Proposed Procedure for Selecting Traffic Signal Control at School Crossings

Transcription

1 TRANSPORTATION RESEARCH RECORD Proposed Procedre for Selecting Traffic Signal Control at School Crossings JAMES A. BoNNESON AND JosEPH D. BLASCHKE This paper describes the crrent criteria sed to determine the need for traffic control at school crossings. It discsses the backgrond and assmptions sed in establishing these crrent criteria and points ot a few of its deficiencies. Based on this assessment, a methodology is proposed that is intended to improve on the crrent criteria. This methodology has the advantages of enabling more eqitable treatment of vehiclar and pedestrian traffic as well as allowing for easier application. The crrent procedre for determining the need for traffic signal control is based on a field stdy techniqe that yields the length of time needed by pedestrians to cross the street and the freqency with which gaps of this dration occr in the vehiclar traffic stream. The proposed procedre is similar to the crrent procedre; however, by assming that the distribtions of pedestrian and vehiclar arrivals are random, time-dependent processes, the Poisson distribtion can be sed to estimate the gap dration and its freqency of occrrence. The intent of this approach is to eliminate the need to condct a field stdy at locations the assmption of random arrivals is valid. As a reslt of this investigation, a procedre is proposed that incorporates the intent of the crrent procedre bt is mch simpler to apply. Additional criteria have been added that address the isse of interrption of pedestrian flows and the need for a minimm pedestrian volme. The goal of this procedre is to provide a means of ensring the niform application of traffic control devices and to avoid the nnecessary installation of traffic signals. The safety of children traveling between home and school is a highly sensitive sbject. There are often conflicting opinions among citizens and pblic officials abot what mst be done to ensre the safety of the children. Citizens typically want additional police officers, crossing gards, and traffic controls on any street they feel is "potentially dangeros." Pblic offi. cials representing the school and the city mst respond to the citizen's concerns by determining a proper corse of action. Their determination is fonded on the desire to maximize both motorist and pedestrian safety, bt it mst be tempered by the effective se of limited fnding resorces and the application of reasonable and niform traffic control policies. (The term "pedestrian" is sed throghot to refer to school children walking along, adjacent to, or across the roadway.) Engineering stdies have shown that the niform application of reasonable traffic control procedres will improve pblic nderstanding and acceptance. of any control measre. In contrast, se of non-niform procedres or controls creates confsion and lessens the respect given to them by pedestrians and motorists alike. Hence, establishing and adhering to a set Texas Transportation Institte, Texas A&M University System, College Station, Tex of reasonable and niform criteria for applying traffic control is a desired goal becase it ensres eqal treatment at similar locations and moderates the inflences of emotion and bias. This paper describes the crrent criteria sed to determine the need for traffic control at school crossings. It discsses the backgrond and assmptions sed in establishing the crrent criteria and points ot a few of its drawbacks. Based on this assessment, a new methodology is proposed that is intended to improve on the crrent criteria. This methodology has the advantages of enabling more eqitable treatment of vehiclar and pedestrian traffic as well as allowing for more convenient application. STATEMENT OF PROBLEM According to the Uniform Vehicle Code, motorists mst yield the right-of-way to pedestrians within crosswalks or within nmarked crosswalks at intersections (1). From this it might be conclded that signal control is never needed becase motorists shold stop whenever a pedestrian crosses within a crosswalk. However, the reality of the sitation is that motorists do not always yield to pedestrians for a variety of reasons. Hence, there is a need for signal warrants at pedestrian crossings, particlarly when the pedestrians are school-age children. A procedre for establishing school crossings is crrently addressed in the Manal on Uniform Traffic Control Devices (MUTCD), Traffic Signal Warrant 4-School Crossing (2). In particlar, the manal sggests that a signal may be warranted when "the nmber of adeqate gaps in the traffic stream, dring the period when the children are sing the crossing, is less than the