Estimating the Daily Volume of Crossing Pedestrians from Short-Counts

Transcription

1 TRANSPORTATON RESEARCH RECORD Estimating the Daily Volume of Crossing Pedestrians from Short-Counts. HocHERMAN, A. S. HAKKERT, AND J. BAR-ZV The main issue of this paper is hether the distribution of pedestrian volumes during the day can be generalized in a ay similar to vehicular flo distribution, so that the daily average can be deduced from short counts. Hourly hole day counts in 86 urban locations ere used to determine the typical daily distributions of crossing pedestrians n residential and central business district streets in srael. For each hour, the standard deviation and coefficient of variation ere calculated, as measures of variation among locations, to determine the best time of day for performing short counts. The standard deviation of the hourly rate as generally 1 to 3. percent of the total daily volume. The coefficient of variation as generally 2 to SO percent of the average hourly volume. Hours during nonpeak periods and afternoon peak ere identified ith relatively lo dispersion. These hours should be preferred henever short counts are performed for the purpose of risk estimates. The average daily estimates can be improved by using counts of 2 or more hours. n addition, 13 daily counts in 1-min intervals ere used to examine the adequacy of such short counts for estimating hourly flos in residential locations. The four 1-mln counts in each full hour ere regarded as four independent samples from the same distribution. Coefficients of variation (CVs) among the 1-mln counts ere calculated for each hour and averaged over locations. The CVs varied across hours but n each case ere greater than 3 percent. t as concluded that 1-min counts should not be used for the estimation of hourly pedestrian flos in residential areas. Data collection is the backbone of experimental research. Even the most sophisticated research tools can lead researchers astray hen the data being analyzed are insufficient, biased, or inaccurate. The current study deals ith the proper gathering of one type of data used in the field of road safety, namely pedestrian counts (PedC). PedC are used both in research and for design purposes. PedC are used to determine arrants for pedestrian facilities such as pavements, crossings, pedestrian signals, and underpasses and overpasses. n safety research, PedC are used together ith vehicle counts to determine exposure and assess risk. The findings are used to identify pedestrian blackspots, to determine the efficacy of pedestrian facilities, or to evaluate the effect of measures aimed at pedestrian safety in before and after studies. Most vehicular traffic counts are automated, and thus relatively simple and inexpensive. Pedestrian counting, hoever, does not lend itself to simple mechanical counting for several reasons: Unlike vehicles, pedestrian movements are not limited to a linear track; Transportation Research nstitute, Technion-srael nstitute of Technology, Technion City, Haifa 32, srael. Pedestrians can change direction, halt, or retrace at any point; and Pedestrians may move in groups, sometimes very close together. When dealing ith safety, the relevant pedestrian activity is usually road crossing. This activity may cause an encounter beteen the pedestrian and a vehicle, thus exposing the pedestrian to the risk of an accident. The observation area may be a marked crossing, its surroundings, a midblock section, or an intersection. Because manual counts by observers are expensive, the estimation of pedestrian flos is often based on short counts of to 2 min duration. For arrants, these short counts are performed during peak hour and then expanded to represent the hole hour count. n safety evaluation studies, short counts may be used to represent exposure during a period of several years. Most pedestrian counting procedures date back to the 19s. n England, Russell (1) divided urban streets into sections of 3 to 1 m. Each section as counted tice for a period of min as the counting team moved along the street. Counts ere performed during the hours of 13 to 4 and 14 to 3. Older (2) increased the count period to 6 min. Neither investigator justified the duration of the counts. Regarding the counting hours, Older explained that he avoided peak hour conditions, hich may exist in some sections and not in others. Russell used short counts to define a measure of risk to pedestrians. Risk as defined as the number of accidents in 2 years divided by the pedestrian volume in 1 min. This measure is based on the hidden assumption that pedestrian exposure during the 2-yr period can be adequately estimated from short counts. Mackie and Older (3) and Jacobs and Wilson ( 4) found that the distribution of pedestrians by place of crossing along the street for the short count as similar to that of the hole day. Hoever, the adequacy of short counts as a measure of exposure for a period of several years as not dealt ith. Studies in other European countries [see Jorgensen and Rabany ()] used to 6-min counts, quoting the aforementioned English studies. n the United States, the Highay Capacity Manual recommends counts of 1 min during peak hour, for the purpose of arranting sidealks and crossings (6). The question of ho ell short counts reprsent exposure for a hole year or more is complex. Generally, the average annual daily pedestrian volume (AADPV) is assumed to be a proxy measure of exposure. The validity of this a sumption presents an interesting problem that is outside the scope of this paper.

