Identify some areas where additional research would be beneficial.

Transcription

1 Estimation of Intersection Turning Movements from Approach Counts BY MARK C. SCHAEFER For most intersection trdffic analyses, a complete set of vehicle turning movements is required. Yet, under some circumstances, only intersection directional approach volume counts are documented or obtained. These circumstances may include traffic field surveys in which only mechanical counting equipment was used (e. g., road tubes) and data from traffic forecasting models (where link volumes, rather than full intersection movements, are output). Manual trial and error techniques for estimating the turning volumes that balance the inbound and outbound intersection approach volumes are both tedious and difficult. Considerable research has therefore been done on estimation methods that are easily employed (i. e., an algorithm suitable for a computer program) and that provide a reasonable degree of accuracy. IThe algorithm relies on an initial estimate of the likely turning properties from each approach. The purpose of this articie is to summarize some of the current efforts in the use of the estimating technique known as Kruithof s algorithm. Specifically, the article will: Document from the Iitcraturc the experience in the use of the algorithm. The algorithm has been used almost exclusively in jurisdictions outside of the United States.. Present the results of my investigations of the application of the average turning proportions technique to the algorithm in a study of 58 intersections in Denver, Colorado. Suggest some approaches in the use of the algorithm in developing turning movements from traffic forecasting model data. Identify some areas where additional research would be beneficial. Intersection Movement Turning Models Within the past several years, a variety of intersection balancing techniques have been suggested to facilitate the estimation of intersection turning movements from approach volumes. The techniques, which include factoring and iterative and non iterative procedures, vary greatly in their theoretical bases, computational rigor, and accuracy. (Sources for a number of these alternative techniques are listed in the bibliography. ) This article will focus on the algorithm described by van Zuylen and more recently by Hauer et al. The algorithm, which involves an iterative balancing of possible turning movements using an initial estimate of the turning proportions, is based on the technique first described by Kruithof in the late 1930s. Hauer and coworkers described the problem as the identification of a likely set of turning movements that balances the prespecified inbound and outbound volumes of each intersection approach. Because there is not a unique solution to the problem (that is, a number of different turning movement combinations will balance the intersection), the algorithm relies on an initial estimate of the likely turning proportions from each approach. From this first estimate the turning movements are balanced to match the prespecified link volumes through an iterative process. The four-step procedure described by Hauer et al. is easily converted to a computer tions: program to speed the computa- Let 0, = The total traffic into the intersection from approach i, D, = The total flow out of the intersection to approach j, T,, = The total traffic flow from approach i to approach j (i. e., the turning movement from approach i to approach j, P,, = The proportion of the approach i traffic flow that turns in the direction of approach j, s= The sum of entering flows (equals sum of exiting flows), and m= The number of intersection approaches. The factors A, and B,, are balanced in an iterative process. That is, A, is first computed as: 0, 4 ITE JOURNAL. OCTOBER 1988 ~41

2 B, is computed as A, is then recalculated as ~ p,, B, x, 1 B, is then computed using the new value for A,. The original and new values of Al are iteratively compared until closure. The estimated values of T,, are then based on the latest values of A, and B, (where T,, = P,, A,B,). The theoretical basis of the algorithm, numerical examples, and the detailed description of its application are described in the literature. Estimates of Turning Movement Probabilities In using the technique proposed by Hauer et al., the critical input is the user s initial estimate of the turning proportions of each approach. Because the solutions to the problem are not unique, the identification of the best solution relies heavily on an accurate initial estimate of the turning probabilities. Several methods have been proposed for developing a good initial estimate of the turning proportions, including those based on: Type of intersection, Historical turning movements, Short period counts, and Average turning proportions. The relative merit of each method is described in the following sections. Type of Intersection In their study of 145 intersections in the Toronto metro area, Hauer and coworkers based their initial turning proportion estimates on the functional classification of the approach roadways to an intersection. From their survey data, the average turning proportions shown in Table 1 were developed (note: arterial is defined as two or more lanes in each direction). Based on these proportions, the algorithm was applied to develop estimates of the observed flows. They observed that the accuracy of the estimation varied by approach type, with the resulting standard deviation in estimated versus observed turning flows ranging from 9.74 vehicles (collector to collector) to vehicles (arterial to arterial). Mountain and Westwell reported a similar unpublished study by Surl in which 128 four-leg intersections in England and Wales were grouped into 20 separate categories (major versus minor approach, method of control, and approach speed). A higher degree of accuracy in the estimates was achieved when the turning proportions of the specific intersection type, rather than overall average or equal turning movement proportions, were applied. Mountain and Steele tested the method of separating intersection approaches by the major axis (pair of approaches carrying the highest flows) and minor axis.4 The mean turning proportions of each axis type were then used as initial estimates for the algorithm. No real improvement was found by using the axis approach over that achieved in the average turning volume approach. Historical Turning Movements Mountain and Westwell tested the accuracy of using historical turning movement records in their analysis of 69 signal-controlled, four-way intersections in Merseyside, England. In this method, an out-of-date turning movement record is used to identify the first estimate of turning proportions. Their analysis revealed the following conclusions: For flows up to about 100 vehicles per hour (vph), the greater the flow, the greater the probability of a larger absolute error. For flows greater than 100 vph, the magnitude of the absolute errors appears to be relatively independent of the magnitude of flow. Table 1. Average Turning Proportions As an example of the achieved accuracy, the authors indicate the probability of a turning flow of 150 vph being estimated to an accuracy of f 10UZOis about For a turning flow of 300 vph, the probability improves to In a later study, Mountain and Steele found that, using the historical count method, 96% of the errors in the estimates were in the range of f 50 vehicles. Average Ibrning Proportions In the absence of field or other historical data, the use of average turning proportions for the algorithm s initial estimate has been suggested. Frequently cited average turning proportions include those presented in the 1965 Highway Capacity Manual (i.e., 10% left, 80 % through, 10 % right). Limited tests have been made of the accuracy of using an average turning proportion approach. van Zuylen reported that, using a distribution of zs~. left, 507. through, and 25?6 right, errors between 0.2T0 and 23q0 were achieved. (This was reported by Mountain and Westwell to be an improvement over Surl s test of equal turning proportions.) Mountain and Steele have provided perhaps the most comprehensive documented test to date of the method in their study of 32 intersections in the Merseyside, England, metro area. In their study, three alternative average turning proportion sets were tested: Equal turning movements one third left, one third through, and one third right; 25% left, 50% through, zs~o right; and Average turning movements based on a sample of other intersections in the Merseyside area (18.2% left, 66.0% through, 15.8% right). (Note: lefthand rule of road.) rhe results of their analysis, summa- ProDorfion Type of Approach Lefl Through Right Central business district 0, Arterial to arterial Arierial to collector Collector to arterial ,32 Collecfor to collecfor 0, SOURCE: Cited reference ITE JOURNAL. OCTOBER 1988

3 rized in Table 2, demonstrate an appreciable improvement in the accuracy of the estimates when the average turning proportions reflect local conditions as opposed to generalized turning proportions. Theauthors note that the analysis revealed a distinct bias in the errors, with greater probability of a positive error than a negative error (for equal turning probabilities, approximately 60% of the errors were positive). Furthermore, the methods were found to underestimate the probability of a through movement and overestimate the probability of left- and right-turn movements. Denver Study To further identify and document the comparative value of the average turning proportions technique, anew study was conducted of 58 signalized, four-leg intersections in the Denver, Colorado, metropolitan area. Data sets were collected for both the morning and evening peak hours. The 116 data sets contained a total turning movement flow of 395,756 vehicles, or an average peak hour intersection turning movement of 3,412 vehicles (Table 3). A Fortran computer program was written to expedite the calculations of the algorithm. For each peak hour data set, inbound and outbound actual link volumes were input into the algorithm with an initial turning movement estimate of 10% left, 80$Z0 through, and 10% right. The results of a comparison between turning movement estimates and actual counts are summarized in Table 4. Short Period Counts Mountain and Westwcll also considered the use of short period counts, where