THE LATENT DEMAND METHOD Bruce W. Ladis, Russell M. Otteberg, Vekat R. Vattikuti SCI, Ic., 18115 U.S. Highway 41North, Suite 600, Lutz, FL 33549, USA Email: bladis@sciworld.et Travel patters i a metropolita area are well described by Newto s law of uiversal gravitatio as applied to trip iterchages, which is show i Figure 1. This relatioship essetially reflects that the umber of trips, regardless of travel mode, betwee two areas is directly related to the umber of trip productios (e.g. populatio resideces) i oe area ad the umber of trip attractios (eg., workplaces, shoppig opportuities, schools, etc.) i the other (destiatio) area. The relatioship also shows that impedaces (e.g., travel distace ad/or time betwee the areas, coditios of the travel eviromet, etc.) play a sigificat role i reducig the amout of trips made betwee those areas. Bicyclig activity patters ca be described by a similar relatioship, see Figure 2. However, ulike those for the automobile travel mode, the impedaces to the bicyclig mode play a greater role. For example, the distace betwee trip origis ad destiatios affects bicyclig more dramatically tha it does for automobile travel. Additioally, the coditio of the bicyclig eviromet affects whether a bicyclig trip is made ad how far, ad what route, a perso is willig to travel (see Figure 3). Furthermore, depedig o the purpose of the bicycle trip, the carryig, or payload capacity plays a role i ot oly the bicycle travel distaces but also whether or ot a bicyclig trip is eve made (Seasoal ad evirometal factors also affect travel distaces, but i a aalysis of roadways withi the same regio, they are ot a factor uless they vary withi the regio). Impedaces are differet for differet trip purposes. For example, people are typically willig to bicycle a greater distace to work tha they are to simply pick up a coveiece item at a eighborhood store. This pheomeo is reflected i atioal survey data, as depicted for three trip purposes i Figure 4. Essetially, the trip makig probability varies accordig to the distace betwee origis ad destiatios, ad it also depeds o the purpose of the trip. The Latet Demad Method accouts for the above outlied characteristics of bicycle travel i a metropolita area. While it is ot a full ad rigorous four-step travel demad model, it icludes the trip iterchage relatioship i a gravity model trip distributio aalysis but is coducted with a segmet-based focus. It models trips accordig to the four geeral utilitaria trip purposes idetified i the Uited States Natioal Persoal Trasportatio Survey (NPTS) show i Figure 5. The Latet Demad Method is a aalysis of the etire regio, usig a corridor-based, geographic iformatio system (GIS) algorithm to quatify relative potetial bicycle trip activity.
The Latet Demad Method Page 2 Ladis, Otteberg ad Vattikuti The Latet Demad Method is a effective aalysis tool for assessig bicycle travel demad. It: Icludes all potetial trip geerators ad attractors Quatifies the potetial trip iterchage betwee geerators ad attractors Recogizes that differet trip types accout for differig shares of the total trips Estimates the trip makig probability of each trip type as a fuctio of distace, ad Ca be employed to assess the latet demad for ay metropolita roadway etwork As previously outlied, the impedaces to bicyclig as a trasportatio mode play a large role i the probability of a bicycle trip occurrig. Oe of the sigificat impedaces, the effect of motor vehicle traffic, is assumed ot to exist for the purpose of calculatig o-liked, or latet trips. This assumptio is based o the premise that if motor vehicle traffic was ot preset, the latet bicycle trips would become revealed trips. Latet bicycle travel activity is directly related to the frequecy, magitude, ad proximity of trip geerators ad attractors to a roadway segmet. Figure 6 is a stylized represetatio of the potetial trip activity aroud a work trip attractor, such as a office complex. The itesity of the shadig o the surroudig street etwork graphically depicts the relative trip activity give that the trips are comig from all directios ad that there is o vehicular traffic o the streets. Figures 7 ad 8 are stylized represetatios of this effect aroud attractors for social/ recreatioal trips ad school trips, respectively. The Latet Demad Method process takes these sapshots of the potetial trip activity for all attractors ad geerators throughout the metropolita area ad essetially assembles them ito a composite, as depicted i Figure 9. The itesity of the shadig of the streets withi this figure depicts the total relative potetial bicycle trip activity surroudig the geerators ad attractors. The street segmets with the more itese areas of shadig represet the corridor areas with the highest potetial bicycle trip activity. Figure 10 shows the basic mathematical expressio of this GIS-based regiowide model. Geerators, Attractors, ad Spatial Queries The first step i the process is to idetify the geerators ad attractors that represet the trip eds for the four geeral trip purposes. Geerators are the origi ed of the trip ad are represeted by every residece i the study area. Attractors are the destiatio ed ad are represeted by every busiess, school, park ad trail, ad social ad service establishmet. The geerators ad attractors form the foudatio of the bicycle travel demad calculatios that the Latet Demad method follows.
