using He Pollaczek-Khintchine formula.

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6 This formula is given ~ Equation 2. D xW(1 +C2) g 2~1 - x) (2) where W is He average senice time (or time spent In the first position In queue), x is the degree of saturation, and Cw is the coefficient of variation of service times. The total average delayis the sum of the time in queue, Dq, and the time spent in He first position, W. TRC 373 AND THE 1994 HCM Between 1987 and 1989, the University of Idaho conducted studies at AWSC intersections in the Pacific Northwest and in Iowa to determine the factors that influence capacitor and delay. Saturation headways were measured and a capacity equation was developed from these data. This capacitor equation, and the supporting data, were published as part of TRC 373 (19911. TRB's Committee on Highway Capacity and Qualify of Senice proposed this method to be used on an interim basis since it provided a significant improvement over the method then Included In the 1985 HCM. After several years of use by the traffic cogineeiing community, Ellis method was published as part of the 1994 - atetothe HCM as the approved procedure to determine the capacitor of an AWSC intersection. The 1994 HCM Update describes the basis for traffic operations at an AWSC intersection: The headway between vehicles departing from a STOP line of an AWSC intersection is a function of the conditions present on the other intersection approaches. Minimum saturation headways are achieved if there is not traffic on any of the other intersection approaches. Maximum saturation headwinds result if tragic is present on ad of the other approaches. This microscopic perspective has a direct analogy at the macroscopic level. The maximum flow rate on a given approach can be achieved if there is not tragic on any of the other approaches. The minimumflow rate on a given approach results if tragic is evenly distributed among all of the intersection approaches. Thus the key variable in the determination of approach capacity is the relative distribution of traffic volumes among the approaches. This variable is called~volume distribution. When tragic is evenly distributed! among the approaches, the capacity of a single-lane approach is approximately 525 vph and the capacity of a four-leg intersection is approximately 2, ]00 vph under ideal condEihons. Research has found the capacity of a single-lane approach, when there is no tragic on any of the other approaches, is ],100 vph under ideal conditions. Data published by Kyte and Marek (1989), by Kyte (1990), subsequently in Transportation Research Circular 373, and now Included In the 1994 Update of He HCM, suggest that four cases are needed to describe He conditions faced by the subject approach driver at an AWSC ~n~io~ These conditions are defined in Table 3. Table 3. Saturation Headway Data for AWSC Idtersechons (1994 HCMUpdabe) ............................................... .......... .. = ~ ''"''""'''1 . ~...... ........................................ . ........................................................ . ~ ~. ~... ,.,., ,. . ~ All data 3.S S.5 6.S Single lane 3.9 S.6 6.S Multi lane 1.S 4.3 6.3 . . Need Single Menses single lane approach mingle saw Multi lane notes multi lane abroad sable sites. Case 1 occurs when the sect vehicle does not fi~cee~a~oangorco~licting vehicles. Case 2 occurs Whence subject vehicle faces only an opposing vehicle. Case 3 occurs u hen We subject vehicle feces ably conflicting vehicles. Case 4 occurs whence subject vehicle faces both opposing and conflicting vehicles. 9.0 9.0 9.3 The four headway cases listed In Table 3 do not directly consider the effects of mining traffic. The case 2 headway, which is a subject vehicle faced by an opposing vehicle and no con Dichng vehicles, does not consider He elects of He interaction of one or both of the vehicles laming and not traveling straight through the intersection. The value of 5.5 seconds givenin Table 3 is assumed to cover the range of combinations that actually make up case 2: for example, pairs of through vehicles with no turning conflicts, one through vehicle opposed by a led turning vehicle, one through vehicle opposing by a rift homing vehicle, etc. While the capacity equation given in the 1994 HCM Update does provide an adjusunent for turning movements, it is based only on the overall proportion of mining movements and not on the microscopic or vehicle- by- vehicle interactions that actually reflect the degree-of- conflict resulting from bulging vehicle conflicts.

