**Suggested Citation:**"Chapter Ten. Recommended Computational Procedures." Transportation Research Board. 1996.

*Capacity and Level of Service at Unsignalized Intersections: Final Report Volume 1 - Two-Way-Stop-Controlled Intersections*. Washington, DC: The National Academies Press. doi: 10.17226/6340.

**Suggested Citation:**"Chapter Ten. Recommended Computational Procedures." Transportation Research Board. 1996.

*Capacity and Level of Service at Unsignalized Intersections: Final Report Volume 1 - Two-Way-Stop-Controlled Intersections*. Washington, DC: The National Academies Press. doi: 10.17226/6340.

**Suggested Citation:**"Chapter Ten. Recommended Computational Procedures." Transportation Research Board. 1996.

*Capacity and Level of Service at Unsignalized Intersections: Final Report Volume 1 - Two-Way-Stop-Controlled Intersections*. Washington, DC: The National Academies Press. doi: 10.17226/6340.

**Suggested Citation:**"Chapter Ten. Recommended Computational Procedures." Transportation Research Board. 1996.

**Suggested Citation:**"Chapter Ten. Recommended Computational Procedures." Transportation Research Board. 1996.

**Suggested Citation:**"Chapter Ten. Recommended Computational Procedures." Transportation Research Board. 1996.

**Suggested Citation:**"Chapter Ten. Recommended Computational Procedures." Transportation Research Board. 1996.

**Suggested Citation:**"Chapter Ten. Recommended Computational Procedures." Transportation Research Board. 1996.

**Suggested Citation:**"Chapter Ten. Recommended Computational Procedures." Transportation Research Board. 1996.

**Suggested Citation:**"Chapter Ten. Recommended Computational Procedures." Transportation Research Board. 1996.

**Suggested Citation:**"Chapter Ten. Recommended Computational Procedures." Transportation Research Board. 1996.

**Suggested Citation:**"Chapter Ten. Recommended Computational Procedures." Transportation Research Board. 1996.

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

123 The procedure is described below in step by step form and Is shown in Figure 70. It follows the general outline of We 1994 HEM Update, in Chapter Ten, Part m, Procedure for Application. . . Chapter Ten RECOMMENDED COMPUTATIONAL PRO CEDUR1ES This documents We computational procedures Mat are recommended for computing capacitor and level of service analysis at TWSC intersections. INPUT. Tic ~ tt NO ~ - CAPACITY AND IMPEDANCE I | | V,, - CO N FLICKING TO LO M E | 1 ~ _ HARDENS OAF. ~ MAJOR LO l - PEDEST. IMP. . CRINOID RT I ~ MINORS TO _ I . MINOR LT 2 - YES PART I I PART 11 1 MBN LT | MIN LT I Two ~ ~ - | 2STAG'E CAP. | _ INTERIM CAPACITY 'NO I AVG QUEUE l NO ~ ~ | FLARED CAPACITY | DELAY +~ DELAY . MOVEMENT .. APPROACH . INTERSECTION - - AL = ~_ | QUEUES I | AVERAGE WARR^NTt;~ Figure 70. Recommended Computational Procedure Step ~ - Input Data and Requirements Identify and document the foBow~ng input data. Refening to Figure 71: Me vehicular volumes by movement for the hour of interest: Vat, V2, V3, V4, Vs' V6, V', Vat, Vg, VIO, Vat,, V,2., and the pedestnan volumes by movement for the hour of interest divided by average group sizes: VL.' VR, VO, Vs. (Note: U-turn tragic is counted as major street left turn). Percentage of heavy vehicles: PHV PHVis the Combination Vehicles(%) + SU/RV(%) Peak hour factor: PHF. Number of through lanes on Me major street: N per direction. Major street left turn has shared lanes or blocks rank ~ flows: saturation discharge flow for major through and major right turns S2&3, S58~6 Number and use of lanes on the minor street approaches. Number of legs at the intersection: L'. Grade of all approaches(°/O). Other geometric features of interest: channelization, two-way left-turn lane, railed/striped median: storage k in median, flared approach: storage k for right turn, upstream signals for each direction i=2 amd/or 5 for the platooned flow(s): cycle Ci, green time gi, initial offset of, saturation flow si, platooned flow Vpi, distance from intersection d Step 2 - Volume Adjustment The only adjustment for the volumes is to convert the Vi ; into 15-m~nute volumes, if a 15-m~nute analysis is desired I in which case all the volumes should be divided by the ' PHF.