2 32 Accepting this assumption, the next question is ho accurate is an estimate of AADPV that is based on a short count. To anser this question, it is necessary to first consider the calculation of such an estimate. First, a short count is usually taken to represent the flo of a hole hour. An estimate of the hourly flo is achieved by multiplying the short count by a factor. Next, the hourly estimate is expanded to represent a hole day's flo. To determine the expansion factor it is necessary to kno the daily distribution of l:rossing pc.::uestrians. Finally, this daily flo is taken to represent a typical day during the study period. f seasonal variations exist, correction should be made for them. n summary TRANSPORTATON RESEARCH RECORD 18 evaluation of var(aadpv), as second derivatives are zero, and var(aadpv) can be conveniently expressed in terms of the coefficients of variation (CV). (CV is defined as the standard deviation divided by the expected value.) f Vis defined as CV2, so that V(X) = var(x)/e 2 (X), then Equation 3 takes the form var(aadpv) = K 2 x c 2 x d 2 x [V(C) + V(D) + V(C) x V(D)] (4) n situations here seasonality exists, Equation 4 can be readily generalized as follos: aadpv = Cij x K x D; x Sj here aadpv = an estimate of AADPV, Cij short-count value in hour i and season j, K = hourly multiplier: 6/minutes of short count, daily expansion factor for houri, and seasonal correction factor for season j. (1) var(aadpv) = K 2 x c 2 x d 2 x s 2 x [V(C) + V(D) + V(S) + V(C) x V(D) + V(C) x V(S) + V(D) x V(S) + V(C) x V(D) x V(S)] () f the variances of C, D and S are small relative to their expected value, var(aadpv) can be approximated by Given that the three sources of variation in aadpv, Cij, D; and Sj are independent, the variance of aadpv, var(aadpv), can be expressed as var(aadpv) = K 2 x f[var(c;). var(d;). var(sj)] (2) Var(C;) measures the day-to-day variation in pedestrian flo counted during the same period of day. t is a function of the count duration, as ell as of site-specific idiosyncrasies. Var(D;) represents the deviation of the expected daily distribution at a specific location, from the mean distribution used to calculate the daily expansion factor, for the specific hour. Thus, var(d;) is a function of the homogeneity of the locations used to calculate the daily distribution. Var(Sj) is a measure of the variation of the seasonality factor ithin the season and among locations. There is little seasonality in traffic flo in srael (7) and this seems to be true for pedestrian flos as ell. Flo distributions do change during school vacation periods and of course on eekend days (Friday and Saturday), but these changes are better dealt ith by calculating special distributions for these periods hen necessary than by using seasonality correction factors. Thus, to major sources of variation remain-random fluctuations ithin location [affecting var(c;)], and variations in daily distribution among locations [affecting var(d;)]. Because these to sources of variation are independent, the variance of aadpv can be expressed as follos (8): var(aadpv) = K 2 x [c 2 x var(d) + d 2 x var(c) + var(d) x var(c)] (3) here c = E(C) and d x E(D). (The subscripts ere dropped for the sake of clarity.) Equation 3 may be obtained by expanding Y = C x D in a Taylor series about its expected value, c x d. t is an exact var(aadpv) = K 2 x c 2 x d 2 x s 2 x [V(C) + V(D) + V(S)] (6) Both sources of variation in Equations 3 and 4 (C and D) are addressed in the present paper. Hoever, because of lack of repeated counts for the same periods and locations on different days, random fluctuations are discussed only in the context of estimating hourly flos from 1 min counts. The use of such short counts for hourly estimates in residential locations is examined. The main issue dealt ith in this paper is hether the distribution of pedestrian volumes during the day can be characterized in a ay similar to vehicular flo distribution, so that the daily average can be deduced from short counts. Hourly hole-day counts are used to determine the typical daily distributions of pedestrians in residential and central business district (CBD) streets in srael and to determine the best time of day for performing short counts. METHODS Existing data from studies carried out at the Road Safety Center during the period 197 to 1972 ere used in this study. The data consisted of full day counts by hours, performed on eekdays, at 86 locations on urbllil streets. Fourteen locations ere in CBDs and 72 on collector and arterial streets in residential neighborhoods. Most of the counts ere performed during the hours 7 to 22; a fe ere 24-hr counts. Some of the counts ere conducted at pedestrian crossings, some near crossings, and others at midblock sections. According to Jacobs and Wilson (4), the daily distribution of pedestrians is not seriously affected by the place of crossing. Thus, data for all sites ere combined and analyzed together. The hourly pedestrian volumes al each site ere converted to percentage of total daily volumes. Thus, for each site a daily

