A Coverage Model for Improving Public Transit System Accessibility and Expanding Access

Transcription

1 A Coverage Moel for Improving Public Transit System Accessibility an Expaning Access Alan T. Murray Department of Geography The Ohio State University Columbus, Ohio USA ( June 17, 2002

2 Abstract Accessible an efficient service are vital features of well utilize public transit systems. Moeling approaches to support the evaluation of transit operations for management an planning are essential for continue improvement. A hybri coverage moel is evelope in this paper for simultaneously expaning service access an increasing accessibility. This paper iscusses the use an integration of this moel in a geographic information system environment for strategic planning. Analysis is presente for public transit service in Brisbane, Australia. The structure moel provies flexibility in eveloping viable policies for aressing system improvements an service expansion, all of which are likely to promote increase utilization of public transit. Keywors Strategic analysis, bus stop spacing, spatial optimization, transit utilization Introuction Public transit continues to be seen as an important component of transportation planning in metropolitan regions. With increase emphasis on achieving sustainability an ecreasing congestion, public transit is put forth as the potential solution to many of the ails of urban regions an moern transportation systems. Spurring the potential of this moe of travel is the fact that in most cities in the Unite States, public transit is woefully uner utilize. A report by Charles River Associates (1997) inicates that only 7% of work trips in the 35 largest Unite States metropolitan regions are taken using public transportation. For a sample of cities in the Unite States, Newman an Kenworthy (1999) report that roughly 9% of work trips are mae on public transit. While these finings may be cause for concern, they also represent potential for alleviating traffic problems (congestion, environmental impacts, etc.) in urban areas because transit can accommoate greater travel eman. In aition, achieving transportation system improvements through increase utilization of public transit is likely to spawn economic growth, enhance quality of life an ecrease impacts on the environment. Significant attention is being place on strategic an operational analysis of public transportation systems in orer to make transit more esirable an to increase utilization. At the strategic level, planners an policy makers have focuse on expaning service to a larger percentage of the urbanize area. For example, in Columbus, Ohio the local transit 1

3 agency has mae increase service to newly populate areas a priority (Central Ohio Transit Authority 2001). In Brisbane, an other maor Australian cities, a strategic policy goal of proviing transit service to at least 90% of the population is stipulate in regional plans, where service is consiere suitable if coverage within 400 meters of a bus, rail or ferry stop exists (Queenslan Government 1997; Murray et al. 1998). The assumption is that expane service access will ultimately result in greater transit utilization. An operational level concern in transit planning focuses on the spatial efficiency of service coverage. Newman an Kenworthy (1999) conclue that it is only in cities with rail systems that marginal increases in public transit riership may be foun in the Unite States. The implication is that origin-estination travel times are influential in transit moe selection, so the ability to increase transit travel spees is essential if greater public transit utilization is to be achieve. For bus-base systems that ominate metropolitan regions in the Unite States, a number of solutions are possible, such as improve routing, express services, integrate hub-an-spoke systems, an minimizing the number of stops along routes. It is this last possibility that is of primary interest in this paper. Routes with fewer stops have faster travel spees as well as less associate operational costs (Wirasinghe an Ghoneim 1981; Levinson 1983; Furth an Rahbee 2000; Saka 2001). The above iscussion highlights that bus-oriente transit management an planning must aress both expaning service coverage an increase efficiency of routes. For an existing public transit system, ientifying inefficiencies will likely enable expane regional coverage to be provie through a reistribution of services. The task of planners an managers is being able to recognize that efficiencies can be achieve. Further, this must be one while simultaneously increasing transit service access. These are the unerlying challenges of public transit agencies hoping to serve a greater proportion of the regional population, as stipulate in the long term plans of cities like Brisbane (Queenslan Government 1997) an Columbus (Central Ohio Transit Authority 2001). However, public transit will not be successful unless travel spees are more competitive with private vehicles, hence the nee to remove system inefficiencies. If a regional goal is to increase public transit utilization, it is essential that service coverage reunancy be minimize (in orer to ecrease transit travel times) an new services be establishe in emergent population growth areas. Strategic planning to support this shoul facilitate appropriate policy evelopment as well as enable planners to assess an monitor the status of existing or propose transit systems. Moeling base approaches are neee for the analysis of this multi-obective problem. 2

