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1 The grade length should include 5% of the length of the ertical cures at the start and end of the grade. With two consecutie upgrades, 50% of the length of the ertical cure joining them should be included. The point of interest is usually the spot heay ehicles would hae the greatest impact on operations: the top of a grade, the top of the steepest grade in a series, or a ramp junction, for example. Exhibit PCEs for Trucks and Buses (E T) on Upgrades The length of the grade is generally taken from a highway profile. It typically includes the straight portion of the grade plus some portion of the ertical cures at the beginning and end of the grade. It is recommended that 5% of the length of the ertical cures at both ends of the grade be included in the length. Where two consecutie upgrades are present, 50% of the length of the ertical cure joining them is included in the length of each grade. In the analysis of upgrades, the point of interest is generally at the end of the grade, heay ehicles would hae the maximum effect on operations. Howeer, if a ramp junction is being analyzed, for example, the length of the grade to the merge or dierge point would be used. On composite grades, the relatie steepness of segments is important. If a 5% upgrade is followed by a % upgrade, for example, the maximum impact of heay ehicles is most likely at the end of the 5% segment. Heay ehicles would be expected to accelerate after entering the % segment. Upgrade Length Proportion of Trucks and Buses (%) (mi) % 4% 5% 6% 8% 10% 15% 0% 5% All > > 3 > > > >0 >3 4 >4 5 >5 6 > > > > > > > > > > > > > > > > > > > > Note: Interpolation for percentage of trucks and buses is recommended to the nearest 0.1. Methodology Page Chapter 11/Basic Freeway Segments January 01

2 4. APPLICATIONS The methodology of this chapter is most often used to estimate the capacity and LOS of freeway weaing segments. The steps are most easily applied in the operational analysis mode, that is, all traffic and roadway conditions are specified, and a solution for the capacity (and /c ratio) is found along with an expected LOS. Other types of analysis, howeer, are possible. DEFAULT VALUES An NCHRP report (10) proides a comprehensie presentation of potential default alues for uninterrupted-flow facilities. Default alues for freeways are summarized in Chapter 11, Basic Freeway Segments. These defaults coer the key characteristics of PHF and percentage of heay ehicles. Recommendations are based on geographical region, population, and time of day. All general freeway default alues may be applied to the analysis of weaing segments in the absence of field data or projected conditions. There are many specific ariables related to weaing segments. It is, therefore, irtually impossible to specify default alues of such characteristics as length, width, configuration, and balance of weaing and nonweaing flows. Weaing segments are a detail of the freeway design and should therefore be treated only with the specific characteristics of the segment known or projected. Small changes in some of these ariables can and do yield significant changes in the analysis results. TYPES OF ANALYSIS The methodology of this chapter can be used in three types of analysis: operational, design, and planning and preliminary engineering. Operational Analysis The methodology of this chapter is most easily applied in the operational analysis mode. In this application, all weaing demands and geometric characteristics are known, and the output of the analysis is the expected LOS and the capacity of the segment. Secondary outputs include the aerage speed of component flows, the oerall density in the segment, and measures of lanechanging actiity. Design Analysis In design applications, the desired output is the length, width, and configuration of a weaing segment that will sustain a target LOS for gien demand flows. This application is best accomplished by iteratie operational analyses on a small number of candidate designs. Generally, there is not a great deal of flexibility in establishing the length and width of a segment, and only limited flexibility in potential configurations. The location of intersecting facilities places logical limitations on the length of the weaing segment. The number of entry and exit lanes on ramps and the freeway itself limits the number of lanes to, at most, two choices. The entry and exit Design analysis is best accomplished by iteratie operational analyses on a small number of candidate designs. Chapter 1/Freeway Weaing Segments Page 1-5 Applications July 01

