National Academies Press: OpenBook

Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability (2008)

Chapter: Chapter 6 - Forecast Future Performance

« Previous: Chapter 5 - Identification of Deficiencies
Page 41
Suggested Citation:"Chapter 6 - Forecast Future Performance." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
Page 41
Page 42
Suggested Citation:"Chapter 6 - Forecast Future Performance." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
Page 42
Page 43
Suggested Citation:"Chapter 6 - Forecast Future Performance." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
Page 43
Page 44
Suggested Citation:"Chapter 6 - Forecast Future Performance." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
Page 44
Page 45
Suggested Citation:"Chapter 6 - Forecast Future Performance." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
Page 45
Page 46
Suggested Citation:"Chapter 6 - Forecast Future Performance." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
Page 46
Page 47
Suggested Citation:"Chapter 6 - Forecast Future Performance." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
Page 47
Page 48
Suggested Citation:"Chapter 6 - Forecast Future Performance." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
Page 48
Page 49
Suggested Citation:"Chapter 6 - Forecast Future Performance." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
Page 49
Page 50
Suggested Citation:"Chapter 6 - Forecast Future Performance." National Academies of Sciences, Engineering, and Medicine. 2008. Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability. Washington, DC: The National Academies Press. doi: 10.17226/14167.
×
Page 50

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.

41 6.1 Introduction The purpose of this chapter is to provide guidance on the es- timation of trip travel times, delays, and reliability when direct measurement of these performance measures is not feasible. Two methods are provided: a sketch planning method that re- quires minimal data and a planning method that requires data to compute the capacity and FFS of the facility. This chapter focuses on planning applications. Methods provided here are designed for rapid application to large batches of facilities requiring minimal field data collection on the characteristics of the facilities. Methods are applicable to the estimation of travel-time, delay, and reliability for trips made on all types of highway facilities. The methods provided here are not as precise as field measurements of travel time, delay, and reliability. They also are not as accurate or as sensi- tive to variations in traffic controls as methods employing mi- crosimulation or HCM (5) techniques. Since this chapter deals with forecasting future performance, the same procedures apply whether or not the agency is data-rich (with continuous surveillance on some of its facilities), or data-poor. The chapter is split into three major sections: estimating/ forecasting travel time, estimating delay, and estimating relia- bility. The travel time section is split into two parts: estimation of trip times, and estimation of road segment travel times. The road segment travel times section provides two methods for estimating segment travel times, a sketch planning method and a planning method. The sketch planning method requires only average daily traffic, signal spacing, and number of lanes. The planning method requires additional information on the road segment to estimate capacity and FFS. 6.2 Estimating/Forecasting Travel Time To estimate trip travel time you need to know the time of day when the trip will be made, the starting point, the end point, and the route taken for the trip. For a trip on a given route at a given time of day, over several different facility types and segments of facilities, it is necessary to estimate the travel time for each road segment and sum them. The estimated travel time for each road segment should include any delay incurred when transition- ing from one segment to the next (for example the delay in making a left turn from one street to another). The road segment travel time can be estimated by dividing the segment length by the mean speed of the traveler over the length of the segment and adding in any segment transition delay. (Eq. 6.1) (Eq. 6.2) where TT = Trip Travel Time (hours); Ti = Road Segment Travel Time (hours); Li = Length of road segment i (miles); Si = Mean speed of vehicle over length of road segment i (mph); and di = Transition Delay. The delay incurred moving from the end of segment i to the start of the next segment. 6.2.1 Identification of Road Segments The route taken by a given trip must be divided into road seg- ments. A road segment is the portion of the road or highway over which neither demand nor capacity varies by more than 10 percent of their average value for the segment. The selected route for the given trip is divided into a series of road segments, and each can be presumed to have relatively uniform demand and capacity over its length. 6.2.2 Sketch Planning Techniques for Estimating Segment Speeds The following equations for estimating road segment speeds are designed for sketch planning purposes. They do T L S di i i i= + TT = ∑Ti i C H A P T E R 6 Forecast Future Performance