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The capacity equation is given in Equation 3. c = loony, + 700p + 200L, - 1ooLo - 300LT' + 200RT' - ~nnr.T + cannot (3) ~vv~eLpc ' ~VV4~7C The parameters In the equation are defined In Table 4. Table 4. 1994 HCM Update AWSC Capacity Equation Parameter Definition .. ...................... ~ I Dehorn.. . .. ~ _ ~ Capacity ofthe subject approach Vp, Proportion of intersection volume on subject approach VpO Proportion of intersection volume on opposing approach ~Number of lanes on subject approach L Number of lanes on opposing approach LTpo Proportion of volume on opposing approach fuming left RTpo Proportion of volume on opposing approach tuning right LT,,, Proportion of volume on conflicting approaches turning left RTp, Proportion of volume on convicting approaches t~= The delay formula now used In the 1994 HEM Update, given In Equation 4, Is based on We volume/capacity ratio, v/c. The mode! Is emp~ncally based but has Me important proper of forecasting an exponentially- increasing value Of delay as the volume/capacity ratio increases. d = e3.S vJc RECENT WORK (4) Two rum studies significantly add to the work previously cited. The first was published in 1994 and the second descnbes the results from Me pilot study from phase one ofNCHRP 3-46. 1994 University of Idaho Study Sanction headway date were collected by Kyte and others (1994) for one approach of an AWSC intersection to determine if there were subsets of these four basic cases described in the 1994 HCM update that would better reflect He vehicle-by-vehicle impedances described earlier. Two separate series of tests were conducted. First, for each of the four cases, the effect of He directional movement ofthe subject approach vehicle was deteImined. Second, subsets of cases 3 and 4 were identified and tested. Table 5 shows the saturation headways for the Trough movement and right turn movement for each of the four cases. Separation of the saturation headways by toning movement results in considerably different saturation headway and capacity estimates, with capacity differences ranging from 27 percent to 50 percent between He Trough movement capacity and He right horning movement capacity. A difference In means test verified the significance of the difference In these measurements at the 0.05 significance level. Table 5. Effect of Tuming Movement on Approach Capacity of AWSC Intersection , , , , . . . ............ .............................. ................................. ......................................... ............ , ......................... ......... .. : . . ~e~ . ~................ .............. ................ ; ~ . ............ ................................ ......................... ................................ ................................ ............ . ~e ................................... ...... = , , . . ~, 1 3.0 2.1 1200 1714 +43% 2 4.2 2.8 8S7 1286 +50% 3 6.3 4.9 S71 73S +29% 4 7.9 6.2 4S6 S81 +27% Note: lUis the~routh movement. RTis~e light~m movement. Another way of improving the AWSC intersection capacity procedure is to detenIiine if the four cases can be divided into subsets that better reGect the conditions faced by the subject vehicle. For example, case 3 states that the subject vehicle Is faced by vehicles on the convicting approach and not on He opposing approach. But this case can include one or two conflicting vehicles, one from the left or one from the right, or both. Several subsets were considered for cases 3 and 4 to determine if additional cases are justified. Table 6 lists these subsets. Table 7 shows He saturation headways that were measured for each of the six subsets.

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8 Table 6. Subsets for Saturation Headway Cases , ~ ., If : 5 - ! 3a One conflicting vehicle Bom Me right 3b One conflicting vehicle Bom We led 3c One conflicting vehicle from both the leR and Me right 4a One conflicting vehicle Bom the leR and one opposing vehicle 4b One conflicting vehicle Bom the right and one opposing vehicle 4c One conflicting vehicle Dom bow Me led and right, and one opposing vehicle , i,. _ . Table 7. Saturation Headways for Subsets for AWSC Intersections .. .. .. . . . . .- ; . . . . . ... . . . . , ; . . . ... , ......................... ....... ... ~ ,~, ,a:' =:e . . ~...... .... 3a S.1 1.60 31 3b S.~6 1.38 20 3c 6.8 1.67 36 4a 6.9 1.62 32 4b 6.8 1.S7 62 4c 8.4 2.39 82 Note: SD is the standard deviation. Obs is the number of observations. First, Me study found Mat there was no statistically significant difference between cases 3a (5. l seconds) and 3b (5.6 seconds). That is, from the standpoint of the subject approach driver, it makes no difference if a conf icing vehicle approaches Mom the left or the right, as tong as there is only one cor~flichng vehicle. But there is a significant difference between cases 3a or 3b and case 3c (5. ~ to 5.6 seconds, and 6.8 seconds). Thus if one conflicting vehicle is present on both the leR and Me right approaches, Me saturation headway for Me subject vehicle is different, in this case longer, Man if the subject vehicle is faced by only one convicting vehicle. Also, there are some differences In the three case 4 subsets. Similar to the results for case 3a and 3b, Mere is not a significant difference between the case 4a (6.9 seconds) and 4b (6.8 seconds) subsets. But Mere are differences between cases 4a and 4b and case 4c (~.4 seconds) subsets. Thus, while Me direction of approach on the conflicting approach does not make a difference, He number of conflichug and/or opposing vehicles is significant. NCHRP 3 46 Pilot Study For the pilot study, Phase ~ of NC~P 3-46 (Kyte, et.al., 1993), saturation headways were measured for a total of 4,863 vehicles for these four cases. These results are shown in Table S. While the specific headway measurements are somewhat different, the relative magnitudes for the two studies (TRC 373 data and NCHRP 3~6 pilot study data) are similar. As discussed above, one of the shortcomings of Me TRC 373 classification system was the I~m~ted number of cases considered, particularly the lack of consideration given to (~) the number of opposing or convicting vehicles faced by the subject approach vehicle, (2) the directional movement of the subject approach vehicle, and (3) the effect of vehicle type. To more accurately assess He effects of opposing and conflicting vehicles, eight cases were proposed. The saturation headways measured during the pilot study were classified into these eight cases and are listed in Table 9. Several conclusions can be drawn from these results: . . . The approach direction of a conflicting vehicle (either from He left or Dom the nght) does not affect the saturation headway of the subject approach vehicle. The saturation headway values for cases 3 and 4 are nearly equal; the values for cases 6 and 7 are also nearly equal. The number of vehicles on the conflicting approach (either one or two) does make a significant difference in the saturation headway of the subject approach vehicle. Note that the values for cases 3 and 4 are lower than for case 5. While the specific approach does make a difference if the subject vehicle faces only one opposing or conflicting vehicle (the headway for case 2 is less clan the headway for either cases 3 or 4), it does not make a difference if the subject vehicle faces two opposing or conflicting vehicles (cases 5, 6, and 7 are nearly He same).