3 Equation 13-8 Exhibit 13-7 Models for Predicting P FD at -Ramps or Dierge Areas Equation 13-9 Equation Equation maneuer. Thus, for off-ramps, the flow in Lanes 1 and consists of all off-ramp ehicles and a proportion of freeway through ehicles, as in Equation 13-8: 1 R F R P FD 1 = flow rate in Lanes 1 and of the freeway immediately upstream of the deceleration lane (pc/h), R = flow rate on the off-ramp (pc/h), and P FD = proportion of through freeway traffic remaining in Lanes 1 and immediately upstream of the deceleration lane. For off-ramps, the point at which flows are defined is the beginning of the deceleration lane(s), regardless of whether this point is within or outside the ramp influence area. Exhibit 13-7 contains the equations used to estimate P FD at off-ramp dierge areas. As was the case for on-ramps (merge areas), the alue of P FD for four-lane freeways is triial, since only Lanes 1 and exist. No. of Freeway Lanes a Model(s) for Determining P FD 4 P FD PFD F R 6 PFD F 0.604U / LUP when U/L UP 0. b P / L FD 8 P Adjacent Upstream Ramp None None None On On On Note: FD F D DOWN SELECTING EQUATIONS FOR P FD FOR SIX-LANE FREEWAYS Adjacent Subject Downstream Ramp Ramp Equation(s) Used None Equation 13-9 On Equation 13-9 Equation or 13-9 None Equation or 13-9 None Equation 13-9 On Equation or 13-9 Equation 13-11, 13-10, or 13-9 On Equation 13-9 Equation or 13-9 a 4 lanes = two lanes in each direction; 6 lanes = three lanes in each direction; 8 lanes = four lanes in each direction. b When U/L UP > 0., use Equation If an adjacent ramp on a six-lane freeway is not a one-lane, right-side off-ramp, use Equation For six-lane freeways, three equations are presented. Equation 13-9 is the base case for isolated ramps or for cases in which the impact of adjacent ramps can be ignored. Equation addresses cases in which there is an adjacent upstream on-ramp, while Equation addresses cases in which there is an adjacent downstream off-ramp. Adjacent upstream off-ramps and downstream on-ramps hae not been found to hae a statistically significant impact on dierge operations and may be ignored. All ariables in Exhibit 13-7 are as preiously defined. Methodology Page Chapter 13/Freeway Merge and Dierge Segments July 01

4 Insufficient information is aailable to establish an impact of adjacent ramps on eight-lane freeways (four lanes in each direction). This methodology does not include such an impact. Where an adjacent upstream on-ramp or downstream off-ramp on a six-lane freeway exists, a determination as to whether the ramp is close enough to the subject off-ramp to affect its operation is necessary. As was the case for onramps, this is done by finding the equilibrium distance L EQ. This distance is determined when Equation 13-9 yields the same alue of P FD as Equation (for adjacent upstream on-ramps) or Equation (adjacent downstream offramps). When the actual distance between ramps is greater than or equal to L EQ, Equation 13-9 is used. When the actual distance between ramps is less than L EQ, Equation or Equation is used as appropriate. For adjacent upstream on-ramps, use Equation 13-1 to find the equilibrium distance: L EQ u For adjacent downstream off-ramps, use Equation 13-13: L EQ all terms are as preiously defined. D In cases Equation 13-1 indicates that Equation should be used to determine P FD, but U /L UP > 0.0, Equation 13-9 must be used as a default. This is due to the alid calibration range of Equation 13-10, and the fact that it will yield unreasonable results when U /L UP exceeds 0.0. This will lead to stepfunction changes in P FD for alues just below or aboe U /L UP = 0.0. A special case exists when both an adjacent upstream on-ramp and an adjacent downstream off-ramp are present. In such cases, two solutions for P FD may arise, depending on which adjacent ramp is considered (both ramps cannot be considered simultaneously). In such cases, the larger alue of P FD is used. As was the case for merge areas, the algorithms used to include the impact of an upstream or downstream ramp on a six-lane freeway are only alid for singlelane, right-side adjacent ramps. Where adjacent ramps consist of two-lane junctions or major dierge configurations, or they are on the left side of the freeway, Equation 13-9 is always applied. Checking the Reasonableness of the Lane Distribution Prediction The algorithms of Exhibit 13-6 and Exhibit 13-7 were deeloped through regression analysis of a large database. Unfortunately, regression-based models may yield unreasonable or unexpected results when applied outside the strict limits of the calibration database, and they may hae inconsistencies at their boundaries. Therefore, it is necessary to apply some limits to predicted alues of flow in Lanes 1 and ( 1 ). The following limitations apply to all such predictions: F F R R Equation 13-1 Equation When both an adjacent upstream onramp and an adjacent downstream off-ramp are present, the larger resulting alue of P FD is used. When an adjacent ramp to a dierge area on a six-lane freeway is not a one-lane, right-side ramp, apply Equation Reasonableness checks on the alue of 1. Chapter 13/Freeway Merge and Dierge Segments Page Methodology July 01