42 not require that the capacity be known, nor the PSL. They re- quire information only on the average daily traffic (ADT), lanes, the number of signals per mile, and the number of in- terchanges per mile. For freeways: Speed (mph) = 91.4 − 0.002 [ADT/Lane] −2.85 [Access Points Per Mile] (Eq. 6.3) For Class I arterials: Speed (mph) = 40.6 − 0.0002 [ADT/Lane] −2.67 [Signals Per Mile] (Eq. 6.4) For Class II and Class III arterials: Speed (mph) = 36.4 − 0.000301 [ADT/Lane] −1.56 [Signals Per Mile] (Eq. 6.5) where Speed = Mean speed during weekday peak hours, average of both directions (mph); ADT = Average daily traffic (total of both directions for weekdays) for road segment; Lane = number of through lanes (total of both directions) on road segment; Access Points = Average number of freeway interchanges Per Mile per mile for freeway segment. Treat par- tial interchanges as full interchanges for purpose of computing the average access points per mile; Signals Per Mile = Average number of traffic signals per mile on road segment; Arterial Class I = Signalized arterial street with at least 1 signal every 2 miles, and with posted speed limit in excess of 40 mph; Arterial Class II = Signalized arterial street with at least 1 signal every one-quarter mile, and with posted speed limits of 30 to 40 mph, inclusive; and Arterial Class III = Signalized arterial street with at least 1 signal every one-quarter mile, and with posted speed limit less than 30 mph. The above equations, taken from NCHRP Report 398, Quantifying Congestion (1), were developed by applying linear regression to various data sets available to the researchers. As such, these equations are unlikely to be accurate for extreme situations not covered in the original NCHRP 398 data sets, such as roads in mountainous terrain. The above NCHRP 398 equations also are not designed to be applied to multilane-rural highways or two-lane rural roads. However, in the absence of better information, the analyst may cautiously use the equivalent arterial speed equations according to the posted speed limit on the highway. Similarly, if the signal density (number of signals per mile) is less than the minimums listed above for each arterial class, the equations for the appro- priate speed limit may still be applied, but the results should be used with caution. A superior approach to using the equations listed above would be to measure speeds in the local region using the methods described in Chapter 3 and using linear regression to fit equations that are more accurate for conditions in the area. Assuming good data collection practices, locally devel- oped equations almost always will be superior in accuracy to the national average equations presented in this Guidebook. 6.2.3 Planning Method for Estimating Speeds The planning method for estimating speed is designed to be applied to specific hours of the day and to specific street segments. The method is sensitive to the posted speed limit, volume, and capacity. A method is provided to estimate capacity based on signal timing and the physical characteris- tics of the facility. This method is taken from NCHRP Report 387: Planning Techniques for Estimating Speed and Service Vol- umes for Planning Applications (7). If it is desired to estimate mean speed over a 24-hour pe- riod, then one can either use the “one-hour” method below, applying it 24 times, for each hour of the day, or one can use the following equations from NCHRP Report 398. The recommended speed estimation technique is an update of the Bureau of Public Roads (BPR) speed-flow curve. The new curve has been fitted to updated speed-flow data con- tained in the HCM and has been validated against speed flow data for both uninterrupted flow facilities and interrupted flow facilities. The facility space mean speed is computed in three steps: 1. Estimate the FFS; 2. Estimate capacity; and 3. Compute the average speed. Look-up tables of defaults can be used to skip the first two steps, but poor choices of the FFS and capacity can seriously compromise the accuracy of the technique. Step 1. Estimate Free-Flow Speed FFS of a facility is defined as the space mean speed of traffic when volumes are so light that they have negligible effect on speed. The best technique for estimating FFS is to measure it in the field under light traffic conditions, but this is not a feasible option when several thousand street links must be analyzed.