4 This paper presents a moel for the strategic analysis of coverage reunancy an service expansion in a bus-base transit system. The next section provies the backgroun context an relate research in this area. Following this, moels for supporting the analysis of transit access an accessibility are reviewe. A hybri coverage moel for simultaneously aressing stop coverage reunancy an expane system access is then etaile. Application results for the pubic transit system in Brisbane, Australia are presente. The paper ens with concluing comments. Backgroun Access to an the accessibility of public transit have always been focal service issues. They are vague concepts, however, as they may be interprete an use in ifferent ways. Murray et al. (1998) iscusses access an accessibility in the context of public transportation. Access typically has to o with proximity to service an its cost, whereas accessibility relates to the suitability of the transit system to move people from where they boar to where they exit in a reasonable amount of time. Given this interpretation, both are important elements of service provision. One access consieration in potential use of public transit is the travel istance or time from one s resience (origin) to a bus stop. Another is the istance from an exiting bus stop to one s intene estination. Other consierations such as cost of service, safety in getting from origin to stop (or from stop to estination), barriers in travel to/from stop, etc. are also influential access factors. In this paper we limit our iscussion of access to origin travel to a bus stop an estination travel from a bus stop. Suitable access to public transit is typically characterize as a reasonable walk uner normal conitions. Survey results reporte in Demetsky an Lin (1982) inicate that most transit firms consier 400 meters an acceptable walking istance. In Columbus, Ohio it is stipulate that resiences not excee walking istances of 400 meters, or 800 meters in low ensity areas, to transit stops (Central Ohio Transit Authority 1999). In Brisbane, Australia the suitable access stanar is 400 meters (Queenslan Government 1997). Such stanars suggest the notion of coverage, where a given location (home, place of employment, school, shopping center, park, etc.) is suitably service by a stop if it is within the stipulate access istance. This assumes, of course, that service goes in the esire irection of travel an that service time is reasonable. Murray et al. (1998) inicate that regional transit service goals are typically evaluate base upon access from 3

5 resiences. An obvious reason for this is that census ata exists to support such analysis. While this may be a limite interpretation of access, it has an uneniable impact on potential use of transit. For this reason planners an managers seek to increase suitable access to transit as a means of bolstering riership. An interactive computerize system was evelope by Moellering et al. (1977) to support the placement of transit stops within a suitable access stanar of resiences. An alternative concern in transit planning is accessibility. As with access, accessibility also has varying interpretations. One feature of accessibility is the ability to get from an origin to a estination. Associate with this is travel time an number of require transfers. Another aspect of accessibility is regularity/frequency of service. Depening on the context in which it is being examine, there are a number of potential approaches for assessing accessibility (see Kwan 1998; O Sullivan et al. 2000). Given that the interest in this paper is enhancing public transit service in orer to increase utilization, we focus on the travel time/spee aspect of accessibility. Stop spacing optimization has receive consierable attention in transit planning (Wirasinghe an Ghoneim 1981; Furth an Rahbee 2000; Saka 2001). This component of operational planning has a irect impact on travel time/spee accessibility. Most urban regions have establishe stanars for the spacing of transit stops. Ammons (2001) states that stop spacing stanars of meters for bus systems are common. Demetsky an Lin (1982) inicate that stanars for spacing between stops in some urban regions are as high as 800 meters. In a stuy of transit travel times, Levinson (1983) conclue that performance coul/shoul be improve by keeping the number of stops to a minimum. Saka (2001) further notes that fewer stops an faster travel spees help to minimize transit fleet sizes, thereby ecreasing operational costs. Given this motivation, moeling approaches for etermining the optimal number of stops along a route continue to be explore. An alternative approach oriente towars the analysis of spatial coverage is the work of Murray (2001) an Gleason (1975). For a system that has evolve over time, an important form of strategic analysis is examining the egree to which reunancy or inefficiency in stop placement exists along service routes. Given two stops an k along a route, reunancy exists when one stop covers the same areas as the other stop, an possibly aitional areas. Coverage is base upon the establishe access stanar, typically 400 meters in the case of public transit. If the set of areas suitably covere by stops an k is represente by N an N k, respectively, then stop is consiere 4