124 Crow Intersection - T-Interseffion ~ 1 ~ ~ to 1~= Rank 1: 2, A, 5, 2: 1,4 ~ i. 8, O a) 3 8~.lll 4e 7.10 Ranl: l: 2, 3, s 2: 4, ~R,S b) S: 7 Eighth 71. Movement Ranks Step 3 - Determination of Critical Gap and Follow-up Time Determination of the critical gaps and follow-up times for each minor steam movement is based on Table 54 and Table 55, which account for Me effect of grades on the minor approach, 2-stage gap acceptance if applicable, and heavy vehicles. Table 54. Recommended Critical Gap Values Example: If Grade(%) = 4, PHr, = 20%, N= 4, ~ = 3, then, for the minor street left turn movement, the critical gap is: (I - P~Jf7.5 + 0.2 x Grade - 0 79 + PHI' ( 7.5 + 2.0 + 0.2 Grade - 0.79 =Q-0.29(7.5+0.2X4-0.77 +0.267.5+2.0+ 0.2x4 - 0.79 = B.0 sec. The follow-up rime is: ( pH'J x3.5 +P,~,x(3.5 + 1) 0.2X4.5 = 3.7 see (1 - 0.29 x3.5 + cad - COP Ad]=tment Factors Heavy Vehicle* Grades% Three-Leg 2-Stage Gap Acceptance** 4.1 1.0 6.2 1.0 0.1 6.S 1.0 0.2 , -1.0 4.1 1.0 0.2 -~0.7 -1.0 2.0 6.9*** 2.0 0.1 - 6.S 2.0 0.2 -1.0 7.S*** 2.0 0.2 -0.7 -1.0 Notes: *Combined critical gap is computed based on the proportion of passenger cars and heavy vehicles; ** In 2-stage gap acceptance situations, only one major street direction is crossed at a time; *** Assumes tum occurs into '`nearest" exit lane.

125 Table 55. Recommended Follow-Up Time Values Ad]~*nent Factors Heavy Vehicle. Note: *O.9-second adjustment for sintle-lane sins, and l.O-second adjustment for multi-Lane sow Combined follows time is computed based on the proportion of passenger cars and heavy vehicles. ** In 2- stage gap acceptance station, use same k as for V7. Vim Step 4 - Adjus~anent of Capacity for Effect of Upstream Signals (cm,8 and cm,,~; cm,7 and c,,,l0) Refer to Figure 61. This step should be used when an upstream signal is less than or equal to I/4 mile Tom Me TWSC intersection. Step 4.~. Obtain the platoon dispersion "spread ratio" for each upstream signal (direction 2 Tom left and direction 5 Tom nght). Use the dine-distance concept In Appendix I of the 1994 HEM as a basis for the method. Add a platoon dispersion sub-model, similar to the recursive aIgon~m used by TRANYST-7F signal analysis software (Van Aerde et al 1995~: Q' = FQ'-T + (1-F)Q,'~ Ohs) where A' are the vehicles Moving at the subject location In time slice t Qua are the vehicles departing from the upstream signal In time slice t Fis ~ /~} +~pta) T=pta to is the distance to upstream signal / average speed of platoon a is the dispersion factor alpha (constant for a given roadway) ,8 is the dispersion factor beta (constant for a given roadway) The algorithm is used to disperse a platoon departing at sanction flow rate from the upstream signal. The "spread ratio" at the TWSC location is defined as ache ratio between the time the dispersed platoon occupies at the TWSC location and the time that the platoon required to discharge Dom the upstream signal. Checks that the spread ratio does notnes~tinjoining of platoons from adjacent cycles, or in flows less Man the non platooned Bows. If either of these situations occurs then there is no effect of signals from that direction. Step 4.2. Calculate the platooned and nomplatooned flow rates at the subject TWSC intersection. The platoon flow is obtained by dividing the platooned flow rate at the upstream signalby~e spread ratio. The unplatooned flow rate is obtained by multiplying the unplatooned volume by the spread ratio. Check that unplatooned flow is less than the platooned flow. If not, Mere is no effect of signals Dom that direction. Step 4.3. Use the cycle lengths, Initial oif;ets, queue discharge times, and the spread ratios to calculate a series of "begin platoon" and "end platoon" events from each major street for the whole analysis period. Step 4.4. Sort these events chronologically and examine their sequence to calculate the proportion of the hour during which each of the following fow arrival flow "regimes" exists: no platoons platoons both directions platoons from left only platoons from right only The flows within each ofthese regimes are obtained in step 4.2. Step 4.5. For each controlled movement at the TWSC intersection, the capacity is calculated as the weighted average (using He proportions in step 4.4) of the capacities within each flow regime (as win He current 1994 HEM method) i.e. steps 4 through 17 are repeated. Step 5 - Computation of Capacity for Rank 2 Major Left Turn Movements (c,,,l anti c,,,) Step 5.1. Compute total conflicting volume Vc 1 and Vc4 based on Table 56.