5 Equation Equation Equation Equation Equation The aerage flow per lane in the outer lanes of the freeway (lanes other than 1 and ) should not be higher than,700 pc/h/ln.. The aerage flow per lane in outer lanes should not be higher than times the aerage flow in Lanes 1 and. These limits guard against cases in which the predicted alue of 1 implies an unreasonably high flow rate in outer lanes of the freeway. When either of these limits is iolated, an adjusted alue of 1 must be computed and used in the remainder of the methodology. Application to Six-Lane Freeways On a six-lane freeway (three lanes in one direction), there is only one outer lane to consider. The flow rate in this outer lane (Lane 3) is gien by Equation 13-14: 3 3 F 1 = flow rate in Lane 3 of the freeway (pc/h/ln), F = flow rate on freeway immediately upstream of the ramp influence area (pc/h), and 1 = flow rate in Lanes 1 and immediately upstream of the ramp influence area (pc/h). Then, if 3 is greater than,700 pc/h, use Equation 13-15: 1 a F,700 If 3 is greater than ( 1 /), use Equation 13-16: 1a F a equals the adjusted flow rate in Lanes 1 and immediately upstream of the ramp influence area (pc/h) and all other ariables are as preiously defined. In cases both limitations on outer lane flow rate are iolated, the result yielding the highest alue of 1a is used. The adjusted alue replaces the original alue of 1 and the analysis continues. Application to Eight-Lane Freeways On eight-lane freeways, there are two outer lanes (Lanes 3 and 4). Thus, the limiting alues cited preiously apply to the aerage flow rate per lane in these lanes. The aerage flow in these lanes is computed from Equation 13-17: a34 F a34 equals the flow rate in outer lanes (pc/h/ln) and all other ariables are as preiously defined. Then, if a34 is greater than,700, use Equation 13-18: 1 1 a F 5,400 Methodology Page Chapter 13/Freeway Merge and Dierge Segments July 01

6 If a34 is greater than ( 1 /), use Equation 13-19: 1a all terms are as preiously defined. F 0 In cases both limitations on outer lane flow rate are iolated, the result yielding the highest alue of 1a is used. The adjusted alue replaces the original alue of 1 and the analysis continues. Equation Summary of Step At this point, an appropriate alue of 1 has been computed and adjusted as necessary. Step 3: Estimate the Capacity of the Ramp Freeway Junction and Compare with Demand Flow Rates There are three major checkpoints for the capacity of a ramp freeway junction: 1. The capacity of the freeway immediately downstream of an on-ramp or immediately upstream of an off-ramp,. The capacity of the ramp roadway, and 3. The maximum flow rate entering the ramp influence area. In most cases, the freeway capacity is the controlling factor. Studies (1) hae shown that the turbulence in the icinity of a ramp freeway junction does not diminish the capacity of the freeway. The capacity of the ramp roadway is rarely a factor at on-ramps, but it can play a major role at off-ramp (dierge) junctions. Failure of a dierge junction is most often caused by a capacity deficiency on the off-ramp roadway or at its ramp street terminal. While this methodology establishes a maximum desirable rate of flow entering the ramp influence area, exceeding this alue does not cause a failure. Instead, it means that operations may be less desirable than indicated by the methodology. At off-ramps, the total flow rate entering the ramp influence area is merely the estimated alue of 1. At on-ramps, howeer, the on-ramp flow also enters the ramp influence area. Therefore, the total flow entering the ramp influence area at an on-ramp is gien by Equation 13-0: R 1 1 R R1 is the total flow rate entering the ramp influence area at an on-ramp (pc/h) and all other ariables are as preiously defined. Exhibit 13-8 shows capacity alues for ramp freeway junctions. Exhibit 13-9 shows similar alues for high-speed ramps on multilane highways and C-D roadways within freeway interchanges. Exhibit shows the capacity of ramp roadways. Locations for checking the capacity of a ramp freeway junction. Freeway capacity immediately downstream of an on-ramp or upstream of an off-ramp is usually the controlling capacity factor. Failure of a dierge junction is usually caused by a capacity deficiency at the ramp street terminal or on the offramp roadway. Equation 13-0 Chapter 13/Freeway Merge and Dierge Segments Page Methodology July 01