6 reunant if N N. Murray (2001) inicates that coverage reunancy is likely to be k quite profoun in an existing transit system, because of the nature of urban growth an emergent transit services. Such reunancy ecreases travel spees an increases operational costs, as note in Saka (2001). The moel iscusse in Murray (2001) supports the strategic analysis of service coverage inefficiency, an stop spacing optimization along a route. This approach is equivalent to that utilize for siting express bus stops in Gleason (1975). The appealing feature of the spatial coverage focus is its corresponence to system access while optimizing regional accessibility. However, the approaches of Gleason (1975) an Murray (2001) are not capable of simultaneously aressing system inefficiency an service expansion, primary concerns of transit agencies an regional planners. Transit Service Analysis Although access an accessibility may be nebulous concepts, precise approaches exist for their evaluation as both are important components of public transit service. It is relatively straightforwar to etermine an evaluate transit service access, provie that the appropriate spatial information exists in a format amenable to analysis. This may be accomplishe by examining the proximity from locations of interest (homes, businesses, etc.) to transit stops. Regional planners an governing boies are often intereste in the proportion of the population covere by the existing (or propose) transit system. For this reason we limit our iscussion to population coverage, although the approach presente in this paper can reaily be extene to account for employment or other travel estinations. While concisely state, the assessment of access coverage is complicate by the practical realities of spatial information (Murray et al. 1998). Often ata is only available in an aggregate spatial format, such as census blocks in the Unite States. This means that proximity to stops must be interprete creatively. One way to approach this is by establishing a buffer aroun stops an interpolating the number of people in the buffers. Another way to evaluate access is to utilize the centroi of the block for assessing the istance from a block to bus stops. Both approaches raise a complicating issue of istance measurement. Shoul istance be measure using a Eucliean or rectilinear metric or the actual street network? Fortunately most commercial geographic information system (GIS) packages offer capabilities for carrying out assessment of access using any of these istance measures. This research utilizes the centroi-base approach an Eucliean istance in the evaluation of access. 5

7 A more complicate task in transit service analysis is evaluating accessibility. With respect to stop placement efficiency, a moeling approach is necessary to support such analysis. One approach is the location set covering problem (LSCP) utilize in Murray (2001), as well as Gleason (1975). First propose in Toregas et al. (1971), the LSCP may be formulate using the following notation: i i S N x i inex of areas provie suitable access; inex of transit stops; shortest istance between area i an stop ; service access istance stanar; { S}; i 1 if existing transit stop is to be inclue in system 0 otherwise. Location Set Covering Problem (LSCP) Minimize Subect to N i x x (1) x 1 i (2) (, ) 0 1 (3) The obective, (1), of the LSCP for public transit system analysis is to minimize the number of stops neee in the system. Constraints (2) ensure that each currently covere service area (neighborhoo, block, etc.) along a route or in the analysis region continues to be provie suitable service by the reuce number of selecte transit stops. Integer restrictions are impose in constraint (3), meaning that either a stop is kept in the system or it is remove. As a strategic approach for evaluating public transit service, the LSCP provies a measure of coverage efficiency in the current (or propose) placement of bus stops. For a region with low transit utilization, the LSCP applie to existing stops inicates the extent to which performance enhancements coul be achieve through improve accessibility (less stops along routes). As a result, it also establishes potential cost savings, if changes are mae. Murray (2001) utilize the LSCP in this context. Moel results may be use to 6