The Latet Demad Method Page 3 Ladis, Otteberg ad Vattikuti While the locatios of may of the geerators ad attractors are idividually idetified, particularly for the school ad social-recreatioal (parks) trip purposes, aggregated data is used for modelig the other trip purposes. For example, while the Latet Demad Method quatifies the trip geeratio of every residece for work trips, it does ot use the physical locatio of every residece withi the study area. Rather, the Method uses the aggregated populatio, as compiled i the Trasportatio Aalysis Zoe (TAZ) data from the regioal trasportatio plaig model. Likewise, the work trip ad work errad demad aalyses are based o TAZ employmet data. Oce the geerator ad attractor data has bee idetified ad geocoded or mapped ito the GIS eviromet, spatial queries are performed aroud the etwork road corridors. The spatial queries capture the data for the calculatio of potetial trip iterchage betwee origis ad destiatios withi various travel distace rages. The travel rages are established from atioal survey data as reported i the NPTS study ad vary accordig to trip purpose. Each travel rage represets a buffer, ad the buffers are the geographic limits of the spatial queries. As the spatial queries are performed, their results are used to populate a database. That database is the programmed to calculate the trips withi each buffer, per trip purpose. Oce all of the trips have bee calculated for each buffer aroud a road corridor, they are summed to determie the Corridor s Latet Demad. The road segmets, are used to represet a corridor area, or travel shed. The followig sectios documet, for each of the four trip purposes, the geerators ad attractors idetified, the mathematical relatioship betwee them, ad how the spatial queries are performed. Work (Wk.) Trips The geerators ad attractors used to estimate the potetial trip activity for this trip type are the TAZs populatio desity ad TAZ total employmet, respectively. The followig equatio shows the computatioal form of the spatial queries. Where: Q Wk = P d d= 1 z= 1 E z ρz E z (1) Q Wk = Total trip iterchage potetial for work trips d = Spatial query buffer = Total umber of buffers P = Effect of travel distace o trip iterchage, expressed as a probability (see Figure 4)
The Latet Demad Method Page 4 Ladis, Otteberg ad Vattikuti z = E = r = TAZ adjacet to roadway segmet Total employmet withi buffer Populatio withi buffer Restrictio: ρ 1 E zz (1a) Figure 11a depicts the three spatial queries performed for work trips. The queries are segmet-based which meas that the queries/buffers are cetered o the idividual road segmets. The buffer width of each query for this trip type (ad ideed all of the trip types) is based o the bicycle trip distaces reported i the NPTS study. While trips to colleges ad uiversities might be cosidered as school trips, they are modeled as work trips due to the similarity of their trip characteristics with work trips (primarily trip legth ad regularity). Furthermore, the geerator for trips to colleges ad uiversities is the same as that for work trips - populatio. The attractors are the colleges ad uiversity locatios. Their idividual full-time erollmets (FTE s) are used i the calculatio of the trip iterchage. Equatio 2 mathematically describes how this trip iterchage is calculated ad how the spatial queries accout for this iformatio. Q C&U = Pd ( FTE) d= 1 A = 1 ρz S FTE (2) Where: Q C&U = Total trip iterchage potetial for college ad uiversity trips d = Spatial query buffer = Total umber of buffers P = Effect of travel distace o trip iterchage, expressed as a probability (see Figure 5) A = Number of attractors FTE = Full-time erollmet of college or uiversity S = Percet of segmet withi TAZ r= Populatio withi TAZ Restrictio: ρ z 1 FTE (2a) The spatial queries for college/uiversity trips are performed differetly from the other work trips. The essetial differece is that the spatial queries for colleges ad
The Latet Demad Method Page 5 Ladis, Otteberg ad Vattikuti uiversities are attractor-based rather tha segmet-based. This meas that the spatial queries are cetered o the idividual colleges ad uiversities (see Figure 11b), rather tha the corridor. As Figure 11b illustrates, the percet of the corridor fallig withi each buffer is used to ormalize the corridor s trip iterchage potetial. Shoppig ad Errads (SE) Trips. As with the work trip, the geerator for shoppig ad errad trips is populatio. The attractor is total employmet per TAZ. The Latet Demad Method further subdivides this trip type ito two categories of shoppig ad errad trips. The first is work-based errads, or those made by, ad betwee, places of employmet. For example, a perso who picks up his/her dry cleaig durig luchtime is performig a work-based errad. The secod category is home-based errads. A example of a home-based errad is a perso goig from their residece to a eighborhood store for a carto of milk or video retal. Equatio 3 is the mathematical expressio that quatifies these two categories of shoppig ad errad trips. Q SE = Pd ( Ez + ρz) d= 1 z= 1 (3) Where: Q SE = Total trip iterchage potetial for the shoppig ad errad trips d = Spatial query buffer = Total umber of buffers P = Effect of travel distace o trip iterchage, expressed as a probability (see Figure 5) z = TAZ adjacet to roadway segmet E = Total employmet r= Populatio withi buffer The spatial queries for the shoppig ad errad trips are segmet-based. Figure 12 graphically illustrates the two spatial queries performed for this trip type. School (Sc) Trips The locatios of elemetary, middle ad high schools are the attractors for this trip type. Sice studets livig withi a two-mile radius of a school are geerally ot eligible to use the school trasportatio system, they are cosidered potetial bicyclists. This two-mile radius costitutes a trasportatio exclusio zoe for which potetial bicycle trip activity is measured. Equatio 4 mathematically expresses the calculatio of potetial school trips. Average school erollmet for the etire school district is the base quatity used i determiig potetial trips.