126 Table 56. Evaluabon of Conflichng Rank Volume V,, Major Street LeR Tunt Minor Sbeet Ri~t Ibm For 2-stage Gap Acceptance Minor Sbeet lbrough Movement Minor Street LeB Turn V2/N ~ + O.S V31) + VR ?) V,/N 2) + O.S V61) + VI, 'J l part I (near side ~om leD) 2Vl+V2+0.S V31)+V5" 2V4 +V, + O.S V61) + VO " 2V1 + V2 + O.S V31) + VS 7) 2V4 + V5 + 0.5 V61, + VO " + part II (far side Bom right) + 2V4+ V, + V6" + VO ~ + 2V1 + V2 + V33) + V31 77 +2V4+VJN+0.5V6~+Vu~+Vll8+V~'J + 2V1+ V2/N + O.SV3 ~ + V6 + V, + VR 1 Notes: 1) If there is a ntht-turn lane on the major street, V3 or V6 should not be considered; 2) If ~ere is more ~n one lane on the rank road, V2 and V5 are considered as ha£lc volumes on the ri~t lane (apprommately 1/N ofthe total volume. N is the number of ~rough lanes); 3) If right-twningt~fF~c from the major road is separated by a biangular island and has to comply with a YIELD or STOP Sign, V6 and V3 need not be considered; 4) Itntht-t~ningtraffic bom the minor road is separated by a triangular island and has to comply wi~ a YIELD or STOP sign, V9 and V~2 need not be considered; S) If movements 11 and 12 are controlled by a STOP sign, V'' and Vl2 should be halved in~is equatio~ Similarly, if movements 8 and 9 are controlled by a STOP sign, V, and V9 should be halved; 6) Omit V9 and V,2 for multilane s~tes, or to halve their values if the minor approach area is flared; 7) Pedestrian groups V, with higher prion~ that conflict with the subject movement may also be ~`ded (Figure 10.2).; 8) Omit thefarthest right turn V3for subyset movement 10 or V6for subject movement 7 if the major street is multi-lane. Step 5.2. Compute movement capacities (c'`,~ C~,4) using Harders equation ~quation 166), or graphs may be provided. vc. J tc 3600 c = V e 1-e 3600 (166) Step 5.3. Compute probability of queue-free state pO i using Equation 167. PO'= 1 - ' (167) m,, where . For major street shared lane, use Equation 168. ~ * 1 1 - po, 1- (S +S f where . =5,ifi=4; k=3,ifi= 1; =6,ifi=4, Sj is the saturation flow rate for major s~eet through traffic streams Sk is the saturation flow rate for major street right turn traffic Step 6. Computabon of Impedance by Pedestrians for Minor Street Approach Movements Step 6.~. Calculate walk t~me for group to cross one trave! lane: tw = ~rnis ~ (N-l),ff (169) (168) i=l,4; j=2,ifi= I; w is the travel lane width; default w = 12 ~ n ~s the number of lanes crossed at a time; default n =l s is the waL~ng speed; defaults: s = 4.5 fps average, s = 3 f~s children or elderly N is the number of rows in peclestrian group; defallltN= ~ if V< 100 ped/h~ measure otherwise tf is the follow up time for consecutive rows of pedestnans; use tf = 2 he above assumptions s~mpliiN,r the equation to: tu, = 2.7