8 guie service improvements eeme to be most beneficial to increasing transit utilization an ecreasing costs. Operationally, this approach ientifies iniviual stops for removal in an existing system, ustifie on the basis of improving overall system performance. This is an all to important consieration when communicating with the public about altere transit services. One potential limitation of the LSCP is the requirement that all currently serve areas remain serve. It is reasonable to anticipate that some service areas woul no longer be viable ue to low riership an excessive operational costs. The maximal covering location problem (MCLP), propose in Church an ReVelle (1974), relaxes the requirement of continue service to all currently serve areas. The formulation of the MCLP will utilize the following aitional notation: a i p y i current / anticipate riership in area i; number of transit stops to select; 1 if area i has suitableaccess to a stop 0 otherwise. Maximal Coverage Location Problem (MCLP) Maximize Subect to N i i a (4) i y i x y i (5) i x y i x p (6) (, ) ( 0, ) i 0 1 (7) 1 The obective, (4), of the MCLP for public transit service analysis maximizes the total proportion of population (those currently affore suitable access) that will continue to receive service coverage. Constraint (5) accounts for whether service areas are covere by transit stops selecte to remain in the system. Constraint (6) specifies that p stops are to be selecte. Finally, constraints (7) impose integer restrictions on the ecision variables. 7

9 Whereas the LSCP requires service to presently covere areas, the MCLP can be utilize to ientify the most esirable areas for continue service. The MCLP represents an approach for structuring the best accessibility given limitations on the size of the transit system. The use of the MCLP enables cost reuctions beyon those ientifie using the LSCP to be foun, because given limite resources the MCLP will not provie coverage to areas not ustifiable for continue service. However, while this is an important strategic eneavor, it is likely that iscontinuing service to some areas is a political risk, particularly given the overriing goal of extening service provision. As a result, governing boies are not receptive to eliminating service to their constituents. Although the LSCP an MCLP eal with accessibility, neither aress the issue of expaning regional access to service. The reason for this is that both moels are limite to covering only those areas presently being serve. However, a maor planning obective is expane regional service as it is influential in the selection of public transit as a moe of travel. Of course this will only be meaningful if the associate route service is relatively fast. In orer to expan coverage, a vital consieration is potential bus stop locations from which it woul be possible to provie service to those areas not previously serve. Assuming that these potential stops are ientifie, an approach for aressing access expansion an improve accessibility woul be to apply the LSCP to existing coverage, then apply a similarly structure LSCP or MCLP to those areas without current coverage. This woul ientify a feasible solution (an an upper boun) to this problem, but it lacks integrate ecision making. The reason for this is that access expansion an accessibility improvement are being treate separately, without any coorination of siting ecisions. As a result of this lack of integration, too many stops woul be ientifie as being neee for the associate level of coverage. An improve approach woul be to exten the LSCP (or the MCLP) for aressing both access expansion an improve accessibility. Moeling Access an Accessibility in Transit Service Regional improvements in public transport require not only eliminating inefficiencies in existing services, but also extening coverage to reach a greater proportion of the total population. Both are expressly stipulate goals of public transit agencies an must be coorinate an integrate. 8

10 We begin by first presenting an extension to the LSCP for aressing increase access to transit an improve system performance. The following aitional notation will be utilize in the evelope coverage moel: l k ˆ y l ˆ x k inex of areas not serve by existing transit stops; inex of potential new transit stops; if previously unserve area l otherwise. otherwise. is provie suitableaccess to a stop if propose transit stop k is to be inclue in system Hybri Set Covering Problem (HSCP) Maximize Subect to N i k N l l a ˆ (8) l y l x 1 i (9) xˆ yˆ l (10) k l x + xˆ k p (11) k x ( 0, 1), y i (, 1) i ˆ ( 0, 1) k, ˆ ( 0, 1) l x k y l 0 (12) The obective, (8), of the HSCP is to maximize aitional regional service access provie by newly site public transit stops. Constraint (9) specifies that each currently serve area must continue to be provie access coverage by at least one transit stop. Note that N i inclues both existing an potential new stops. Constraint (10) accounts for aitional coverage provie by newly site transit stops. Constraint (11) specifies the number of transit stops (existing an new) to be selecte. There are implications for appropriate values of p if a feasible solution is to exist for the HSCP. The value of p must be no less than the number of stops necessary to provie continue coverage to currently service areas, as require in Constraint (9). The minimum value coul be foun using the LSCP as etaile above. It is worth noting that p may be increase until complete 9