nmber of mintes in the same period (2,p.4C-5). " The intent of this warrant is to limit the time a child mst wait to cross to less than 6 sec. This maximm has been established becase stdies have shown that pedestrians will become impatient after waiting 3 sec to cross and will edge ot into the roadway after 4 sec (3-6). The application of this warrant reqires the condct of a traffic engineering stdy to determine the dration of an "adeqate" gap and the availability of these gaps in the vehiclar traffic stream. Althogh this type of stdy is simple to condct, it has the drawback of consming both time and resorces. Another drawback of this warrant is that it considers only the delay to pedestrians, which is not necessarily the safest or best operation of the crossing. For example, at those crossings pedestrian flows are characterized by high volme and random arrivals, it is entirely likely that motorists (stopped

2 24 TRANSPORTATION RESEARCH RECORD 1244 for pedestrians) will experience near 1 percent stopping and high delays and will often be seen exhibiting the same impatient attitdes that are displayed by pedestrians waiting for gaps in vehiclar traffic. This sitation often precipitates nsafe actions, sch as motorists "weaving" throgh the pedestrian streams, diverting onto nearby streets, and disregarding the basic rles of vehiclar and pedestrian right-of-way at intersections. Other drawbacks of the MUTCD school crossing warrant and its application inclde the following: It does not have a minimm pedestrian flow rate below which signal control shold not be considered. As a reslt, it cold take only one school-age pedestrian wanting to cross a " _ JHdJUl illltlldl LU "-'' Wd.lldlll - _; 1;,..J ----=-- d. MblJi:lUL.C::U \.,lu;:'):")hlb The procedre for determining adeqate gap size does not reflect the distribtion of the arriving pedestrian flow bt, rather, the size of the pedestrian grop accepting a gap provided by the vehiclar stream. Hence, the gap size stdy is affected by the distribtion of vehiclar gaps and, as a reslt, is biased toward higher grop sizes. The procedre does not identify a minimm period or dration dring which the pedestrian flow rate wold eqal or exceed the minimm rate. Each of these drawbacks has been considered for this paper and will be discssed in the following sections. Determining the Need for School Crossing Control The procedre for determining the dration of an "adeqate" gap and the freqency of its occrrence was originally described in an Institte of Transportation Engineers (ITE) pblication (3). The procedre has since been reprodced in the Transportation and Traffic Engineering Handbook (7). This procedre is based on field srvey techniqes in which the size of the pedestrian grops crossing the roadway and the dration of the gaps between vehicles traveling on the roadway are recorded for a common interval of time. Obviosly, this interval is associated with the periods before and after school when children are crossing the roadway. The adeqate gap time is calclated by sing the following formla: G = R + (WIS) + K * (N - 1) (1) G = adeqate gap time (sec), R = pedestrian perception and reaction time (sec) (assmed to be 3. sec), W = crb-to-crb width of the street crossed (ft) S = walking speed of child (ft/sec) (assmed to be 3.5 ft/sec), K = time between sccessive rows (sec/row) (assmed to be 2. sec/row), N = nmber of rows in the 85th percentile pedestrian grop size ronded p to the next integer vale { = integer[(q85/n) + l]}, Q85 85th percentile pedestrian grop size observed dring the field srvey, (pedestrians/grop), and n nmber of pedestrians in each "row" crossing the street (assmed to be five pedestrians per row). This stdy wold be condcted dring a normal school day dring the heaviest period of pedestrian crossing activity. Once the dration of the adeqate time gap is known, the nmber of gaps of eqal or greater size in the vehiclar traffic stream is determined and compared with the nmber of mintes that transpired dring the period of pedestrian activity. If the nmber of adeqate gaps is fewer than the nmber of mintes (implying an average wait of more than 6 sec), then a signal may be installed to artificially create the necessary gaps. Basis for Proposed Procedre n ;_; ; ;...._; J 1"t<.:g11t Illg lilt llllllldllull Ul Lilt l,;ulltlll µ1<.:tuu1t, it µ1posed procedre was formlated that cold be sed to determine the pedestrian and vehiclar volme conditions that wold reqire some type of control to improve safety and minimize delay. The proposed procedre for determining the need for school crossing control is based on and intended to spplement the existing warrant criteria. It is offered as a tool to simplify the evalation of