the turning proportion estimates are based on a partially manual technique of using a relatively short duration turning count to estimate the turning proportion matrix. In their study, a one-hour count was used to establish first guess estimates for an overall six-hour analysis period, resulting in a marginally narrower error distribution than from the use of reliable historical data. Mountain and Steele s later study showed that, using the partially manual approach, 9X% of the estimate errors were within ~ 50 vehicles. The overall absolute error for the entire data set was 83,910 vehicles, or 21.2% of the actual turning movements. (In other words, applying the 10,80, 10 turning proportions resulted in a total absolute deviation of the estimated flows versus the actual flows of 83,910, or 21.2% of the 395,756 vehicles recorded in the actual data set. ) The results on a per movement basis are shown in Table 5. Overall, less than 209. of the actual turning flows were estimated within t 10%, ranging from 7.A~o (for actual volumes between O and 99 veh/hr) to 100% (for volumes between 1,500 and 2,200 vph). As a general trend, accuracy (based on the * lo% measure) improved as the magnitude of flows increased. The overall proportion of estimates within t 50 vehicles of the actual estimate was Table 2. Tests ot Average Turning Proportion Estimates Averaae Turnina Proportion 56.7 Yo approximately equal to the accuracy achieved by Mountain and Steele s equal turning proportion tests. A typical intersection from the data set is shown in Figure 1. Actual turning proportions at this particular site ranged from 3% to 44%. As shown, the use of 10%, 80%, 10% for the initial estimate of turning proportions resulted in a somewhat rough approximation of the actual turning movements. The overall pattern of turning movements (such as the heavy right turn on the northbound leg and the heavy left turn on the westbound leg), however, was reasonably maintained in the resulting estimate of turning movements. Left Through Right Accuracy (Proportion of Errors (%] (%] (%] in Range of *50 Vehicles) (7.] SOURCE Summarized from cited reference 4. Table 3. Data Set Characteristics, Denver Metropolitan Area Number of intersections Total turning movements Average intersection peak hour fuming movements Range Standard deviation Weighted average intersectionflows ( 7.) Left turns Through Right turns 58 (morning and evening peak counts for each) 395,756 vehicles 3,412 vehicles 726-5,992 vehicles 1,276 vehicles Table 4. Turning Movement Estimates Based on 10, 80, 10 Initial Proportions (Intersection Basis) Overall absolute error 83,910 vehicles (21.2%) Average absolute deviation per peak hour per intersection 83, = 723 vehicles Minimum deviation 2,7~o (112 vehicles at an intersection with a total flow of 4,083 vehicles) Maximum deviation ss.o~o (1,542 vehicles at an intersection with a total flow af 2,751 vehicles) Standard deviafian ITE JOURNAL. OCTOBER

4 While the algorithm generally underestimated the actual flows (58% of the estimates were lower than the actual count) the estimates for larger flows (such as those above 500 vph) were typically higher than the actual counts. Looking at left and right turns alone (which composed a majority of the smaller flows in the data base), the algorithm overestimated only 15% of the actual counts, in contrast to the findings of Mountain and Steele, who found that left and right turns were consistently overestimated. Discussion The technique described by Hauer et al. provides a quick method of estimating intersection turning movements based on prespecified inbound and outbound link volumes. Although primarily proposed in the literature as a means of economizing on the collection of intersection traffic data, I have found the algorithm s greatest usc to be in the development of intersection turning movements from the link volumes generated by traffic forecasting models. When applied to forecasted traffic data, the method can be of particular value when The cost or time for a new model run to secure a small number of intersection turning movements is prohibitive, Link data from the model have been manually smoothed (consequently, turning movements from the model are no longer applicable), or Estimates of peak hour turning movements are to be made from average daily traffic model forecasts (and link volumes have been adjusted by peak period and directionality factors). Long-range forecasts are often made on roadway facilities and intersections not yet constructed. Use of the algorithm requires an initial estimate of the turning proportions of each intersection approach. Because there is not a unique solution to the problem, the closer the initial estimates are to the actual (unknown) turning proportions, the closer the resulting turning movements will be to the actual movements. The selection of appropriate values for the initial turning movements can be arrived at in several ways. Hauer and coworkers suggest that reasonably accurate turning movement estimates can be made if the initial turning proportions are estimated by the use of preselected intersection types. Use of Hauer s method requires either the acceptance as a general guideline of