43 The paragraphs below provide a recommended set of equations for estimating FFS in the absence of field measurements of FFS. Option 1a. Equations for Facilities Without Signals Two separate linear equations are provided for estimating free-flow speed for facilities with less than one signal every 2 miles (3.2 km). One equation is for facilities with posted speed limits in excess of 50 mph (80 kph). The other equation is for facilities with lower posted speed limits. High-Speed Facilities [PSL in excess of 50 mph (80 kph)]. Sf (mph) = 0.88 * Sp + 14 (Eq. 6.6) Sf (kph) = 0.88 * Sp + 22 (Eq. 6.7) Low-Speed Facilities [PSL is 50 mph (80 kph) or less]. Sf (mph) = 0.79 * Sp + 12 (Eq. 6.8) Sf (kph) = 0.79 * Sp + 19 (Eq. 6.9) where Sf = FFS in either mph or kph; and Sp = PSL in either of mph or kph. Option 1b. Equations for Signalized Facilities FFS for signalized facilities must take into account both the FFS measured mid-block between signals and the signal delays along the street (which occur even at low volumes). The mean FFS (including signal delay) is computed using the following equation that adds together the free-flow travel time between signals and the delay time at signals (under free- flow conditions). (Eq. 6.10) where Sf = FFS speed for urban interrupted facility (mph or kph); L = Length of facility (miles or km); Smb = Mid-block FFS (mph or kph); = 0.79 (PSL in mph) + 12 (mph); and = 0.79 (PSL in kph) + 19 (kph); N = Number of signalized intersections on length L of facility; and D = Average delay per signal per Equation 6.11 below (seconds). The average delay per signal is computed using the follow- ing equation: D = DF * 0.5 * C(1 − g/C)2 (Eq. 6.11) S L L S N D f = + ( ) mb * 3600 where D = The total signal delay per vehicle (seconds); g = The effective green time (seconds); C = The cycle length (seconds); If signal timing data is not available, the planner can use the following default values: C = 120 seconds; and g/C = 0.45. DF = (1 − P)/(1 − g/C) where P is the proportion of vehicles arriving on green. If P is unknown, the following defaults can be used for DF: DF = 0.9 for uncoordinated traffic actuated signals; DF = 1.0 for uncoordinated fixed time signals; DF = 1.2 for coordinated signals with unfavorable pro- gression; DF = 0.90 for coordinated signals with favorable progres- sion; and DF = 0.60 for coordinated signals with highly favorable progression. Option 1c. Default FFS Planners may wish to develop a look-up table of FFSs based upon the facility type and the area type where it is lo- cated in order to simplify the estimation of FFSs. Depend- ing upon local conditions, the planning agency may wish to add terrain type (e.g., level, rolling, mountainous) and frontage development types (commercial, residential, un- developed) to the general development types used in Exhibits 6.1 and 6.2. The accuracy of the speed estimation procedure is highly dependent on the accuracy of the FFS and capacity used in the computations. Great care should be taken in the creation of local look-up tables that accurately reflect the FFSs present in the locality. Step 2. Estimate Link Capacity The HCM (5) provides a set of procedures for estimating facility capacity for operations analysis purposes. These pro- cedures vary by facility type and generally require a great deal of information on the facility. The following equations sim- plify the application of the HCM methods for use in planning applications. Option 2a. Capacity Equation for Freeways The following equation is used to compute the capacity of a freeway at its critical point: Capacity (vph) = Ideal Cap * N * Fhv * PHF (Eq. 6.12)

44 Area Type Local Central Business District 50 Urban 56 Suburban 64 Rural Freeway 80 88 96 104 Expressway 72 80 88 96 Arterial 64 72 80 88 Collector 56 64 72 80 72 Exhibit 6.2. Example default FFSs (in kilometers per hour). where Ideal Cap = 2,400 passenger cars per hour per lane (pcphl) for freeways with 70 mph (110 kph) or greater FFS; and = 2,300 (pcphl) for all other freeways [FFS < 70 mph (110 kph)]; N = Number of through lanes. Ignore auxiliary lanes and exit only lanes. Fhv = Heavy vehicle adjustment factor. = 100/(100 + 0.5 * HV) for level terrain; = 100/(100 + 2.0 * HV) for rolling terrain; and = 100/(100 + 5.0 * HV) for mountainous terrain. HV = The proportion of heavy vehicles (including trucks, buses, and recreational vehicles) in the traffic flow. If the HV is unknown, use 0.05 heavy vehicles as default. PHF = Peak-hour factor (the ratio of the peak 15- minute flow rate to the average hourly flow rate). If unknown, use default of 0.90. Option 2b. Capacity Equation for Unsignalized Multilane Roads The following equation is used to compute the capacity of a multilane road with signals (if any) spaced more than 2 miles apart: Capacity (vph) = Ideal Cap * N * Fhv * PHF (Eq. 6.13) where Ideal Cap= 2,200 (pcphl) for multilane rural roads with 60 mph FFS; = 2,100 (pcphl) for multilane rural roads with 55 mph FFS; = 2,000 (pcphl) for multilane rural roads with 50 mph FFS; N = Number of through lanes; ignore exclusive turn lanes; Fhv = Heavy vehicle adjustment factor; = 100/(100 + 0.5 * HV) for level terrain; = 100/(100 + 2.0 * HV) for rolling terrain; = 100/(100 + 5.0 * HV) for mountainous terrain HV = The proportion of heavy vehicles (including trucks, buses, and recreational vehicles) in the traffic flow. If the HV is unknown, use 0.05 heavy vehicles as default; PHF = Peak-hour factor (the ratio of the peak 15- minute flow rate to the average hourly flow rate). If unknown, use default of 0.90; Option 2c. Capacity Equation for Two-Lane Unsignalized Roads The following equation is used to compute the capacity (in one direction) for a two-lane (total of both directions) road with signals (if any) more than 2 miles apart: Capacity (vph) = Ideal Cap * N * Fw * Fhv * PHF * Fdir * Fnopass (Eq. 6.14) Area Type Local Central Business District 30 Urban 35 Suburban 40 Rural Freeway 50 55 60 65 Expressway 45 50 55 60 Arterial 40 45 50 55 Collector 35 40 45 50 45 Exhibit 6.1. Example default FFSs (in miles per hour).