127 seconds average, or 4.0 seconds for children or elderly). The equivalent "volume/capaci~" ratio of pedestnan groups Vh required to calculate impedance would be: Vh~t,,/3600 (1703 Then, Me impedance factors for h = C, R. 0, S are (refer to Figure 71~: pa,,` = 1 - (vlc3h Aim . Table 57 shows approximate impedance factors that may be appropriate for planning applications. The assumptions would need to be vended wad empirical data. Table 57. Sensitivity Test for Impedance Factor Due to Pedestrians (s = 4 Ups, w = 12 ft) 0.96 0.86 n77 Two of the four pedestrian crosswalks h = it, R. O. S watt be crossed by each minor approach vehicle. The movement capacity C''4 for aD minor street movements i depends on calculation of a capacity adjustment factor which accounts for Me impeding effects of higher-ranked pedestrian movements. This pedestrian capacity adjustment factor is denoted fir for all movements h and, for ad minor street movements i, cart be expressed as: fop typo, h (172) where Poh is the probability that conflicting pedestnan movement h wiR operate in a queue-free state and i is the street movements only. An adjustment factor p' for Me statistical dependence between queues of different pedestnan steams is not accounted for since pedestrian flows are expected to be light. Step 7. Computation of Capacity for Rank 2 Minor where Street Right Turn Movements tc,~,, and c~,,,2) Step 7.~. Compute total conflicting volume vc9 and Vc~2 based on Table 58. Step 7.2. Compute potential capacities using Harders equation (Equation 166~. Step 7.3. Compute movement capacities,, c. ). Can i = Cp i X f' (173' where i=9,12, if i = 9 then h = S,R ifi=12thenh=O,L A'= capacity adjustment factor = product of conflicting pedestrian pO' =PsXPRfori= 9 =POxpLfori= 12 Step 8. Computation of Capacity for Rank 3 Movements (c-,8 and cull) Step S.1. Compute total conflicting volume Vc8 andVcl1 Step 8.2. Compute potential capacities(cp8, c pl) using Harders equation. Step 8.3. Compute movement capacities,, c. . Cm ~ = Cp i X I' (174) where . . . . i= 8, 11; A= capacity adjustment factor =f,p X poll x Pok (Ifj, k are shared lanes use p*), j=4; kin 1; Step 8.4 Compute probability of queue-free state pO i Tom Equation 167. Step 9. Computation of Capacity for Rank 4 Movements(c,,,7 and c-,1O) Step 9.L Compute total conflicting volume Vce7 and Vat lo . Step 9.2.Compute potential capacities(cp,, cp1O) using Harders equation. Step 9.3 Compute movement capacities(cm,, Cal, 1O). Cm i = Cp i X f' (175)

128 where and if . i= 7, 10; Hi= capacity adjustment factor = ~ x pi' x pOj; P/i = 0.6spl/i P. i + 0.6 ~(17~ P i = Po k X fk (17~ · i=7, h=~;L j= 12, k= 11; =10, h=O3R j=9, k=8; Step 10. Adjustment of Capacity for Effect of Two- Stage Priority (c, .,8 and c,~,,l1; C,,,, 7 atld c,, ,IJ Step 10.~. Determine storage size k for each movement in the median from design or field observations (if k = 0 skip to step ~ I). Step ·0.2. For each of the four movements (7,8,10,!I), perfonn the follow ng additional capacity calculations. The example is presented for movement 8: . . Define conflicting volumes using Table 56. vl + v2- volume of priority street left turning traffic at part I + volume of major street through traffic coming from the left at part I in Figure 50. vs= volume of the sum of all major street flows comingirom the right at part ~ In Figure 50. From Step 4 through 8: c~v,+v2+vs)= capacity at a cross intersection for minor through traffic with a major street traffic volume of v~+v2+vs Repeat steps 4 Trough 8 with relevant conflicting movements to get: cave + vie= capacity at part cove)= capacity at part II Calculate adjustment factor a, and intermediate variable y a = 1 - 0.32e~l3~ for k> 0 (178) C(V1 + v2) - c(vl + is + Vs) (179) ~V; - V1 - ~V1 + V2 + as) . Calculate ct = total capacity of the intersection for subject movement C = a xt~xt'' i-l)x[<Vs)-Vl]~-l)x~vl ~V2+VS)) (180) for y ~ 1 C`=~kx[c(vs)-vl] ~C(v1 ~V2+VS)} (181) for y= 1 Step 10.4. If Were is no separate lane for the subject leR and Croup movements in either the central storage area or on the approach to Part I, then the mixed lane formula (Equation 10-9 of the HCM, 1994) has to be used to calculate the total capacity for the minor street left turn and through movements 7 and 8, or 10 and ~ (see step ~l). Step 10.5. Delay estimations for Me two-stage priority situation can beperfomled using the general delay formula (see step 12~. An alternative to steps 10.1 through 10.5 is to use the following graphical procedure (see Figures 72 and 73~: Calculation of cove + v2), [veh/h] Calculation of c~v5~[vehlh] Calculation of c0 [vehlh] Calculation of cove + v2~/c0 Calculation of [C(V5) - VI]/CO Determine cTA - CHICO Tom Me graph for the subject k Calculation of CT = CTA X CO