3 Hocherman el al. distribution of crossing pedestrians as calculated. The use of percentage distributions, rather then absolute nnbers, as needed because of the ide range of hourly volumes in our data. For example, pedestrian volumes in non-cbd locations during peak hours ranged from 17 to 99 and in CBD locations from 233 to 4,671. This ide range reflects not only differences among streets but also differences in the idth of the sections that ere counted. The average distributions for CBD sites and for residential sites ere calculated, along ith the hourly standard deviations (SD) and coefficients of variation (CV: defined as the SD divided by the mean). These measure the stability of the hourly share of total daily volume among sites for each hour. Thus the SD and CV serve as measures of stability of the different daily expansion factors, hich are based on hourly counts. Periods ith relatively small coefficients produce better estimates of the daily expansion factor, yielding better estimates of the daily volumes. For many of the sites, the hourly volumes consisted of four 1-min intervals. Some of these sites ere counted again after a fe months. Counts of less than a full day ere also used. n all, there ere 13 daily counts by 1-min intervals. These 1- min counts ere used to assess the adequacy of short counts to represent hourly volumes. Most sites ere in residential neighborhoods. Counts ere carried out during the main hours of pedestrian activity, beteen 7 and 22. The average of pedestrian volumes as relatively lo: 8 to 1 pedestrians per 1 min. The four 1-min counts in each full hour ere regarded as four independent samples from the same distribution. The assumption of independence seems reasonable (9). The assumption of identical distribution implies no trend ithin the hour. This may not alays be correct, especially during morning peak hour. During other parts of the day volumes are fairly constant. When trends do exist, the assumption of common distribution results in an overestimate of the variation. SDs ere calculated for each hour to measure the dispersion among the four 1-min counts and, thus, the reliability of an hourly flo estimate based on a 1-min count. To compare among different sites, the SD as standardized by dividing by the average of the four counts (m) to produce the CV. RESULTS Dally Volume Distributions in Residential Neighborhoods Presented in Figure 1 are the average daily (24-hr) volume distributions in four residential neighborhoods in the city of Haifa. The distributions are fairly similar and display three peak periods: a morning peak beteen 7 and 8, a noon peak beteen and 13, and an afternoon peak beteen and 19. The average daily distributions in to cities, Haifa and Givatayim, are compared in Figure 2. As counts in Givatayim ere performed during day and evening hours only, both distributions are displayed and compared for this period. Again, a high degree of similarity can be observed beteen the to distributions. Therefore, all 72 residential sites ere combined LEGEND 17 NEGHBOURHOOD A-- B--- 1 c l 13 / c.!l ;:: 11 z tj 1 a:: a.. ' 9 \ \ 8 \ 4 t \ D TME (HOURS) FGURE 1 Daily distribution of crossing pedestrian volumes (percentages) in four residential neighborhoods in Haifa.

4 1B (!) 11 <: f- z 1 u E:i GVATAYM ' i \ i "\ / \ \ \ ' \ ' \... \ ' TME (HOURS) FGURE 2 Comparison of daily distribution of crossing pedestrian volumes (percentages) in Haifa and Givatayim. 19 1B UJ "' 1 u E:i 9 Cl /, J TME (KOU RS) FGURE 3 Daily distribution of crossing pedestrian volumes (percentages) in residential neighborhoods in srael (average and standard deviation).

5 llocherman el al. to calculate an average, or typical, distribution of pedestrian volumes in urban residential areas. This average distribution and the standard deviation of hourly pedestrian volumes are displayed in Figure 3. The same data are presented in Table 1, together ith the hourly CVs. The main results for residential areas are summarized as follos: Pedestrian volume during night hours, 22 to 7, constitutes only 3 percent of the total daily volume. Counts TABLE 1 DALY DSTRBUTON OF HOURLY PEDESTRAN CROSSNG VOLUMES N RESDENTAL AREAS Hour rn Mean(%) Norn: Sample size = 72 sites. SD(%) CV(%) that do not include these hours are therefore almost complete. This result is based on the 24-hr counts performed in residential locations in Haifa. The daily distribution of crossing pedestrians has three peaks: a steep morning peak beteen 7 and 8, hich carries 14 percent of the daily volume; an afternoon peak beteen and 19, ith an hourly flo of 8 to 1 percent of the total daily volume; and a midday peak beteen and 13, containing 9 percent of the daily volume. The standard deviation of the hourly rate is 2 to 3. percent of the total daily volume, except for the morning peak, hich has an SD of 6.1 percent. The loest variation occurs during the nonpeak periods: 8 to 1 and 14 to, hen the SD is about 2 percent. The CV is generally 3 percent to percent of the average hourly volume (except for the hour 21 to 22, hen pedestrian traffic is already very lo). The loest CVs occur again in the off-peak periods from 8 to 9 and from 1 to, hen variance is lo, but also during the afternoon peak from to 19, hen the variation in pedestrian volumes and the average flo are relatively high, so that their ratio remains relatively lo. Dally Volume Distributions in CBD Areas The average daily distribution of pedestrian crossing volumes in 14 CBD locations for the period of activity, from 7 to 22, is shon in Figure 4. The same information is presented together ith the hourly SDs and CVs in Table 2. n addition, ll '-" 1 z: u 9 o< "- 6 s 4. > s TME (HOURS) FGURE 4 Daily distribution of crossing pedestrian volumes in the CBD (percentages).