45 where Ideal Cap = 1,400 (pcphl) for all two-lane rural roads; Fw = Lane width and lateral clearance factor; = 0.80 if narrow lanes and/or narrow shoulders are present; = 1.00 otherwise; Narrow lanes are less than 12 feet (3.6 m) wide; Narrow shoulders are less than 3 feet wide (1.0 m); Fhv = Heavy vehicle adjustment factor; = 1.00/(1.00 + 1.0 * HV) for level terrain; = 100/(100 + 4.0 * HV) for rolling terrain; = 100/(100 + 11.0 * HV) for mountainous terrain; HV = The proportion of heavy vehicles (including trucks, buses, and recreational vehicles) in the traffic flow. If the HV is unknown, use 0.02 heavy vehicles as default; PHF = Peak-hour factor (the ratio of the peak 15-minute flow rate to the average hourly flow rate). If not known, use default of 0.90; Fdir = Directional Adjustment Factor; = 0.71 + 0.58 * (1.00 – Peak Direction Propor- tion); Peak Direction Proportion is the proportion of two-way traffic going in peak direction. If not known, use default of 0.55 peak direction; Fnopass = No-Passing Zone Factor; = 1.00 for level terrain; = 0.97 – 0.07 * (NoPass) for rolling terrain; = 0.91 – 0.13 * (NoPass) for mountainous terrain; NoPass is the proportion of length of facility for which passing is prohibited; and If NoPass is unknown, use 0.60 NoPass for rolling terrain and 0.80 for mountainous ter- rain. Option 2d. Capacity Equation for Signalized Arterials The following equation is used to compute the one di- rection capacity of any signalized road with signals spaced 2 miles or less apart: Capacity (vph) = Ideal Sat * N * Fhv * PHF * Fpark * FBay * FCBD * g/C * Fc (Eq. 6.15) where Ideal Sat = Ideal saturation flow rate (vehicles per lane per hour of green) = 1,900; N = Number of lanes (exclude exclusive turn lanes and short lane additions); Fhv = Heavy vehicle adjustment factor; = 1.00/(1.00 + HV); HV = The proportion of heavy vehicles (including trucks, buses, and recreational vehicles) in the traffic flow. If the HV is unknown, use 2 percent heavy vehicles as default; PHF = Peak-hour factor (the ratio of the peak 15-minute flow rate to the average hourly flow rate). Use 0.90 as default if PHF not known; Fpark = On-street parking adjustment factor; = 0.90 if on-street parking present and parking time limit is one hour or less; = 1.00 otherwise; FBay = Left-turn bay adjustment factor; = 1.10 if exclusive left-turn lane(s) (often as a left-turn bay) are present; = 1.00 otherwise; FCBD = Central Business District (CBD) Adjustment Factor; = 0.90 if located in CBD; = 1.00 elsewhere; g/C = Ratio of effective green time per cycle; If no data available, use following defaults; Protected left-turn phase present: g/C = 0.40; Protected left-turn phase NOT present: g/C = 0.45; Other defaults may be developed by the local planning agency based upon local conditions. Additional defaults might be developed based upon the functional classes of the major and crossing streets; and Fc = Optional user specified calibration factor nec- essary to match estimated capacity with field measurements or other independent estimates of capacity (no units). Can be used to account for the capacity reducing effects of left and right turns made from through lanes. Option 2e. Construction of Localized Capacity Look-Up Table The accuracy of the speed estimates is highly dependent on the quality of the estimated capacity for the facility. Con- sequently it is recommended that each planning agency use capacities specific to the critical point of the selected study section whenever possible. However it is recognized that this is not always feasible for planning studies. Consequently the following two tables show a procedure for selecting default values and computing a look-up table of capacities by facil- ity type, area type, and terrain type. Other classification schemes may be appropriate, depending on the nature of local roadway conditions. Exhibit 6.3 shows a set of selected default parameters for the calculation of capacity for freeways, divided arterials,