MUTCD's signal warrant criteria for school crossings; it also addresses some of the drawbacks of the ITE field stdy procedre. The proposed procedre is based on the following assmptions: Both pedestrian and vehiclar flows are random processes. The assmed vales sed in Eqation 1 are reasonable. The average wait of 6 sec describes the threshold of pedestrian patience. If these assmptions do not hold or if the sitation reqires special consideration for other reasons, then the ITE field stdy procedre shold be sed. The development of the proposed new procedre is described in the next section. DEVELOPMENT OF THE PROPOSED PROCEDURE The proposed prol:edre is direded toward the development of a series of graphs that relate traffic volme, pedestrian volme, and the type of control needed. The graphs are similar to those sed for MUTCD Signal Warrant 11-Peak Hor Volme-in that the volme levels are assigned to the horizontal and vertical axes and the recommended control is identified by a region within the graph. The intent of this procedre is to avoid the need for a field stdy to determine the adeqate gap size or the freqency of its occrrence. The steps in the procedre's development are described in the following sections. Determination of Adeqate Gap The procedre for determining the adeqate gap (Eqation 1) was sed withot modification, recognizing that some of the assmed vales may not be niversally accepted. In particlar, it has been sggested by some that. the reaction time be less than 3. sec (6,8). In addition, it has been sggested that the width of the street be redced by the width of the far-side crb parking lane (9). It has also been implied that all pedestrians will cross as a single row (i.e., N = 1) regardless of

3 Bonneson and Blaschke the pedestrian volme (6,8-1). These deviations are recognized here only for completeness; the vales recommended else (7) are sed for this analysis. By sing the assmed vales stated in Eqation 1, the size of adeqate gap was calclated by sing the following eqation: G = 3. + (W/3.5) + 2. * (N - 1) (2) G = adeqate gap time (sec) N = integer[(q85'/5) + 1), Q85' = estimated 85th percentile pedestrian grop size, (q*t) + k * (q*t) S q = pedestrian flow rate averaged over 15 or more mintes (pedestrians/second) t = time interval between acceptable gaps (sec) (eqal to 6 sec or 1 gap/min), k = nmber of standard deviations the 85th percentile volme is away from the mean volme (assmed to be 1.), and (q*t) 5 = standard deviation of the Poisson distribtion. Using the above assmed vales, the nmber of rows of pedestrians (N) that wish to cross each minte can be calclated as N = integer [ (q*6) + (q*6) 5 J (3) By sing Eqations 2 and 3, the size of the 85th percentile pedestrian grop size can be estimated given only the pedestrian flow rate and the width of the street to be crossed. Vales of the adeqate gap size ( G) have been calclated for varios roadway widths and are shown in Figre 1. This approach attempts to model grop size as a fnction of arriving demand and not as it wold be observed in a field stdy in which the distribtion of gaps in the vehiclar stream wold artificially "bnch" the pedestrian grops. What is typically measred by a stdy of pedestrian flow at the crosswalk is not the tre demand verss the time profile bt the maximm flow rate throgh a bottleneck. Based on this observation, it is sggested that the t,raditional stdy of demand at the crosswalk will likely yield an inflated estimate of the grop sizes of arriving pedestrians. The conseqences of overestimating pedestrian grop size wold be the exclsion of traffic gaps that are, in fact, sfficient for pedestrian se. Freqency of Adeqate Gaps The calclation of the freqency of adeqate gaps is based on the assmption of random arrivals. This assmption implies that the probability that any one gap is eqal to or greater than the adeqate gap ( G) is P(g G) = exp( - v * G) (4) G = adeqate gap time from Eqation 1 or 2 (sec), v = vehiclar flow rate averaged over 15 or more mintes (vehicles/second), and exp(x) = the base of the natral loge ( ) raised to the power x. From this relation, the nmber of adeqate gaps can be calclated by sing PG = [v*t * exp(-v * G)) I [l - exp(-v * G)] (5) PG = nmber of adeqate pedestrian gaps [gaps/interval (t)] (defined as one gap/interval), v = vehiclar flow rate averaged over 15 or more mintes (vehicles/second), I = time interval between acceptable gaps (sec) (eqal to 6 sec), and G = adeqate gap time from Eqation 1 or 2 (sec). 25 ::J.r. I/) ""' "O Cl) a. cu +' a::: 3:: G: c: 'L: +' I/) Cl) "'O Cl) a x 24' Street Width o 36' Street Width a 48' Street Width O 6' Street Width "---ill Adeqate Gap, seconds FIGURE 1 Adeqate gap verss pedestrian flow rate.