The Latet Demad Method Page 6 Ladis, Otteberg ad Vattikuti Q Sc = Pd d= 1 A= 1 ( 2 ASE S) (4) Where: Q Sc = Total trip iterchage potetial for home-based school trips d = Spatial query buffer = Total umber of buffers or TAZ s P = Effect of travel distace o trip iterchage, expressed as a probability (see Figure 5) A = Number of attractors ASE = Average school erollmet S = Percet of road segmet withi buffer As with colleges ad uiversities, the spatial queries for this trip type are attractor-based. Figure 13 illustrates the two spatial queries performed for this trip type, ad how the percet of the road segmet fallig withi each buffer is likewise calculated. Recreatioal ad Social (RS) Trips Public parks, ad trails are the attractors used for the recreatioal ad social (RS) trip purpose demad assessmet. The total trips associated with these attractors are give i equatio 5, below. Q SRC ρz = Pd Tt + = d 1 T t (5) Where: Q SRC = Total trip iterchage potetial for social/recreatioal trips d = Spatial query buffer = Total umber of buffers or TAZ s P = Effect of travel distace o trip iterchage, expressed as a probability (see Figure 5) T t = Total umber of park trips (or Q parks ) + total umber of urba trail trips (or Q trails ) r= Populatio withi buffer As show above, T t is separated ito two categories of recreatioal / social trips: parks ad urba trails. The reaso for separatig urba trails from the parks ad trail-heads lies i how the spatial queries are performed. A urba trail is, i effect, a liear park. Therefore, the spatial query is performed outward from the trail to quatify the portio of the study segmet proximate to the trail. Thus, the spatial queries for urba trails are attractor-based, whereas the spatial queries for parks are segmet-based. The followig paragraphs documet the trip calculatios for each category.
The Latet Demad Method Page 7 Ladis, Otteberg ad Vattikuti Prior to performig spatial queries o parks ad trail-heads, the parks were stratified ito three categories; major parks, staffed parks, ad mior parks. The reaso: the attractiveess of differet types of parks. For example, a park that has ball fields ad a swimmig pool geerally attracts more users tha a park of equal size with fewer ameities. Accordigly, the trip attractio for the former will be higher tha that for the latter. A defiitio of each park type alog with its associated trip geeratio follows: Major Parks (ad Trail Heads) these are characterized as parks that have regularly programmed evets ad large, staffed evets. Trip geeratio = 3,058 trips. [This is based o a average major park size of 309.41 acres multiplied by a trip geeratio rate of 2.28 trips per acre.] Staffed Parks these typically have itermittetly programmed evets ad staffed evets. Trip geeratio = 375 trips [This is based o a average staffed park size of 82.97 acres multiplied by a trip geeratio rate of 4.57 trips per acre.] Mior parks these geerally do ot have programmed evets or do they have staffed evets. Trip geeratio = 28 trips [This is based o a average mior park size of 17.46 acres multiplied by a trip geeratio rate of 1.59 trips per acre.] Due to their trip attractio potetial, trail-heads are cosidered major parks, ad are assiged the same trip geeratio. The quatificatio of trip iterchage for parks ad trail heads is show i Equatio 5a, below. Q parks = 4 c= 1 A= 1 A TG (5a) Where: Q Parks = Total trip iterchage potetial for park ad trail head trips c = Categories of parks A= Number of attractors = Total umber of buffers TG = Trip geeratio rate Figure 14a is a graphic represetatio of the segmet-based spatial queries used for the park ad trail head latet demad aalysis. As previously described, quatificatio of the travel demad associated with trails has bee separated from parks due to the fact that the spatial queries are attractor-based, or more appropriately cetered o the trail itself. The geerator used i the trip iterchage calculatio for this category is oce agai the populatio surroudig the subject road segmet. The trip geeratio used for the calculatio is 375 trips (same as staffed park).
The Latet Demad Method Page 8 Ladis, Otteberg ad Vattikuti Equatio (5b) represets the calculatio of potetial trip activity for trails: Q trails = S TG = A 1 (5b) Where: Q trails = Total trip iterchage potetial for trail trips A = Number of attractors = Total umber of buffers S = Percet of segmet withi buffer TG = Trip geeratio rate Figure 14b depicts the two spatial queries performed for this trip purpose, which are attractor-based. Puttig it Together: The Total of Potetial Bicycle Trips The sum of the idividual trip purposes for each roadway corridor, whe multiplied by its associated trip share from the NPTS study, is the Bicycle Latet Demad for that roadway corridor. The mathematical expressio for this is give by Equatio 6. LDS = 4 = 1 ( Q TTS ) (6) Q= Total umber of potetial bicycle trip iterchages calculated by spatial queries, per trip purpose = Bicycle trip purpose ( e.g., work, persoal/busiess, recreatio, school) TTS = Trip purpose share of all bicycle trips (calculated usig NPTS data)