129 1.0 0.9 0.8 0.7 0.6 a, 0.5 0.4 0.3 ~ .~> 0.1 0.0 Figure 72. Tw~Stage Gap Acceptance, k~1 ~ k- 1 ~ i ,~ ~ . . . 0.0 0.1 0.2 ~ .... .... .... .... ... .... ~ 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 [C|V5)-V1]1C~ (-) . . . 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 [C(V5)-v1llco (_) - 0.9 0.8 -0.7 -0.6 _ _0.5 - 0.4 Figure 73. Tw~S1age Gap Acceptance, ~2 Step 11. Computation of Shared Lane Capacity If minor sheet approach has shared lane, or a flared approach to accommodate two vehicles alongside at the stop line, fiche shared lane capacity should be calculated using equation IS2. Al + VT + VR Hi., Vat + Yr + OR (182) cm, L cm. T cm' R where cn,R is the mtenm capacity of right turn movement in shared lane, veh/hr. Step 12. Computation of Delay Comoutadon of vehicle delaY for each lane. Note: CSH is Me capacity of shared lane, veh/hr; Vat is the volume of left turn movement In shared VT is we volume of through movement in shared ~ = 3600 + 90~}T ': Vr lane, veh/br; VRis We volume of r~ghtt~n movement In shared lane, vehlhr, cat is the interim capacity of led turn movement in shared lane, veh/hr; CAT is the interim capacity of Trough movement In shared lane, veh/hr, If were is a flared lane on a minor shared approach, then d should also be calculated for each movement as if they had exclusive lanes; If upstream signal effect was included (step 4), then equation IS3 may overestimate random delay. An adjustment may be provided from filture research. I 3600 US ]2 4, C-es - (~83) J 4507 where · d is the average vehicle delay, sec/veh; C~,X is the capacity for movement x, or for shared lane, Thor; Vx is the traffic volume for movement x, or for