Hauer s survey of 145 Toronto intersections or the study of turning proportion patterns in the jurisdiction in question. Where traffic flow patterns have remained consistent, the use of a previous turning movement count may provide a first estimate and, as Mountain and Westwell report, a reasonable degree of accuracy may be obtained (depending on the purpose of the survey), The need to obtain the historical data and the requirement that turning patterns remain substantially unchanged arc two inherent weaknesses of the historical data approach. When using the algorithm with traffic forecasting data, it is unlikely that historical patterns will remain sufficiently constant. Furthermore, in many cases, long-range forecasts arc often made on roadway facilities and intersections not yet constructed. Table 5. Results Based on 10, 80, 10 Initial Proportions (Per Movement Basis) Proportion of Percent of Estimates Turnina Total Mean Standard Estimates Within Over/Under VolumZ Actual Total Error/ Error Deviation *10 * 50 Estimated fvehicles) A! Flow Error Actual (Vehicles) fvehicles) of Actual Vehicles [%] ,002 15,357 0, / ,726 17,114 0,38 54, , i ,534 11,683 0, , I ,075 10, , , / ,738 4, , , / ,514 4, ,292 2, / ,397 1,923 0, ~ ,324 3,239 0,12 104, , / ,594 2, , /09 1,000-1, ,315 2, , /00 1,400 1, ,643 2, /00 1,200 1, ,918 3,019 0, /03 1,500 2, ,390 1,455 0, /10 TOTALINTERSECTIONFows = 395,756 vehicles TOTALERROR = 83,910 vehicles (21.27.) NOTE.Two intersection flows greater than 2,200 vph were omitted from this summary, but they are included in totals. N = Tofal number of actual flows in volume class Total Actual Flow = Sum of actual flows in volume class Total Error = Sum of absalufe deviation, (actual estimated). Error/Actual = Total error/total actual flow for each volume class. 44. ITE JOURNAL. OCT08ER 1988

5 Perhaps the most accurate means of identifying initial turning proportions, the use of short period counts and other in-the-field techniques, introduces the need (and consequently greater expense) formanually collected data. Although this technique is of value forcstimating current flows when historical data arc not available, it is of limited use for testing traffic forecasting data. In the absence of any prior data on intersection volumes, the use of average turning proportions has again been demonstrated to provide somewhat coarse approximations. While reasonably accurate estimates were achieved for large intersection movements (say over 700 vph) and on an overall basis for intersections, the technique provided rather poor estimates of Iow-volume movements. Given the uniqueness of any given intersection and the specific needs of the analysis, it is difficult to state with certainty the most appropriate technique for developing an initial turning movement proportion for use with the algorithm. As a general guide, however, the use of an out-of-date turning movement count appears to provide the most reasonable accuracy at the lowest cost for turning estimates of current or neartcrm forecasted traffic. For developing turning movements from long-range forecasting model data, however, the value of historical data is minimized because the model data generally reflect significant land use and roadway network shifts. Similarly, the collection of current intersection field data (short period count) for use with long-range model data may have minimal value and should be viewed as an inadvised expenditure. Thus, for Iong-range forecasts, initial estimates based on intersection type or generalized turning proportions currently provide the best approach for developing initial turning estimates. Additional research is needed to determine whether accuracy might be further improved by adjusting generalized proportions for specific intersection characteristics, including Location in the metropolitan area (e. g., the estimated turning proportions for a morning peak period would generally be oriented toward the central city, major land use, or nearby freeway). Relative magnitudes of the outbound Type of intersection control. volumes. Number of approach lanes/relative importance (e.g., arterial, collector) of intersecting streets DIRECTIONAL Additionally, sensitivity tests for specific traffic analyses can be conducted to reflect the possible range of estimating r= o o r- J APPROACH VOLUME, : I : P.M. PEAK HOUR - m : 75(32)~ 909(980) + 153(125] ~ - ACTUAL COUNT (000] - PREDICTED VOLUME USING ALGORITHM AND U3 10%-80%-10% INITIAL TURNING PROPORTION ESTIMATE ON ALL LEGS Figure 1. Typical intersection h 125(87] + 382(473) ~ 391 (338) Ttr ITE JOURNAL. OCTOBER