4 26 From Eqation 5, the maximm vehiclar flow rate can be calciated that wiii yidd nt: gap f adt:qalt: sizt: al an avt:rage of every 6 seconds. The relation sed in Eqation 5 is an extension of other gap relations that have been sed by other athors bt does not share their limitations. These other relations inclde PG PG v * t * exp( - v * G) (6 /G) * exp( - v * G) Eqations 5, 6, and 7 are compared in Figre 2. As shown in this figre, Eqation 6 is in close agreement with Eqation 5 nder high-volme conditions, bt it also implies that there is a maximm size to the gaps in the traffic stream. The problem with Eqation 6 is its failre to recognize the potential for more than one pedestrian grop to cross dring the longer traffic gaps. Additional insight into this problem is described else (1). Eqation 7 also appears to be in close agreement with Eqation 5 nder low-volme conditions. The discrepancy between these eqations appears in the higher volme range. Eqation 7 yields mch too conservative an estimate of the maximm vehiclar flow rate for small gap sizes. The problem with Eqation 7 is that it estimates the nmber of gaps that can occr in one minte (i.e., 6/G) rather that the actal nmber of gaps in traffic per minte (i.e., v*t). As a reslt, it nderestimates the nmber of gaps available for pedestrian se, particlarly for higher volme conditions. Based on the preceding discssion, Eqation 5 appears to agree with Eqations 6 and 7 nder specific volme conditions. The advantage of Eqation 5 is that it yields reasonable estimates over the entire range of volme conditions. In recognition of these benefits, Eqation 5 is sed in the development of the proposed procedre. By applying Figres 1 and 2, it is possible to determine the size of the adeqate gap reqired by pedestrians and whether or not gaps of this size are available in the existing vehiclar (6) (7) TRANSPOR TA TION RESEARCH RECORD 1244 stream. If the combination of existing vehiclar traffic and pedestrian gap length is so great as to fall above the solid line in Figre 2, then signal control is warranted. Interrption of Pedestrian Flow Occasionally the volme of pedestrians is so high that, once given the right-of-way, they do not relinqish it for a considerable time. This can reslt in lengthy delays for motorists and is the reverse of the problem jst described (i.e., pedestrians delayed by motorists). Motorists can, and shold be expected to, tolerate longer delays than pedestrians becase of the added protection of motorists from inclement weather and becase of the added danger to pedestrian3 standing along the roadside. However, a threshold level of pedestrian volme shold be determined in some artificial means of interrption (sch as a traffic signal or crossing gard) is necessary to allow a minimm nmber of vehicles to pass. The following discssion describes the calclation of sch a threshold. Based on the assmptions of random arrivals of pedestrians and that motorists will contine to yield as long as pedestrians are in the crosswalk, Eqation 5 is again sed to calclate the nmber of available gaps. However, this time the available gaps are in the pedestrian flow and they are entered by a standing qee of vehicles. The eqation sed is defined as follows: VG= NL* [q*t* exp( -q * a)]/[1 - exp( -q * b)] (8) VG = maximm nmber of adeqate vehiclar gaps (gaps/ hor), q = pedestrian flow rate averaged over 15 or more mintes (pedestrians/second), T = dration of pedestrian crossing activity (sec) (assmed to be 36 seconds), L. ' et: 15 :i: Li: L FIGURE 2 5 Trattic Signal Control Not warranted 1 Tratf io siqnal control Warranted - Arleqaie gap verss vehiclar flow rate Adeqate Gap, seconds -Eqation 5 - -Eqation Eqation

5 Bonneson and Blaschke a = minimm gap for one vehicle to cross (sec) r + (WIS), r = motorist perception and reaction time (sec) (assmed to be 2. seconds), W = crb-to-crb width of the street crossed (ft), S walking speed of child (ft/sec) (assmed to be 3.5 feet/second), b minimm headway between vehicles on a two-way, two-lane street (assmed to be 2.57 sec), and NL nmber of traffic lanes within street (assmed to be 2 for W < 4 ft and 4 for 4 < W < 65 ft). Recognizing that this represents the maximm nmber of vehicles that can cross throgh a pedestrian flow (i.e., vehiclar capacity), a lower vale was selected that reflected a more stable, nominal delay condition. Conslting the Highway Capacity Manal's level-of-service descriptions