131 shared lane, veh/hr; · T is the analysis time penod, hr. (T = 0.25). Step 13. Determination of Delay to Rank ~ Vehicles {;P2, D3, Ds, D6) If the major street left turns 1, 4 share a lane with rank ~ movements 2 and 3, 5 and 6 respectively, then these rank ~ movements may experience delay due to blockage by the major left turns. The proportion of rank 1 vehicles being blocked is 1-p*oi as defined belong. Note that on a multilane road, only the major street volumes In the lane which may be blocked should be used in the calculation as V `' and V i2. On multilane roads if it is assumed that blocked rank 1 vehicles do not bypass the blockage by moving across into over Trough lanes (a reasonable assumption under conditions of high major street flows) then Vi, = VAN. The average delay to.rank 1 (through j or right turn k at,,= vehicles on this approach is Even by: ~ (i - pa;) x d'"°P~kp X ~ Vl,[ Vit ~ yin N21 (~84) (I po')Xd~kfl N=1 As defined In step 4 (and In 1994 HEM Equation 10-3~: p*0 = 1- Pa i 1- (S'+S ~ where (185) i=1,4; j = 2, if i = 1, or =5,ifi=4; kit 3, if i= 1, or =6, ifi=4; Sj is the saturation flow rate for major street through traffic streams So is the saturation flow rate for major street right turn traffic Step 14. Determination of Level of Service Step 14.1. Check volume/capacibr ratio for each minor street movement. If V/c2 1, then LOS ="F". Determine levelofservice according to Table 58 for each minor street movement or approach lane, and the major street leR turn. (Note that the LOS thresholds have been adjusted to be equivalent to those for signalized intersections, so that direct comparisons for a given movement are more valid). Step 14.2. Detente weighted average total delays and LOS aggregated for each approach. Step 14.3. Determine the weighty average total delays and LOS aggregated for ad delayed vehicles, including 1be delayed rank ~ vehicles, in the entire intersection Step 14.4 Determine the weighted average total delays and LOS for aggregated for all movements, including un- delayed rank ~ vehicles, In We entire ~ntersechom Table 58. Determination of LOS Based on Average Delay ll E | s6.S >6.6 and s l9.S >19.6 and s32.S >32.6 and sS2 >S2.1 and s78 >80 Step 15. Determination of Average Queue Lengths (delay in vehicle-hours) For each of the four levels of aggregation in Step 14 calculate the average queue, the product of Me number of subject vehicles and the average delay divided by 3600. Step 16. Adjustment of Capacity for Flared Minor Approach (c, .,8 and c', ,~; C,,,, 7 and c,,, I) Refer to Figure 74: Step 16.~. Let the shared lane case be the worst case. Calculate the total approach capacity cam, then delay in vehicle hours (step 14~. This is equivalent to the average queue on the approach for the shared lane case. Step 16.2. Let the separate lane case be the best case. Calculate the total approach capacity c,~ = c708+c,, then delay in vehicle hours (i.e. skip the sham lane calculation in step Il. Den recompute steps 12 Trough 15~. This is equivalent to the average queue on the approach for the separate lane case. Step 16.3. Derive amaximumieng~ in vehicles A,,, of the flared area above which traffic flows approximately like it would tee on two separate lanes. This could be assumed to be equivalent to the average queue in 16.2 plus one vehicle rounded up to an integer number of vehicles (alternatively, a more conservative approach would be to calculate and

132 use the 95th percentile queues Tom the HEM 1994, Figure 10.S instead office average queues in steps 16.1 and 16.2~. Step 16.4. Using the queue storage Kit,,,., at the site, make a linear interpolation between Me shared lane formula capacity (w~thk=O) andante sum ofseparate lane capacities (w~thk determined in step 3~. This can be shown to yield Me following capacity equation: Casual = (Ccepar~C~ Cot K~ / ~ + Cat = c',p,,~,, k,m,,, / k,,= + Cody 1- ken,,,/ kit (~86) Step 16.5. Recompute steps 12 through 15 using the capacity Bom step 16.4) Step 17. Comprehensive Assessment of V/C, Delay, Queue Measures of Effectiveness For Me worst delayed lane, obtain: . average delay per vehicle from step 14.1 average queue Dom step 15 volume/capacity Lookup the above three parameters on Figure 75 to obtain a comprehensive assessment of the performance of the critical movement or lane group. This step may also be repeated for any lane group. ., ~ FACTUAL ~ 43: J ad: CSEPARATE- CFLARED CSHARED ILL 1~1 ~ 11 1A 11 1 , , KACTUAL QUEUEk Figure 74. Capacity Approximation at Intersections with [fared Minor Street Approach _: OX al, K~x

133 REGION 2 1 000 100 ~n - CO a) C] a) O) 10 CO 0 1 0/ 7 REGION ~ - ' = Figure 75. Queue/Delay Relationship Queue/Delay Relationship REGION 3 I! ~ ~ v/c - 0.2 v/c - 0.4 ~. . . . .. . . .. . . . . . .. . . . . . ... Average Queue 10 . __ _ lYY4 AM _ ~ :, '' -A- 100 v/c - 0.6 v/c- 0.8 V/C- 0.9 via- 1.0 v/c- 1.2 via- 1.4

134 lo.,