11 coverage is achieve. Constraints (12) impose integer restrictions on the ecision variables. What is unique in the HSCP is that it ensures continue coverage to presently serve areas an minimizes necessary bus stops, as oes the LSCP, but it also selects new stops to establish for transit service base upon anticipate riership potential ( a l ). This accomplishes the stipulate goals of transit organizations to improve accessibility an expan service access. As a result, the HSCP an the LSCP (an MCLP) are completely ifferent spatial optimization moels, though relate structurally. Application Results The public transit system in the city of Brisbane, Australia will be the focus of the strategic analysis of access an accessibility presente in this paper. Brisbane City is a inepenent entity of the larger South East Queenslan region, with Brisbane City Council as the aministrative boy responsible for the provision of public transit within the city. Greater utilization of public transit in the South East Queenslan region is seen as critical because of experience, an further anticipate, rapi growth (Queenslan Government 1997). Presently, only some 7% of all trips in the region are mae using public transit, although Newman an Kenworthy (1999) inicate that transit garners a higher percentage of work trips (14.5%). The low moal share of transit suggests that enhancements are neee to increase utilization. The population of Brisbane City is 806,292, as reporte in the 1996 census. This region is comprise of 1538 collection istricts (the finest level of spatial etail in the Australian census hierarchy). The average collection istrict size is approximately km 2. Population is use as the measure of potential transit riership, a i. Although public transit in this region consists of bus, rail an ferry service, the bus system is the ominant service with 7543 stops. Given this, we focus only on bus service in this paper. As state previously, the transit access stanar is stipulate as 400 meters, with subsequent analysis inicating that roughly 86% of the regional population (1356 collection istricts) has suitable coverage. This means that 14% of people (182 collection istricts) in the region o not have suitable access to transit. In orer to consier expaning service to the remaining 182 collection istricts, it is necessary to ientify new potential bus stop locations. Consist with transit stop siting practices (Furth an Rahbee 2000), all street intersections are permitte as new bus stop locations. This prouces 11,776 sites for potentially locating new stops. Due to the spatial structure of the transportation system, 10

12 however, it is only possible to provie access coverage to 165 of the 182 collection istricts presently not serve. Thus, it is possible to serve approximately 13% of the region using the new 11,776 stops, which woul bring total suitable access to public transit in Brisbane City to almost 99% if all current an propose stops were utilize. The analysis in this paper was carrie out on a Pentium III/1000 personal computer running Winows NT (version 4.0) with 524 MB memory. ArcView version 3.2, a commercial geographic information system (GIS) package, was utilize to support the strategic analysis of the Brisbane City transit system. Specific GIS functionality, in aition to basic spatial information management an isplay, inclue spatial query, feature buffering, overlay, proximity evaluation, an etermining street intersections. In aition, an Avenue script, the ArcView interface language, was written to prouce the corresponing optimization problems in text file format. The generate problems are then solve externally to ArcView using ILOG CPLEX version 7.0. A result file is exporte from CPLEX an rea back into ArcView for subsequent isplay an analysis. For the LSCP applie to the Brisbane City transit system, Murray (2001) reporte that only 1 in 10 stops were actually neee to continue to provie suitable access, as stipulate by the 400 meter stanar. This inicates that there is a substantial amount of inefficiency in the current transit system an suggests that operational costs coul be reuce. Base upon the strategic analysis of the system, there woul appear to be room for improvement on a route by route basis as low system utilization (7% of all trips) is likely ue to slow travel times. This oes not, however, aress the goal to provie expane access to transit service. Extening the initial work of Murray (2001), the HSCP has been evelope an applie in this paper in orer to incorporate both access expansion an improve accessibility consierations in the analysis of the Brisbane transit system. The resulting moel requires 19,484 ecision variables an 1522 constraints. Application finings are summarize in Table 1 for a range of p values (number of existing an new stops). The first scenario of interest is where complete access coverage is provie to Brisbane. For 685 stops (p685) suitable access coverage to 98.88% of regional population is achieve using the HSCP. Associate access an stop selections/placement is shown in Figure 1. As iscusse previously, this is consiere complete coverage ue to the inability to cover 17 of the 1356 collection istricts not previously covere. Solving the HSCP require 48,259 iterations an 11,610 branches (680 secons) for p685. The 685 stops shown in Figure 1 correspon to 525 existing 11