6 36 TRANSPORTATON RESEARCH RECORD 18 TABLE 2 DALY DSTRBUTON OF HOURLY PEDESTRAN CROSSNG VOLUMES N THE CBD Hour Mean(%) SD(%) CV(%) Norn: Sample size = 14 sites. TABLE 3 ACCURACY OF SHORT 1-MN COUNTS AS AN ESTMATE OF THE HOURLY VOLUME Hour of Counting CV No. of Sites Ranking of Estimate Accuracy data on pedestrian activity in the CBD during night hours ere also available, but are not displayed here, to facilitate comparison ith the daily distribution in residential areas. The main findings for CBD areas are summarized as follos: Pedestrian volume during night hours, 22 to 7, constitutes only 7 percent of total the daily volume. Counts that do not include these hours are therefore almost complete. The daily pedestrian distribution in CBD locations is similar to that in residential locations and also contains three peak periods: morning (7 to 8), noon (11 to 13), and afternoon ( to 19). The main difference beteen the to distributions is that the morning peak in the CBD is not as steep and contains only 7 percent of the daily volume. This difference reflects the fact that there are no schools in CBD areas (schools in srael start beteen 7 and 8), hereas shops open only at 9. The hourly variation is generally loer in CBD locations than in residential areas and amounts to 1 to 3. percent of the daily pedestrian volume. The variation is higher at peak hours than at off-peak periods, in accordance ith the findings for residential sites. The CVs vary beteen 2 and percent of the average hourly volume. CVs do not exceed 3 percent for the periods from 8 to 13 and 1 to 17, and they are loest ( <2 percent) for the hours from 9 to 1 and to 17. Short Counts CVs for 1-min counts for each hour are presented in Table 3. The CVs are averaged over locations and range beteen 33 and 69 percent. The largest variations stem from trends ithin the hour, but even for hours ith constant flos of pedestrians, the variation among short counts ithin the same hour is 33 to percent. These findings are in accordance ith those of Haynes (9), ho recommends full hour counts hen pedestrian flos are less than 1 pedestrians per minute. SUMMARY AND DSCUSSON Analysis of the daily distribution of pedestrian crossing volumes leads to a number of conclusions ith practical implications for improved pedestrian counting. These can be used in the design of crossing facilities and for the study of pedestrian risk and safety. Typical daily distribution of pedestrian crossing volumes ere developed for both residential and CBD locations in urban areas in srael. These distributions can be used to estimate daily pedestrian volumes during the main hours of activity, 7 to 22. Total 24-hourly volumes can be estimated from 1-hourly volumes by multiplying by 1.3 for residential sites and by 1.7 in the CBD. The daily distribution for srael as compared ith similar distributions obtained for Germany and Australia. Neumann (1) conducted detailed counts at 111 sites in various German cities. Cameron (11) counted pedestrian volumes at 29 sites in Melbourne, Australia. The respective daily distributions are plotted in Figure. t can be seen that the three distributions have similar shapes, ith differences reflecting differing lifestyles (e.g., school, ork, and shopping hours). The standard deviation of the hourly rate in residential areas is generally 2 to 3. percent of the total daily volume. The hourly variation is generally loer in CBD locations and ranges beteen 1 and 3. percent of the daily pedestrian volumes. The loest SDs occur during nonpeak periods. The coefficient of variation in residential areas is generally 3 to perl:enl of the average hourly volume. CVs smaller than 3 percent occur during the hours beteen 8 and 9 and 1 and 18. n CBD areas the CVs vary beteen 2 and percent of the average hourly volume. CVs do not exceed 3 percent for the periods 8 to 13 and 1 to 17. These hours should be preferred henever short counts are performed for the purpose of risk estimates. Counts during peak hours are still needed if facility design is the major aim. The average daily estimates can be improved by using counts of 2 or more hours. Tables 1 and 2 can be used to calculate the resulting SDs and CVs of such counts in srael.