for nsignalized intersections, it was fond that a reserve capacity of 1 to 199 vehicles per hor per lane (vphpl) described a condition of "long traffic delays" (11). This was denoted as level-ofservice "D." Based on this description, it was determined that the vehiclar capacity calclated from Eqation 8 shold be redced by 1 vphpl. Ths, the threshold vales of pedestrian volme that wold still yield a level-of-service "D" condition for traffic were calclated as NG = VG - NL * 1 (9) The nmber of gaps available (NG) was frther adjsted to accont for an assmed 55/45 percent directional split in vehiclar demand. Minimm Pedestrian Flow Rate The reason for establishing minimm pedestrian and vehiclar flow rates is to avoid the indiscriminate installation of traffic signals. Installing and maintaining nwarranted signals will lead to intentional violation, increased hazard, and nnecessary delay. Frthermore, the cost of installing and maintaining nwarranted signals does not constitte an efficient se of limited safety fnds. Recognizing that minimm volme warrants are more often based on rational jdgment and experience rather than on theoretical analysis, a review of the literatre was condcted to determine if any formally adopted pedestrian volme warrants existed. One agency that has established sch warrants is the California Department of Transportation (COOT) (12). These warrants are reasonable and consistent with the intent of this paper. More importantly, they imply that there are minimm pedestrian and vehiclar volmes below which signal control is not necessary. In recognition of this general agreement, the minimm pedestrian flow rates developed for the proposed procedre are loosely based on CDOT warrants for school crossing traffic signals. In general, it is recommended that the minimm pedestrian flow rate be established at 1 per hor. This minimm may be redced to 5 pedestrians per hor if 1. A crossing is being considered at a location the nearest existing traffic signal, controlled crossing, or pedestrian overpass is over 3 ft away, or 2. The crossing is in an area adeqate and safe sidewalks are not available to and from the location with the existing signal, crossing, or overpass. In addition, it is sggested that a minimm of 5 pedestrians se the crossing dring an average day. If tbe crossing is in a rral area or when the 85th percentile speed exceeds 4 mph, then 7 percent of the above minimms shold be sed. The period of analysis shold correspond to the period of peak pedestrian demand. However, the minimm period of analysis is a 15-minte interval (even if the dration of pedestrian demand is shorter). The vehiclar and pedestrian flow conditions mst occr dring the same peak period and mst be representative of the average day. The intent of these minimms is to eliminate the nnecessary installation of signalized pedestrian crossings. This is not to sggest that pedestrian flow rates less than these minimms do not need traffic signal control bt only that other forms of control or transport (of the stdents across the street) shold be considered. Combination of Pedestrian and Vehiclar Demand As discssed at the beginning of this section, the goal was to develop a graph with the pedestrian and vehiclar flow rates on horizontal and vertical axes, respectively. The approach jst described accomplishes this goal. Frthermore, this approach incorporates the determination of adeqate gap size for pedestrian flow rates and, thereby, eliminates the need to condct the ITE field stdy procedre. This procedre also considers the possible need for interrption of pedestrian flows to maintain reasonable vehiclar operation. All variables were eliminated in the derivation of this procedre except the width of the cross street (W). As a reslt, a series of graphs were constrcted for selected street widths. These graphs are shown in Figres 3, 4, 5, and 6 for street widths of 24, 36, 48, and 6 ft, respectively. There are essentially three determinations (identified by regions) that can be made from these graphs based on the known vehiclar and pedestrian flow rates: 1. Pedestrian and vehiclar demands are sfficiently light that no control is necessary. 2. Pedestrian demand is heavy and vehiclar demand is light (or vice versa) and therefore some type of control is necessary to interrpt pedestrians to maintain a minimal level of vehiclar service. The control considered may inclde a crossing gard or a traffic signal. 3. Both pedestrian and vehiclar demands are sfficiently heavy that a traffic signal may be needed to separate the two conflicting flows. Each of these regions is identified on the graphs appropriate. The left-most vertical bondary represents a minimm flow rate of 1 pedestrians per hor. This bondary shold be shifted left if a lower minimm flow rate is selected. Validation of Proposed Procedre Becase of a limited amont of field data, pedestrian crossing activity was compter simlated for the prpose of validating 27