46 Functional Class Area Type Terrain Type Lanes Free Speed Lane Width PHF % Heavy Vehicles Direction Split % No Pass Parking Left- Turn Bay G/C Rural Level All > 70 mph 0.85 5% Rolling All > 70 mph 0.85 5% Mountain All < 70 mph 0.85 5% Freeway Urban All All < 70 mph 0.90 2% Rural Level >2 60 mph 0.85 5% Rolling >2 55 mph 0.85 5% Mountain >2 50 mph 0.85 5% Suburb All All 0.90 2% No Yes 0.45 Urban All All 0.90 2% Yes Yes 0.45 Divided Arterial CBD All All 0.90 2% Yes Yes 0.45 Rural Level 2 Standard 0.85 5% 55% 0% Rolling 2 Standard 0.85 5% 55% 60% Mountain 2 Narrow 0.85 5% 55% 80% Suburb All All 0.90 2% No No 0.45 Urban All All 0.90 2% Yes No 0.45 Undivided Arterial CBD All All 0.90 2% Yes No 0.45 Collector Urban All All 0.85 2% Yes No 0.40 Exhibit 6.3. Example default values for computing capacity by functional class and area/terrain type. undivided arterials, and collectors. Each facility type is further subclassified according to the area type (urban or rural), ter- rain type (level, rolling, mountainous), and number of lanes (total of two lanes both directions, or more). A separate set of default parameters is then selected for each subclassification of each facility type. For example, a rural freeway in level or mountainous ter- rain is assumed to have a FFS in excess of 70 mph (112 kph), 5 percent heavy vehicles, and a peak-hour factor of 0.85. An urban freeway is assumed to have a FFS below 70 mph (112 kph), 2 percent heavy vehicles, and a peak-hour factor of 0.90 to reflect the lower design speeds, heavier passenger car vol- umes, and flatter peak volumes in urban areas. Divided arterials in rural areas are assumed to have FFS that decrease as the difficulty of the terrain increases. The as- sumed FFS for level terrain is 60 mph (96 kph), for rolling terrain 55 mph (88 kph), and for mountainous terrain 50 mph (80 kph). Any road in a rural area is assumed in this table to have signals (if any) spaced farther than 2 miles apart. Urban area roads are assumed in this table to have signals at least 2 miles apart. The local planning agency should modify these assumptions if they are not appropriate for its particular jurisdiction. Exhibit 6.3 shows assumptions only for two-lane rural undivided arterials, but the planning agency can add ad- ditional rows of data for multilane rural undivided arterials. Exhibit 6.4 shows the computation of the capacities by fa- cility type based upon the assumptions contained in Exhibit 6.3. The results have been rounded off to the nearest 50 or 100 vehicles per hour per lane. The capacities per lane contained in this table would then be multiplied by the number of lanes (in one direction) at the critical point to obtain the critical point capacity for the facility. Step 3. Compute Average Speed If it is desired to compute mean speed for each hour of a day, then once the link capacity and free-flow speed are known, the updated BPR equation (Equation 6.16) can be used to predict the space mean vehicle speed for the link at forecasted traffic volumes. The same equation is used for both metric and customary units. This method requires that ca- pacity be measured or estimated. (Eq. 6.16) where s = predicted space mean speed; sf = FFS; v = volume; c = capacity; a = 0.05 for facilities with signals spaced 2 miles or less apart, and = 0.20 for all other facilities; and b = 10. The two keys to success in applying the updated BPR curve are to have an accurate estimate of the FFS and the capacity for the facility. Once those two key parameters are accurately known, the updated BPR curve can estimate speeds for both s s a v c f b = +1 ( / )