7 Hocherman el al < 1 '--' 9 "- 8 ' " / \ AUSTRAL A \ \ \ TME (HOURS) FGURE Comparison of daily distribution of crossing pedestrian volumes (percentages) in srael, Germany, and Australia. Haynes (9) studied the accuracy of short pedestrian counts. Pedestrians ere counted at 11 crossing sites in Norich, England, ith varied levels of activity. Counts ere made during 1-min intervals for 2 hr. The data ere then cleared of trends. Trend-cleared counts at 1-min intervals ere found to be nearly normally distributed and independent of each other. The variance as found to be proportionate to the mean, hich indicates that the accuracy of estimates based on these counts increases as pedestrian volumes increase. Assuming normality, Haynes developed a series of curves for various levels of activity. The relationship beteen maximum expected sampling error and length of count is shon for various levels of pedestrian activity in Figure 6. This figure can aid in choosing count duration to comply ith a desired level of accuracy. t can be seen that for volumes of 3 pedestrians or more per minute, an error of less than 1 percent can be achieved ith 'i r- i - >.! L! 3.!:! ;: Cl ;;; ') 6 2 ii E ;c.. : 1!- r. (a) = ped/min (b) = 1 ped/min 'ii >.!!., (c) = 2 ped / m in 4 - j (d) = 3 ped/ min.!:! " ' (e) = 4 ped/ min c. ----r--.2' () = ped/ min ii E 1 ".. :i BO 1 Sampling time FGURE 6 The relationships beteen maximum expected sampling error and sampling time for various levels of pedestrian activity (9).

8 38 - to 1-min counts. For levels of 1 pedestrians per minute, full-hour counts are needed. Similar analysis on 1-min data at residential sites ith relatively lo pedestrian volumes as conducted in this study. The CV as found to change ith the hours but in each case as greater than 3 percent. t is concluded that 1-min counts should not be used for the estimation of hourly flos in residential areas. When used to estimate daily flos, the shortco1t error is compounded to the error in the hourly expansion factor. Pedestrian counts of varying durations are used to estimate AADPV, hich serves as a measure of exposure. Further research on the day-to-day variation in hourly or daily counts is needed to fully address the issue of accuracy of these estimates. This ill enable the estimation of var(aadpv) according to Equation 3. Although the data used in the study date back to the early 197s, il is nul cxpc1.:lcu Lhal pt:tfosliia.i1 uisliiuuliurn; have changed because basic life-styles in srael have not changed during this period. Hoever, this assumption should be checked periodically and the distributions updated if necessary. REFERENCES l. C. A. F. Russell. Relative Risk to Pedestrian or Crossings and Elsehere. RN-131-CAFR. Road Research Laboratory, Crothorne, England, Jan. 19. TRANSPORTATON RESEARCH RECORD S. J. Older. A Survey of the Risk to Pedestrians Crossing Seven Roads in West London. RN-467-SJO. Road Research Laboratory, Crothome, England, Oct A. M. Mackie and S. J. Older. A Study of Pedestrian Risk in Crossing Busy Roads in the nner Suburbs of London. LN 72. Road Research Laboratory, Crothome, England, Dec G. D. Jacobs and D. G. Wilson. A Study of Pedestrian Risk in Crossing Busy Roads in Four Tons. Report LR. Road Research Laboratory, Crothorne, England, W.. Jorgensen and Z. Rabani. Fodgaengerees sikkerhed i og ved fodgaengerovergange. Report No. 7. Radet for Trafiksikkerhedsforskning, Copenhagen, Denmark, Special Report 29: Highay Capacity Manual. TRB, National Research Council, Washington, D.C., Y. Gur, A. S. Hakkert, and. Hocherrnan. Optimization of Traffic Counts in srael (in Hebre). Report No Transportation Research nstitute, Technion, srael, L. A. Goodman. On the Exact Variance of Products. Journal of the American Statistical Association, Vol., No. 78, R. Haynes. Sampling Time and Sampling Error in Pedestrian Counts. Traffic Engineering Control, Vol. 18, No. 2, London, England, Feb L. Neumann. Further Studies on the Criteria for the nstallation of Pedestrian Crossing Facilities. BASt Project Report FP 832. Bundesanstalt fiir Strassenesen, Bergisch-Gladbach, Federal Republic of Germany, M. H. Cameron. Accident Risks at Zebra Crossings. Australian Road Research Board (ARRB), Nunaading, Victoria, Publication of this paper sponsored by Committee on Pedestrians.