6 28 TRANSPORTATION RESEARCH RECORD :::J '--.. a::: Li: :::J iii C"....:IVV - No control needed. <a) - consider crossing gard or traffic signal to reglate pedestrians - Traffic signal control warranted r '=t--r---r , Pedestrian Flow Rate, peds/hor FIGURE 3 Pedestrian verss vehiclar flow rate: 24-ft street width. 3 :::J '--.. a::: Li: :::J Ci) - No control naaded. - Consider cro ing gard or traffic signal to reglate pedestrians. - Traffic oiqnal control warranted FIGURE , , r=""'-r-.---, r.----j Pedestrian Flow Rate, peds/hor Pedestrian verss vehiclar flow rate: 36-ft street width. the proposed procedre. In particlar, that portion of the procedre that theoretically determines the adeqate gap size and the freqency of these gaps was compared with simlation reslts for similar demand conditions. Before the reslts are discssed, it will be helpfl to recall the objective of the ITE field stdy procedre (and the procedre proposed in this paper). This objective is to limit the time pedestrians mst wait for an adeqate gap. In an attempt to satisfy this objective, ITE proposed two field stdies that are intended to ensre that 85 percent of all pedestrians can find an adeqate gap in less than 1 minte, on average. Ths, in an indirect manner, the ITE procedre attempts to limit the day experience by 85 pe1ceni f the peestrians L less than 6 seconds. It is this delay criterion that was sed in the simlation reslts for comparative prposes. The reslts of the simlation are shown in Figre 7. As allded to in the previos paragraph, the simlation data reflect the threshold combination of demands that wold case 85 percent of all pedestrians to experience delays of 6 seconds or less. In general, the ITE and proposed procedres appear to yield reslts that are consistent with the delay criterion, which is not srprising since they were both formlated to do jst that. In smmary, these simlation reslts indicate that the proposed procedre can predict demand combinations that yield pedestrian delays of abot 6 seconds or less; which is cnsistenl wilh the prcere's ngmai bjeclive.

7 Bonneson and Blaschke i::..i::. " 2 i a:: 15 G:: '- 1.Q ::I c 5 CD Pedestrian 8 Flow <!) - No control needed.. - Consider crossing qard or traffic siqnal to reglate pedestrians - Traffic signal control warranted. 1 ' I Rate, peds/ hor FIGURE 5 Pedestrian verss vehiclar flow rate: 48-ft street width i::..i::. " 2..., a:: 15 G:: '- 1 :; c 5 Ci) - No control needed. - Consider oroa1ing gard or traffic siqnal to reqlate pedestrians G) - Trarric siqnal control warranted. O +-CD, "'----.-:=-r """"T""---r r--""""T"" Pedestrian Flow Rate, peds/hor FIGURE 6 Pedestrian verss vehiclar flow rate: 6-ft street width. PROPOSED PROCEDURE The following procedre is sggested for determining the need for traffic control at school crossings. It is intended as a sbstitte for the ITE field stdy procedre (3) and shold be sed only when the assmption,s stated in the Statement of Problem section are valid. In any case, engineering jdgment mst be sed to ltimately determine the need and type of traffic control to se at any school crossing. The first step is to determine the period and dration of highest pedestrian activity (the minimm dration is 15 mintes) at the crossing of interest. This dration shold be no longer than the period of pedestrian demand. Typical drations range from 3 mintes to 2 hors. The second step is to determine the total daily pedestrian demand for the same crossing. If the minimm pedestrian flow rate and volme levels can be satisfied, then the analysis can proceed. The third step is to identify the traffic volme that occrs dring the same period previosly identified (i.e., the period of highest pedestrian demand). Then, convert both the pedestrian and vehiclar volmes to horly flow rates and conslt the figre (i.e., Figres 3-6) that most closely relates to the width of the roadway being crossed.