47 Functional Class Area Type Terrain Type Lanes Ideal Cap PHF Fhv Fw Fdir Fnopass Fpark Fleft Fcbd G/C Cap/ Lane Freeway Rural Level All 2400 0.85 0.98 2000 Rolling All 2400 0.85 0.91 1900 Mountain All 2300 0.85 0.80 1600 Urban All All 2300 0.90 0.98 2000 Divided Arterial Rural Level >2 2200 0.85 0.98 1800 Rolling >2 2100 0.85 0.91 1600 Mountain >2 2000 0.85 0.80 1400 Suburb All All 1900 0.90 0.98 1.00 1.10 1.00 0.45 850 Urban All All 1900 0.90 0.98 0.90 1.10 1.00 0.45 750 CBD All All 1900 0.90 0.98 0.90 1.10 0.90 0.45 650 Undivided Arterial Rural Level 2 1400 0.85 0.95 1.00 0.97 1.00 1100 Rolling 2 1400 0.85 0.83 1.00 0.97 0.93 900 Mountain 2 1400 0.85 0.65 0.80 0.97 0.81 500 Suburb All All 1900 0.90 0.98 1.00 1.00 1.00 0.45 750 Urban All All 1900 0.90 0.98 0.90 1.00 1.00 0.45 700 CBD All All 1900 0.90 0.98 0.90 1.00 0.90 0.45 600 Collector Urban All All 1900 0.85 0.98 0.90 1.00 1.00 0.40 550 Exhibit 6.4. Example computation of default capacities by functional class and area/terrain type. arterials and freeways with accuracies approaching those of the HCM and simulation models. 6.2.4 Estimating Transition Delays Delay incurred by a traveler moving from the end of one segment to the beginning of the next segment usually can be neglected in the case of freeways, highways, and rural roads. The segment to segment transition delay also can be neg- lected for through travel along a signalized arterial street since the methods described for estimating segment speeds include a nominal delay per signal in their estimates. If the analyst is evaluating a route that involves left turns on signalized streets, the analyst may wish to improve the accuracy of the travel time estimate by adding a nominal delay per left turn to the estimated total travel time for the trip. Actual field measurements of delay are best. HCM is the next best method for estimating left-turn delay, but this re- quires a great deal of information on signal timing and turn- ing movements at the intersection. In the absence of this data, an estimate of one-half the cycle length for the signal may be used for the left-turn delay. (This assumes that a left turner is equally likely to arrive at any point in the signal cycle, so the average wait for the left-turn arrow will be half the cycle length of the signal.) (Eq. 6.17)d C i i = 2 3600* where di = Average left-turn delay at signal at end of segment i (hours). Ci = average cycle length of signal at end of segment i (sec- onds). If cycle length is not known, assume 120 seconds for suburban intersection, 90 seconds for downtown intersection. 6.2.5 Verification and Calibration of Travel-Time Estimates The above equations for estimating trip travel time are based on national average conditions. It is good practice for the analyst to verify the estimates produced by these equations for a select sample of trips in the local area. Chapter 3 suggests the appropriate methods for developing local measurements of travel time for verifying the estimates produced by the methods in this chapter. If the selected field measurements of trip travel times are within an acceptable range of the estimated trip travel times, the method can be considered to be verified against local conditions. The methods described in Chapter 3 can be used to determine the acceptable range for the results. If the results are not acceptable, the analyst should check for errors in the data used to estimate the travel times. Once the possibility of input data error has been ruled out (or at least reduced to an acceptably low probability), the analyst should calibrate the estimated trip travel times to better match observed times in the field.