7 cars. The aggregate impact of heay ehicles on the traffic stream, howeer, increases as the number and percentage of heay ehicles increase. Exhibit PCEs for Trucks and Buses (E T) on Upgrades Percent Length Proportion of Trucks and Buses Upgrade (mi) % 4% 5% 6% 8% 10% 15% 0% 5% All > > 3 > > > >0 >3 4 >4 5 >5 6 > > > > > > > > > > > > > > > > > > > > Note: Interpolation for percentage of trucks and buses is recommended to the nearest 0.1. Exhibit PCEs for RVs (E R) on Upgrades The grade length should include 5% of the length of the ertical cures at the start and end of the grade. With two consecutie upgrades, 50% of the length of the ertical cure joining them should be included. Percent Length Proportion of RVs Upgrade (mi) % 4% 5% 6% 8% 10% 15% 0% 5% All > > > > > >4 5 > > > > >0.50 Note: Interpolation for percentage of RVs is recommended to the nearest 0.1. The length of the grade is generally taken from a highway profile. It typically includes the straight portion of the grade plus some portion of the ertical cures at the beginning and end of the grade. It is recommended that 5% of the length of the ertical cures at both ends of the grade be included in the length. Where two consecutie upgrades are present, 50% of the length of the ertical cure joining them is included in the length of each grade. Methodology Page Chapter 14/Multilane Highways January 01

8 Equation 15-1 Equation Capacity may be limited by the directional distribution of traffic and the total two-way base capacity of 3,00 pc/h. The effectie length of a passing lane is longer than its actual length. c dats 1,700 fg, ATS fhv, ATS c dptsf 1,700 fg, PTSF fhv, PTSF c dats = capacity in the analysis direction under preailing conditions based on ATS (eh/h), and c dptsf = capacity in the analysis direction under preailing conditions based on PTSF (eh/h). For Class I highways, both capacities must be computed. The lower alue represents capacity. For Class II highways, only the PTSF-based capacity is computed. For Class III highways, only the ATS-based capacity is computed. One complication is that the adjustment factors depend on the demand flow rate (in ehicles per hour). Thus, adjustment factors for a base flow rate of 1,700 pc/h must be used. Technically, this alue should be adjusted to reflect grade and heay ehicle adjustments. This would create an iteratie process in which a result is guessed and then checked. In practical terms, this is unnecessary, since the highest flow group in all adjustment exhibits is greater than 900 eh/h. It is highly unlikely that any adjustments would reduce 1,700 pc/h to less than 900 eh/h. Therefore, in capacity determinations, all adjustment factors should be based on a flow rate greater than 900 eh/h. Another characteristic of this methodology must be considered in ealuating capacity. When the directional distribution is other than 50/50 (in leel and rolling terrain), the two-way capacity implied by each directional capacity may be different. Moreoer, the implied two-way capacity from either or both directions may be more than the limit of 3,00 pc/h. In such cases, the directional capacities estimated are not achieable with the stated directional distribution. If this is the case, then base capacity is restricted to 1,700 pc/h in the direction with the heaiest flow, and capacity in the opposing direction is found by using the opposing proportion of flow, with an upper limit of 1,500 pc/h. Directional Segments with Passing Lanes Proiding a passing lane on a two-lane highway in leel or rolling terrain improes operational performance and therefore may improe LOS. A procedure to estimate this effect is described in this section. This procedure should be applied only in leel and rolling terrain. On specific grades, added lanes are considered to be climbing lanes, which are addressed in the next section. Exhibit 15- illustrates the operational effect of a passing lane on PTSF. It shows that the passing lane proides operational benefits for some distance downstream before PTSF returns to its former leel (without a passing lane). Thus, a passing lane s effectie length is greater than its actual length. Methodology Page 15-8 Chapter 15/Two-Lane Highways January 01