8 3 TRANSPORTATION RESEARCH RECORD 1244 I... :J.s::..s::. " , q) :: 15 G:: I... 1 I ----==- :; -1 '.E 5 -- Proposed Procedre -+- Simlation , r , t FIGURE 7 Procedre verss simlation reslts. Pedestrian Flow Rote, peds/hor The last step is to find the combination of flow rates intersect on the appropriate figre and determine the sggested traffic control for that location. Other Considerations Althogh this procedre is based on the assmption of random arrivals in the vehiclar stream, this procedre can still be applied to streets with platooned arrivals. In general, platooned flows have longer, althogh less freqent, gaps for pedestrians to se. In most instances, these flows reslt in more opportnities for pedestrians to cross than wold be sggested by an analysis based on random arrivals (9). As a reslt, the proposed procedre can also be sed to determine traffic control needs on streets with vehiclar progressionas long as it is recognized that the analysis is conservative. Becase the assmption of random arrivals is conservative, field stdies are not necessary when the procedre indicates that no control is needed. Similarly, high vehiclar an<;! pedestrian volme combinations that fall well within the warrant region (i.e., region 3) wold not jstify a field stdy regardless of arrival distribtion. The only time a field stdy shold be considered is when the volme combinations jst satisfy the proposed warrant for traffic control (based on an inadeqate nmber of gaps) and it is known that the traffic stream has platooned arrivals. Under these circmstances, it is possible that an adeqate nmber of traffic gaps are available in the platooned arrivals and that control is still not needed. At locations traffic signals exist within 3 ft along the street to be crossed, the relocation of the pedestrian crossing to the existing traffic signal shold be considered before a pedestrian crossing is installed. If a traffic signal is recommended by this procedre, locating the signal at the nearest nsignalized intersection is preferred over a midblock location. CONCLUSIONS The prpose of this paper was to develop a procedre for selecting traffic signal control at school crossings. This procedre was developed to spplement and extend the procedre recommended by the MUTCD-Traffic Signal Warrant No. 4. Extensions to the MUTCD procedre inclde (a) the minimm daily pedestrian volme and flow rate criteria, and (b) a procedre for determining when pedestrian volmes are so high that they mst be reglated to improve traffic flow. The procedre presented in this paper is based on the crrent MUTCD warrant criteria for traffic control at school crossings. The ITE procedre sed in evalating this warrant reqires field stdies of pedestrian demand and traffic gap distribtion, both of which can be time-consming and expensive to condct. In contrast, the proposed procedre eliminates the need for these complex field stdies by sing a probabilistic approach based on reasonable assmptions of vehiclar and pedestrian arrival distribtions. By sing this procedre as a screening tool, local jrisdictions will be able to evalate proposed school crossings in the office and eliminate those that wold not satisfy the MUTCD warrant. This will enable jrisdictions to more efficiently allocate limited resorces to other safety improvement programs by redcing the need for field stdy to jst the "borderline" cases. This paper has described the theoretical basis of the proposed procedre. Unfortnately, field verification and comparative assessment with the ITE procedre are beyond the scope of this paper. However, limited se with the proposed

9 Bonneson and Blaschke procedre combined with simlation reslts, indicate that the procedre will consistently yield reslts that limit pedestrian delays. REFERENCES 1. Uniform Vehicle Code and Model Traffic Ordinance. National Committee On Uniform Traffic Laws and Ordinances, Washington, D.C., Manal on Uniform Traffic Control Devices. FHWA, U.S. Departll)ent of Transportation, A Program for School Crossing Protection. Institte of Transportation Engineers, Washington, D.C., P. C. Box and Associates. Assembly, Analysis and Application of Data Warrants for Traffic Control Signals. National Joint Committee on Uniform Traffic Control Devices, FHWA, U.S. Department of Transportation, March G. F. King. Pedestrian Delay and Pedestrian Signal Warrants. In Transportation Research Record 629, TRB, National Research Concil, Washington, D.C., 1977, pp S. A. Massey. Mathematical Determination of Warrant for Pedestrian Cro ing. Traffic E11gi11eeri11g, Sept pp Institte of Transportation Engineers. Transpor1ati'.o11 and Traffic Engineering Handbook, 2nd ed. Prentice-Hall, Inc., Englewood Cliffs, N.J. 1982, pp R. T. Underwood, in D. L. Gerlogh and M. J. Hber. In Special Report 165, Traffic Flow Theory-A Monograph. TRB, National Research Concil, Washington, D.C., 1975, p JHK and Associates. Gap-Based Criteria For Traffic Signal Warrants. FHWA, U.S. Department of Transportation, Feb D. L. Gerlogh and F.. Barne. Poisson and Other Distribtions in Traffic. ENO Fondation, agatck, Conn., Special Report 29: Highway Capacity Manal. TRB, National Research Concil, Washington, D.C., School Area Pedestrian Safety. In Traffic Manal, Chapter 1. California Department of Transportation, Sacramento, Calif., Pblication of this paper sponsored by Committee on Traffic Control Devices. 31