48 If the sketch planning method was used to estimate seg- ment travel times, the analyst should enter field measured and estimated travel times for each segment into a spread- sheet and use the linear regression function to find the ap- propriate parameters for ADT/lane, signals per mile, access points per mile, and constant. If the planning method was used to estimate travel times, the field data and the estimated trip times should be entered into a spreadsheet and the optimization function used in the spreadsheet to find the values of the parameters a and b in Equation 6.16 that minimize the squared error between the field data and the estimates. The search should be limited to positive values for a and to values greater than 1.00 for b. 6.3 Estimating Delay Once travel time is known, delay can be estimated by sub- tracting the ideal travel time (often the travel time during un- congested periods of the day) from the actual travel time. 6.3.1 Definition of Ideal Travel Time The ideal travel time against which delay is measured should be set by agency policy. Several definitions of the ideal travel time are possible; two are provided here: One perspective is to take the “no other cars on the road” travel time as the ideal travel time. This method would as- sume that all signals are green, so that all travel is at the PSL. This is often called the FFS or zero-flow travel time. FFS however is not readily measurable in the field. So an approximation of the FFS would be the mean travel time and speed measured under low flow conditions. This method of measuring speed and travel time includes nominal delays at signals due to modest amounts of traffic on the main street and the side street. This speed would be defined as the mean speed measured over the length of the trip during a nonpeak hour, say 10:00 a.m. to 11:00 a.m. or 2:00 p.m. to 3:00 p.m. This speed would generally be lower than the posted speed limit for signalized streets, but could be higher than the PSL for freeways, highway, and rural roads. 6.3.2 Computation of Delay Delay is the difference between the actual and ideal travel time. (Eq. 6.18) where d = Delay (hr:min:sec); Ta = Actual Travel Time (hr:min:sec); and T0 = Ideal Travel Time (hr:min:sec). d T Ta= − 0 6.4 Estimating Reliability All of the reliability metrics can be computed from the travel-time variance data. This section provides a method to predict the variance in the travel time given the variance in the volume and the variance in the capacity. Traffic operations improvements generally affect the prob- ability of the facility being able to deliver a given capacity, and have minor effects on the variability of the volume of traffic. Thus this method predicts how changes in the variability of the delivered capacity for the facility affect the travel-time variance and ultimately reliability. 6.4.1 Predicting Changes in Capacity Variance The expected (mean) value of the inverse of capacity and the square of the inverse of capacity are needed to predict the travel-time variance. If the expected value of capacity can be considered as the ideal capacity (C0) minus a random variable (x), then the expected values of the inverse values can be com- puted using the following formulae. 0 <= xi C0 (Eq. 6.19) 0 <= xi < C0 (Eq. 6.20) For each study segment Exhibit 6.5 would be constructed. The probability of a given capacity reduction (ai*C0) is computed as a function of the frequency of that event type occurring each year and the average number of hours that the capacity reduction endures for each event. (Eq. 6.21) It also is possible that an ITS project might cause an inci- dent to have a lesser impact on capacity. Then one would cre- ate two incident types, one before ITS, and the same one after ITS. Each event type would have a different capacity reduc- tion. The probability of after ITS incident happening before would be set to zero; the same for the before ITS incident hap- pening after. 6.4.2 Computation of Travel-Time Variance The travel-time variance is a function of the variance in the volume/capacity ratio (A simple linear travel-time function with a breakpoint at v/c = 1.0 has been assumed to facilitate the computation of the travel-time variance from the v/c variance). P x a Ci( * )= =0 Events/Year * Hours/Event Hours/Year E C P x C x i i N i 1 1 2 1 0 2 ⎛⎝⎜ ⎞⎠⎟ = −( )=∑ ( )* E C P x C x i i N i 1 1 1 0 ⎛⎝⎜ ⎞⎠⎟ = −= ∑ ( )*