9 W OL = outside lane width (ft), W s = paed shoulder width (ft), V = hourly directional olume per lane (eh/h), W e = aerage effectie width of the outside through lane (ft), and %OHP = percentage of segment with occupied on-highway parking (decimal). Equation Step 4: Calculate the Effectie Speed Factor The effect of motor ehicle speed on bicycle quality of serice is primarily related to the differential between motor ehicle and bicycle trael speeds. For instance, a typical cyclist may trael in the range of 15 mi/h. An increase in motor ehicle speeds from 0 to 5 mi/h is more readily perceied than a speed increase from 60 to 65 mi/h, since the speed differential increases by 100% in the first instance compared with only 11% in the latter. Equation shows the calculation of the effectie speed factor that accounts for this diminishing effect. S ln( S 0) t p S t = effectie speed factor, and S p = posted speed limit (mi/h). Equation Step 5: Determine the LOS With the results of Steps 1 4, the bicycle LOS score can be calculated from Equation 15-31: BLOS ln( 7.066(1/ P) OL BLOS = bicycle leel of serice score; ) S ( HV ) 0.005( W ) e t OL = directional demand flow rate in the outside lane (eh/h); HV = percentage of heay ehicles (decimal); if V < 00 eh/h, then HV should be limited to a maximum of 50%; P = FHWA s 5-point paement surface condition rating; and W e = aerage effectie width of the outside through lane (ft). Finally, the BLOS score alue is used in Exhibit 15-4 to determine the bicycle LOS for the segment. Methodology Page Chapter 15/Two-Lane Highways January 01

10 4. EXAMPLE PROBLEMS Exhibit List of Example Problems Problem Number Description Type of Analysis Find the LOS of a Class I highway in rolling terrain Find the LOS of a Class II highway in rolling terrain Find the LOS of a Class III highway in leel terrain Find the LOS of a Class I highway with a passing lane Find the future bicycle LOS of a two-lane highway Operational analysis Operational analysis Operational analysis Operational analysis Planning analysis EXAMPLE PROBLEM 1: CLASS I HIGHWAY LOS The Facts A segment of Class I two-lane highway has the following known characteristics: Demand olume = 1,600 eh/h (total in both directions) Directional split (during analysis period) = 50/50 PHF = % no-passing zones in the analysis segment (both directions) Rolling terrain 14% trucks; 4% RVs 11-ft lane widths 4-ft usable shoulders 0 access points/mi 60-mi/h BFFS 10-mi segment length Find the expected LOS in each direction on the two-lane highway segment as described. Comments The problem statement calls for finding the LOS in each direction on a segment in rolling terrain. Because the directional split is 50/50, the solution in one direction will be the same as the solution in the other direction, so only one operational analysis needs to be conducted. The result will apply equally to each direction. Because this is a Class I highway, both ATS and PTSF must be estimated to determine the expected LOS. Step 1: Input Data All input data were specified aboe. Step : Estimate the FFS FFS is estimated with Equation 15- and adjustment factors found in Exhibit 15-7 (for lane and shoulder width) and Exhibit 15-8 (for access points in both directions). For 11-ft lane widths and 4-ft usable shoulders, the adjustment factor Example Problems Page Chapter 15/Two-Lane Highways January 01