6 errors and the errors inherent in the traffic forecasting process. Conclusions I have found the use of the algorithm described by Hauer et al. to be a useful tool for developing intersection turning movement estimates from traffic forecasting model link volumes in those circumstances where turning movement volumes cannot be economically obtained. Selection of an appropriate initial estimate of the intersection turning proportions is key to developing an accurate estimate of the actual flows. Use of generalized turning proportions, when appropriately modified by judgments based on the particular characteristics of the study intersection, may provide a degree of accuracy in predicting intersection turning flows that is appropriate for the accuracy of traffic forecasting data. Future Research Needs Current research in the field, as evidenced by the current literature, indicates a continuing focus on the use of the algorithm (and similar models) as a means of economizing on the collection of intersection turning movement data. In particular, the emphasis is on the replacement of some or all manual traffic observers with automatic (machine) counts. Whether a turning flow technique is developed to economize on current data collection or to assist in the development of 20-year forecasts, continued research on the subject is needed. In particular, future research should focus on Expanding the data base of experience Subscribe to /1 EJourna/ Your Information Source in the use of current techniques for developing initial estimates and identifying a consistent basis for comparing results; and Developing additional, easily used, and reliable estimating techniques, with particular focus on the ease of use by practicing transportation engineers and planners. Use of Bayesian techniques has been reported to show some promise for certain applications (Mountain et al.). References 1. van Zuylen, Henk J. The Estimation of Turning Floyvs on a Junction. Traffic Errgirreerirrg and Control (November 1979). 2. Hauer, E., E. Pagitsas, and B.T. Shin. Extirpation of Turning Flows from Automatic Counts. Transportation Research Record 795 (1981 ). 3. Mountain, Linda J.,and Paul M. Westwell. The Accuracy of Estimation of Turning Flows from Automatic Counts. Traffic Etrgitreerihg and Control (January 1983). 4. Mountain, Linda, and David Steele. Prior Information and the Accuracy of Turning Flow Estimates. Traffic.Errgineering and Contro[ (December 1983). 5. Mountain, Linda J., M. Maher, and S. Maher. The Estimation of Turning Flows from Traffic Counts at Four-Arm lrrtcrscctions. Traffic Engineering and Con/rol (October 1986). 6. Mountain, Linda J., M. Mahcr, and S. Maher, The Estimation of Turning Flows from Traffic Counts at Five-Arm Intersections. Traffic Engineering and Control (November 1986), Bibliography Adebisi, Olrsscgun. Improving Manual Counts of Turning Traffic at Road Junctions. Journal of Transportation Engineering (May 1987). Bell, M.G. H. The Estimation of Junction Turning Volumes from Traffic Counts: The It s tough keeping current with new adwdnces and techniques in transportation engineering. But ITE Journal, the monthly magazine written and edited for transportation engineers, makes that job easier. Each month, it brings you articles and departments covering the latest developments, practices, techniques, and products in the field of transportation engineering. For only $40 ($55 outside the U. S., Canada, and Mexico), you can get your own subscription to ITE Journal. All it takes is a phone call today: call the ITE Bookstore at 202/ (please have your MasterCard or Visa number handy). Or send your order with payment (check or credit card information) to Institute of Transportation Engineers 525 School St., S. W!, Suite 410 Wasington, D.C Role of Prior Information, Traffic Engineering and Contro/ (May 1984). Buehlcr, Martin G. Forecasting Intersection Traffic Volumes. Journal of Transportation Engineering (July 1983). Fleet, Christopher R. Increasing the Relevance of Planning for Project Development and Pavement Design, prepared for National Conference on Transportation Planning Applications, Highway Research Board. High way Capacity Manual. Special Report 87. Washington, DC.: Highway Research Board, Jeffreys, Martyn, and Michaci Norman. On Finding Realistic Turning Flows at Road Junctions. Traffic Engineering and Control (January 1977). Maher, M.J. Estimating the Rsrning Flows at a Junction: A Comparison of Three Models. Traffic Engineering and Control (May 1984). Marshall, M.L. Labour-saving Methods for Counting Traffic Movements LitThree- and Four-arm Junctions. Traffic Engineering and Control (April 1979). Mckky, Ali. On Estimating Turning Flows at Road Junctions. Traffic Engineering and Control (October 1979). Norman, M., and N. Hoffman. Non-iterative Methods for Generating a Realistic Turning Flow Matrix for a Junction. Traffic Engineering and Control (Dcccmbcr 1979). Pedcrscn, N. J., and DR. Samdahl. Highway Traffic Data for Urbanized Area Pro]- cct Planning and Dcsigrr. NCHRP Report 255. Washington, D. C.: Transportation Rcsca-ch Board, Dcccmbcr I Mark C. Schaefer is u senior transportation engineer with Parsons Brinckerhoff Quade & Douglas, Inc., in Denver, Colorado. A registered professional engineer in Colorado, he has a B.S. C. E. degree from Marquette University and an M. B.A. from the University of Colorado at Denver Schaefer is an Associate Member of ITE and is secretaryltreusurer of the Colorado/ Wyoming Section. The Fortran program used in the data analysis was developed while the author was employed with Centennial Engineering, A rvada, Colorado. A Lotus (Release 2) version of the algorithm is available at nominal cost from the Center for Microcomputers in Transportation (McTRANS) at the University of Florida, Gainesville. 46. ITE JOURNAL. OCTOBER 1988