49 Capacity Reducing Event Capacity Reduction Probability Before ITS Probability After ITS No Incident x=0 Pb (x=0) Pa (x=0) Shoulder Incident x = a1*C0 Pb (x=a1*C0) Pa (x=a 1*C0) Bad Weather – Type 1 x = a2*C0 Pb (x=a2*C0) Pa (x=a 2*C0) Bad Weather – Type 2 x = a3*C0 Pb (x=a3*C0) Pa (x=a 3*C0) Shoulder Work Zone x = a4*C0 Pb (x=a4*C0) Pa (x=a 4*C0) Single-Lane Closure x = a5*C0 Pb (x=a5*C0) Pa (x=a 5*C0) Two-Lane Closure x = a6*C0 Pb (x=a6*C0) Pa (x=a 6*C0) Three-Lane Closure x = a7*C0 Pb (x=a7*C0) Pa (x=a 7*C0) Total Closure x = C0 – 1 Pb (x= C0 – 1) Pa (x= C0 – 1) Note: “x” is never allowed to exceed C0-1. This avoids divide by zero problems when computing the expected value of 1/C. Exhibit 6.5. Capacity reductions. HCM Facility Type Free-Flow Speed (MPH) Speed at Capacity (MPH) Free-Flow Travel- Time Rate (T0) (Hours/Miles) Capacity Travel- Time Rate (TC) (Hours/Mile) Calibration Parameter a=TC-T0 (Hours/Mile) Freeway 75 53.3 0.0133 0.0188 0.0054 70 53.3 0.0143 0.0188 0.0045 65 52.2 0.0154 0.0192 0.0038 60 51.1 0.0167 0.0196 0.0029 55 50.0 0.0182 0.0200 0.0018 Multilane Highway 60 55.0 0.0167 0.0182 0.0015 55 51.2 0.0182 0.0195 0.0013 50 47.5 0.0200 0.0211 0.0011 45 42.2 0.0222 0.0237 0.0015 Arterial 50 20.0 0.0200 0.0500 0.0300 40 17.0 0.0250 0.0588 0.0338 35 9.0 0.0286 0.1111 0.0825 30 7.0 0.0333 0.1429 0.1095 Two-Lane Highways 55 40.0 0.0182 0.0250 0.0068 Sources: 1. Freeways: Exhibit 23-2 HCM. 2. Multilane Highways: Exhibit 21-2 HCM. 3. Arterials: HCM Exhibits 15-8, 15-9, 15-10, 15-11, Middle Curve. 4. Two-lane Highways: Exhibit 20-2, HCM. Exhibit 6.6. Free-flow and capacity travel-time rates per HCM. For v/c < = 1.00 Var (T) = a2 * Var (v/c) (Eq. 6.22) For v/c > 1.00 Var (T) = b2 * Var (v/c) (Eq. 6.23) where T = predicted travel time (hours); T0 = Free-flow travel time (hours); TC = Travel time at capacity; a = Calibration parameter = TC – T0; and b = 0.25 (average delay per deterministic queuing theory). The variance of the travel time is equal to the variance in the v/c ratio times the square of the slope of the linear travel- time function for the facility. According to the HCM, the following free-flow and capac- ity travel-time rates (hours/mile) are appropriate (Exhibit 6.6).

50 The variance in the volume/capacity ratio can be com- puted from the expected value (the mean) of the volume (v), the volume squared, the inverse of the capacity, and the in- verse of the capacity squared. Var (v/c) = E(v2) * E(1/c2) – [E(v)]2 * [E(1/c)]2 (Eq. 6.24) 6.4.3 Computation of Reliability Metrics The following equations are for use with forecasted travel times, where only the mean and variance are known. The dis- tribution of times in this case must be assumed. For these equa- tions we have assumed that travel time is Gamma distributed with mean equal to mean (T) and variance equal to Var (T). Percent Variation The following equation is used to compute percent varia- tion based on the forecasted mean and variance in travel times. (Eq. 6.25) Buffer Index BI is computed according to the following equation, which assumes a Gamma distribution for the travel times. % ( ) ( ) %V T T = Var Mean * 100 (Eq. 6.26) On-Time Arrival The Percent On-Time Arrival is computed using the fol- lowing equation, which assumes a Gamma distribution for the travel times. (Eq. 6.27) where Gamma is the cumulative Gamma probability distri- bution with Mean = Mean (T) and variance = Var (T). Misery Index The Misery Index is computed according to the following equation, which assumes a Gamma distribution for the travel times. Since it is inconvenient to compute the mean of the top 20 percent of the values of a function, we have approximated this value with the 85 percentile highest value for the distribu- tion. For Gamma (T): (Eq. 6.28) where Gamma–1 is the inverse of the cumulative Gamma distribution with Mean = Mean (T) and variance = Var (T). MI T = [ ] − −Γ 1 85 1 % ( )Mean % [ . * ( )]OnTime Mean= Γ 1 10 T BI T T = − ⎡ ⎣⎢ ⎤ ⎦⎥ 3 0 1 100 2 . * ( ) ( ) * % Var Mean

Next: Chapter 7 - Alternatives Analysis »
Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability Get This Book
×
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

TRB's National Cooperative Highway Research Program (NCHRP) Report 618: Cost-Effective Performance Measures for Travel Time Delay, Variation, and Reliability explores a framework and methods to predict, measure, and report travel time, delay, and reliability from a customer-oriented perspective.

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  6. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  7. ×

    View our suggested citation for this chapter.

    « Back Next »
  8. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!