11 Step 4: Determine Critical Headways and Follow-Up Headways The critical headways t c,x and follow-up headways t f,x must be determined for the major-street left turns ( c,1 and c,4 ), the minor-street right turns ( c,9 and c,1 ), the major-street U-turns ( c,1u and c,4u ), the minor-street through moements ( c,8 and c,11 ), and the minor-street left turns ( c,7 and c,10 ) as they occur at a TWSC intersection. To compute the critical headways for each moement, the analyst begins with the base critical headway gien in Exhibit and makes moementspecific adjustments relating to the percentage of heay ehicles, the grade encountered, and a three-leg ersus four-leg intersection, as shown in Equation 19-30: t c,x t c, x tc, base tc, HV PHV tc, GG t3, LT = critical headway for moement x (s); t c,base = base critical headway from Exhibit (s); t c,hv = adjustment factor for heay ehicles (1.0 for major streets with one lane in each direction; for major streets with two or three lanes in each direction) (s); P HV = proportion of heay ehicles for moement (expressed as a decimal; e.g., P HV = 0.0 for % heay ehicles); t c,g = adjustment factor for grade (0.1 for Moements 9 and 1; 0. for Moements 7, 8, 10, and 11) (s); G = percent grade (expressed as an integer; e.g., G = for a % downhill grade); and t 3,LT = adjustment factor for intersection geometry (0.7 for minor-street leftturn moement at three-leg intersections; 0.0 otherwise) (s). Base Critical Headway, t c,base (s) Vehicle Moement Two Lanes Four Lanes Six Lanes Left turn from major U-turn from major N/A 6.4 (wide) 6.9 (narrow) 5.6 Right turn from minor Through traffic on minor Left turn from minor 1-stage: 6.5 -stage, Stage I: -stage, Stage II: 1-stage: 7.1 -stage, Stage I: 6.1 -stage, Stage II: stage:6.5 -stage, Stage I: -stage, Stage II: 1-stage: 7.5 -stage, Stage I: 6.5 -stage, Stage II: stage: 6.5* -stage, Stage I: * -stage, Stage II: * 1-stage: 6.4 -stage, Stage I: 7.3 -stage, Stage II: 6.7 * Use caution; alues estimated. Note: Narrow U-turns hae a median nose width < 1 ft; wide U-turns hae a median nose width 1 ft. Equation t 3,LT is applicable to Moements 7, 8, 10, and 11 Exhibit Base Critical Headways for TWSC Intersections The critical headway data for four- and six-lane sites account for the actual lane distribution of traffic flows measured at each site. For six-lane sites, minorstreet left turns were commonly obsered beginning their moement while apparently conflicting ehicles in the far-side major-street through stream pass. The alues for critical headway for minor-street through moements at six-lane streets are estimated, as the moement is not frequently obsered in the field. Chapter 19/Two-Way STOP-Controlled Intersections Page Methodology January 01

12 Equation Similar to the computation of critical headways, the analyst begins the computation of follow-up headways with the base follow-up headways gien in Exhibit The analyst then makes moement-specific adjustments to the base follow-up headways with information gathered on heay ehicles and the geometrics of the major street per the adjustment factors gien in Equation t f, x t f, base t f, HV P HV t f,x = follow-up headway for moement x (s), t f,base = base follow-up headway from Exhibit (s), t f,hv = adjustment factor for heay ehicles (0.9 for major streets with one lane in each direction, 1.0 for major streets with two or three lanes in each direction), and P HV = proportion of heay ehicles for moement (expressed as a decimal; e.g., P HV = 0.0 for % heay ehicles). Exhibit Base Follow-Up Headways for TWSC Intersections Base Follow-Up Headway, t f,base (s) Vehicle Moement Two Lanes Four Lanes Six Lanes Left turn from major U-turn from major N/A (wide) 3.1 (narrow).3 Right turn from minor Through traffic on minor Left turn from minor 3.8 Note: Narrow U-turns hae a median nose width < 1 ft; wide U-turns hae a median nose width 1 ft. Values from Exhibit and Exhibit are based on studies throughout the United States and are representatie of a broad range of conditions. If smaller alues for t c and t f are obsered, capacity will be increased. If larger alues for t c and t f are used, capacity will be decreased. Step 5: Compute Potential Capacities Equation 19-3 Step 5a: Potential Capacity If No Upstream Signal Effects Are Present The potential capacity c p,x of a moement is computed according to the gapacceptance model proided in Equation 19-3 (6). This model requires the analyst to input the conflicting flow rate c,x, the critical headway t c,x, and the follow-up headway t f,x, for moement x. c e c, x c, x p, x c, x c, xt f, x 1 e t / 3,600 / 3,600 c p,x = potential capacity of moement x (eh/h), c,x = conflicting flow rate for moement x (eh/h), t c,x = critical headway for minor moement x (s), and t f,x = follow-up headway for minor moement x (s). Methodology Page Chapter 19/Two-Way STOP-Controlled Intersections January 01