13 stops an 160 new stops. It is worth pointing out that the 685 stops are best thought of as stop pairs, where a stop is locate on both sies of the street. Viewe as stop pairs, the total number of iniviual stops woul be 1370 (2 x 685), which still represents significantly fewer stops than the 7543 in the current system (less than 20%). The implications of the HSCP results are that substantial stop placement reunancy exists in the current transit system an that it is possible to achieve complete coverage with very little further investment. In fact, it is plausible that accommoating extene service woul not aversely impact accessibility. From a strategic perspective, these finings are important because they inicate to planners an policy makers where moifications shoul be focuse in orer to increase transit utilization. Further, this moeling approach may be use to establish an monitor aitional regional performance goals. Also of interest woul be the iea that access only be selectively extene, rather than cover the entire region. This is accomplishe using the HSCP by examining values of p<685, as presente in Table 1. Doing this ensures that all currently covere areas remain serve, but service to new areas is base upon the greatest anticipate riership. In the cases where p<685, computational effort increase substantially an branching was not successful in resolving optimality gaps. CPLEX terminate when it ran out of available memory ue to branching without resolution. As a result of the remaining gaps, it is not known whether complete coverage can actually be achieve with less than 685 stops. However, given the strategic nature of this analysis, the remaining gaps are not problematic as a ecrease of a few stops will not aversely impact the general implications of these finings. What is valuable is the coverage traeoff associate with varying the values of p. This is shown in Figure 2 for p in increments of 5. For example, for p650 there woul be 35 fewer stops (522 existing an 122 new stops), but nearly 98% of the population woul be provie suitable access. Given resource limitations, this scenario ientifies where service shoul be allocate in orer to provie aitional access to public transit. It was mentione that the analysis of access an accessibility coul be approache as two separate problems using the LSCP for currently covere areas an the LSCP or the MCLP applie to those areas without service. For comparison to the HSCP using p685, this woul correspon to the use of the LSCP for both covere an non-covere areas. The use of LSCP to the existing transit system an LSCP applie to the 165 areas without service inicates that 738 stops are necessary (588 existing stops an 150 new stops). However, using the HSCP it was foun that only 685 stops is actually neee for an equivalent level of service coverage. This means that nearly 8% more stops woul be 12

14 ientifie if the HSCP were not use. The HSCP ientifies a more integrate system, an as a result nees fewer total stops to provie the same level of access. Further, with fewer overall stops, it woul be expecte that travel times woul be faster, something that is likely to bolster transit utilization. Conclusions Access an accessibility are important components in the provision of public transit services. In orer to increase future utilization, transit agencies nee to re-evaluate current an planne services using strategic approaches such as those etaile in this paper. Through such analysis, service inefficiencies may be ientifie an emerging growth areas may be targete for future services. The hybri set cover problem (HSCP) was propose for supporting the analysis of both access an accessibility in public transit service. The HSCP was utilize to examine the public transit system in the city of Brisbane, Australia. The strategic analysis suggeste that significant efficiency gains are possible for improving accessibility, even while extening service access. In fact, it seems reasonable to provie suitable access to nearly the entire region, provie that accessibility is enhance through eliminating an relocating stops. This woul excee current stanars targeting only 90% of the regional population. While it is possible to view this problem as two separate LSCPs, one for existing stops an the other for potential new stops, oing so woul result in an inferior solution requiring 8% more total stops than the number ientifie using the HSCP. The ability to view this problem in an integrate way using the HSCP is clearly an important an valuable strategic approach. From a computational stanpoint, the application results were both encouraging an iscouraging. For the strategic analysis conucte in this research, the optimality gaps in solving the HSCP using CPLEX were not problematic. Informe planning an policy formulation is achieve using the above finings. However, resulting gaps might not be acceptable in other applications or for larger problem instances. There is clearly a nee for further research exploring alternative approaches for solving this problem. It is conceivable that recently evelope solution techniques for the LSCP an MCLP (Caprara et al. 1999; Galvao et al. 2000) may be successfully extene to solve the HSCP. Acknowlegements 13