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Table 8. Saturation Headway Data ,., ,.,. , , , _ ,, , , ,. ,,, . . , . ,. ~.. ,.,, ...... ....... 1. No other vehicle on any 2. One or more vehicles on the opposing abroad only 3. One or more vehicles once conflicting approaches only 4. One or more vehicles on both Me opposing and conflicting approaches . ~, .................. . . .......... ~.2 ~................. . 3.2 3.9 4.9 S.6 6.3 6.S 8.0 9.0 The saturation headways for each of the three directional movements of Me subject approach vehicle were computed and are Even In Table 10. The following conclusions can be drawn from the information presented in this table. The tuning movement direction has a significant effect on We saturation headway of the subject approach vehicle. In seven of the eight cases listed, the saturation headway for the left turning vehicle is higher Man for the through movement, which in tum is higher than for the right turn movement. Table 9. Saturation Headway Data for AWSC Intersections, Pilot Study 9 . . K the through movement Is taken as the base case, adjustment factors can be computed for Me effect of fuming vehicles on the saturation headway. For left turn vehicles, this adjustment factor is 0.90. This means that the capacity reduction due to left turning vehicles is 10 percent. For right En vehicles, the adjustment factor is 1.36, or 36 percent higher than for through vehicles. The assessment of saturation headways without respect to subject vehicle turning movement did not show a (difference between cases 3 and 4, and cases 6 and 7. Such a difference, however, might be e2~1 when the directional movement of the subject vehicle is considered. The data presented in the table do not support this expectation. The saturation headway measurements for passenger cars and heavy trucks show a significant difference. Table ~ ~ shows the computed saturation headways for these two vehicle types. In every case, Me saturation headway for passenger cars is lower than that for heavy trucks. This difference averages I.5 seconds, or 22 percent. These headways can be translated into capacity flow rates, 563 veh/br for passenger cars and 462 veh/hr for trucks. This results in a passenger car equivalent of I.2 for trucks at AWSC intersections. . F ~ ~ ~ ~ ~ ....... 1 ~ . ~ ~ , ~.. ~ . 1 I No odes vehicle | No other vehicles 1 3.0 1 3.0 l 2 One vehicle No other vehicles 4.7 4.8 3 No other vehicle One vehicle from the left approach 5.7 5.9 4 No over vehicle One vehicle from We light approach 5.7 5.6 S No other vehicle One vehicle from both the left and right approaches 7.3 7.1 6 One vehicle One vehicle from the left approach 7.3 7.2 7 One vehicle One vehicle from the right approach 7.4 7.3 8 One vehicle One vehicle from both the left and right approaches 9.1 9.2 Notes: The values are based on the mean ofthe mean values measured for each ofthe 13 subject approaches of this pilot study. 4L5L4 is Leg single lane approach sites.

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10 Table 10. Saturation Headways by Subject Approach Movement Direction ...................................................... . ~.~ 1 52 ~' ''~1 ,, .,. _ "'" ''"'"''"''' ~""i' ':""''"""'"''''"'" ' -; it_ ~ . ~.' ~''""'"''"'1'''"" ~''''1'"' ' 'I'""''' ~q 1 4.0 85 1.7 3.7 200 2 6.2 71 1.8 5.0 288 3 S.9 60 1.6 5.6 149 4 6.2 20 1.4 6.0 69 S 7.1 39 1.S 7.3 107 6 8.0 134 2.0 7.0 308 7 8.9 37 2.1 7.5 151 8 10.7 70 4.6 9.2 203 S16 6.4 1475 l , . -.-.~.-.-.-.-.-.-.-. ~BJ.~C~V.:~VEJA-'OIL L-~* .43-.- ~ .-..... :::::::::::::::::::~.:::::::::::: :-: 4.0 6.2 S.9 6.2 7.1 8.0 8.9 10.7 . 1.3 1.S 1.S 1.3 1.6 1.8 1.8 2.7 2.8 3.8 S.2 4.S 6.4 6.3 S.4 8.0 71 60 42 19 18 37 11 22 1.3 1.3 1.8 1.1 1.1 1.8 1.1 2.1 Mean 7.1 4.7 280 Notes: Hazy is the saturation headway, Obs is the number of observations; StDev is the standard deviation. Table 11. Saturation Headways for Passenger Cars and Trucks 1 2 3 4 S 6 7 8 3.2 4.8 S.7 S.7 7.4 7.2 7.6 9.2 798 758 355 341 521 624 668 694 4.6 S.9 7.6 8.7 8.3 7.9 7.9 11.6 15 19 3 12 IS 17 18 Total 64 4759 7 g , , , , . , 104 l Note: Obs is He number of observations.