13 Base Saturation Headway (s) Case No. of Veh. 1 3a 3b 4a 4b Step 10: Compute Departure Headways The departure headway of the lane is the expected alue of the saturation headway distribution, gien by Equation 0-8. h 64 P i d h si i1 i represents each combination of the fie degree-of-conflict cases and h si is the saturation headway for that combination. Equation 0-8 Step 11: Check for Conergence The calculated alues of h d are checked against the initial alues assumed for h d. If the alues change by more than 0.1 s (or a more precise measure of conergence), Steps 5 through 10 are repeated until the alues of departure headway for each lane do not change significantly. Step 1: Compute Capacity The capacity of each lane in a subject approach is computed under the assumption that the flows on the opposing and conflicting approaches are constant. The gien flow rate on the subject lane is increased and the departure headways are computed for each lane on each approach until the degree of utilization for the subject lane reaches 1. When this occurs, the final alue of the subject lane flow rate is the maximum possible throughput or capacity of this lane. Step 13: Compute Serice Times The serice time required to calculate control delay is computed on the basis of the final calculated departure headway and the moe-up time with Equation 0-9. t s h d m t s is the serice time, h d is the departure headway, and m is the moe-up time ( s for Geometry s 1 through 4;.3 s for Geometry s 5 and 6). Capacity is estimated for a stated set of opposing and conflicting olumes. Equation 0-9 Chapter 0/All-Way STOP-Controlled Intersections Page 0-15 Methodology July 01

14 (0) 3(0.088) (0.05) AdjP ( 5) 0.01 (0.05) AdjP ( 16) Therefore, the adjusted probability for Combination 1, for example, is as follows: P '(1) Step 9: Compute Saturation Headways The base saturation headways for each combination can be determined with Exhibit They are adjusted by using the adjustment factors calculated in Step 4 and added to the base saturation headways to determine saturation headways as follows (eastbound illustrated): i h base h adj h si Step 10: Compute Departure Headways The departure headway of the lane is the sum of the products of the adjusted probabilities and the saturation headways as follows (eastbound illustrated): h d ( )(3.963) (0.313)(4.763) (0.0875)(5.863) (0.054)(7.063) 7 Step 11: Check for Conergence The calculated alues of h d are checked against the initial alues assumed for h d. After one iteration, each calculated headway differs from the initial alue by more than 0.1 s. Therefore, the new calculated headway alues are used as initial alues in a second iteration. For this problem, four iterations are required for conergence. EB EB WB WB NB NB SB SB L1 L L1 L L1 L L1 L Total Lane Flow Rate hd, initial alue, iteration x, initial, iteration hd, computed alue, iteration Conergence? N N N hd, initial alue, iteration x, initial, iteration hd, computed alue, iteration Conergence? N N N hd, initial alue, iteration x, initial, iteration hd, computed alue, iteration Conergence? Y Y N hd, initial alue, iteration x, initial, iteration hd, computed alue, iteration Conergence? Y Y Y Chapter 0/All-Way STOP-Controlled Intersections Page 0-5 Example Problem July 01

15 Step 1: Compute Capacity The capacity of each lane in a subject approach is computed by increasing the gien flow rate on the subject lane (assuming the flows on the opposing and conflicting approaches are constant) until the degree of utilization for the subject lane reaches 1. This leel of calculation requires running an iteratie procedure many times, which is practical for a spreadsheet or software implementation. Here, the eastbound lane capacity is approximately 70 eh/h, which is lower than the alue that could be estimated by diiding the lane olume by the degree of utilization (368/0.49 = 748 eh/h). The difference is due to the interaction effects among the approaches: increases in eastbound traffic olume increase the departure headways of the lanes on the other approaches, which in turn increases the departure headway of the lane(s) on the subject approach. Step 13: Compute Serice Times The serice time required to calculate control delay is computed on the basis of the final calculated departure headway and the moe-up time by using Equation 0-9. For the eastbound lane (using a alue for m of for Geometry 1), the calculation is as follows: t s h Step 14: Compute Control Delay d m The control delay for each lane is computed with Equation 0-30 as follows (eastbound illustrated): d (0.5) 4.97(0.508) 450(0.5) s By using Exhibit 0-, the eastbound lane (and thus approach) is assigned LOS B. A similar calculation for the westbound and southbound lanes (and thus approaches) yields 1 and 10.6 s, respectiely. The control delays for the approaches can be combined into an intersection control delay by using a weighted aerage as follows: (1)(368) (1)(41) (10.6)(158) d 1.8 s This alue of delay is assigned LOS B. Step 15: Compute Queue Length The 95th percentile queue for each lane is computed with Equation 0-33 as follows (eastbound approach illustrated): Q This queue length would be reported as 3 ehicles..9 eh Example Problem Page 0-6 Chapter 0/All-Way STOP-Controlled Intersections July 01