15 This research was supporte in part by a see grant from Center for Urban an Regional Analysis at The Ohio State University. Preliminary analysis was initiate through a grant from the Australian Research Council while the author was a research fellow at the University of Queenslan in the Department of Geographical Sciences an Planning. References Ammons, D.N. (2001). Municipal Benchmarks: Assessing Local Performance an Establishing Community Stanars, secon eition (Thousan Oaks: Sage). Caprara, A., Fischetti, M. an Toth, P. (1999). A heuristic metho for the set covering problem. Operations Research 47, Central Ohio Transit Authority (1999). Planning an Development Guielines for Public Transit (Columbus: COTA). Central Ohio Transit Authority (2001). The new an improve COTA: a summary. May (accesse August 1, 2001). Charles River Associates (1997). Builing transit riership: an exploration of transit's market share an the public policies that influence it. Transit Cooperative Research Program, Report 27 (Washington, D.C.: National Acaemy Press). Church, R. an ReVelle, C. (1974). The maximal covering location problem. Papers of the Regional Science Association 32, Demetsky, M.J. an Lin, B. (1982). Bus stop location an esign. Transportation Engineering Journal of ASCE 108, Furth, P.G. an Rahbee, A.B. (2000). Optimal bus stop spacing through ynamic programming an geographic moeling. Transportation Research Recor 1731, Galvao, R.D., Espeo, L.G.A. an Boffey, B. (2000). A comparison of Lagrangean an surrogate relaxations for the maximal covering location problem. European Journal of Operational Research 124, Gleason, J.M. (1975). A set covering approach to bus stop location. Omega 3, Kwan, M. (1998). Space-time an integral measures of iniviual accessibility: a comparative analysis using a point-base framework. Geographical Analysis 30, Levinson, H.S. (1983). Analyzing transit travel time performance. Transportation Research Recor 915, 1-6. Moellering, H., Gauthier, H.L. an Osleeb, J.P. (1977). An interactive graphic transit planning system base on iniviuals. Urban Systems 2,

16 Murray, A.T Strategic analysis of public transport coverage. Socio-Economic Planning Sciences 35, Murray, A.T. an Davis, R Equity in regional service provision. Journal of Regional Science 41, Murray, A.T., Davis, R., Stimson, R.J. an Ferreira, L. (1998). Public transport access. Transportation Research D 3, Newman, P. an Kenworthy, J. (1999). Sustainability an Cities: Overcoming Automobile Depenence (Washington, D.C.: Islan Press). O'Sullivan, D., Morrison, A. an Shearer, J. (2000). Using esktop GIS for the investigation of accessibility by public transport: an isochrone approach. International Journal of Geographical Information Science 14, Queenslan Government (1997). Integrate Regional Transport Plan for South East Queenslan (Brisbane: Queenslan Government). Saka, A.A. (2001). Moel for etermining optimum bus-stop spacing in urban areas. Journal of Transportation Engineering 127, Toregas, C., Swain, R., ReVelle, C. an Bergman, L. (1971). The location of emergency service facilities. Operations Research 19, Wirasinghe, S.C. an Ghoneim, N.S. (1981). Spacing of bus-stops for many to many travel eman. Transportation Science 15,

17 Table 1. HSCP application results. p Obective Population Covere Optimality Gap Iterations Branches Time , % 1.20% 193,331 94, , % 0.93% 209, , , % 0.89% 142,970 83, , % 0.70% 164,974 81, , % 0.76% 293,990 79, , % 0.76% 191,309 84, , % 0.01% 867,715 99, , % - 48,259 11, CPU secons on a Pentium III/1000 personal computer.

18 Area Cove by Existing Stops Area Covere by New Stops Selecte New Stops Selecte Existing Stops Kilometers N Figure 1. HSCP results for p685.

19 Figure 2. HSCP Coverage Traeoff Regional Population Covere Number of Stops Locate (p)