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THREE USEFUL TEMPLATES FOR PUBLIC TRANSPORTATION DR. CHIALIN CHEN
This study is part of the Research Partnerships to Revitalize Rural Economies project, a research initiative of The Monieson Centre at Queen’s School of Business funded by the Social Sciences and Humanities Research Council of Canada (SSHRC) Partnership Development Grant program, as well as significant partner‐based funding. Project resources are available online at www.economicrevitalization.ca.
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THEMONIESONCENTRE
ThreeUsefulTemplatesforPublicTransportation
SSHRCResearchPaper
Dr. Chialin Chen
This paper discusses the impacts and challenges of rural public transportation and proposes three templates that can be used to increase efficiency and potentially reduce costs.
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TableofContents1.0 Introduction ............................................................................................................................................ 3
1.1 Canada’s Major Challenges ................................................................................................................. 3
1.2 Templates for Improvement ............................................................................................................... 4
2.0 Template 1 – On‐Demand Transit ........................................................................................................... 5
2.1 Method ............................................................................................................................................... 6
2.2 Case Study: Prince Edward County Specialized Transit ...................................................................... 9
3.0 Template 2 – Evaluating Existing Public Transit .................................................................................... 13
3.1 Method ............................................................................................................................................. 13
3.2 Case Study: North Hastings Public Transit ........................................................................................ 15
4.0 Template 3 – Resource Sharing ............................................................................................................ 23
4.1 Method ............................................................................................................................................. 23
4.2 Case Study: Prince Edward Lennox Addingston (PELA) Hospital Transfers ...................................... 25
5.0 Discussion and Concluding Remarks ..................................................................................................... 30
6.0 References ............................................................................................................................................ 32
Appendix A – Rural Communities with Public Transit Systems .................................................................. 35
Appendix B – Detailed Flowcharts .............................................................................................................. 37
Appendix C – Ambulance Routes (Iterative Method) ................................................................................. 40
Appendix D – Ambulance Routes (Eulerian Circuit) .................................................................................... 42
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1.0 Introduction
“Implementing effective rural transportation systems can increase accessibility to essential services,
make personal travel easier, and increase the quality of life for citizens in rural communities. Rural
transportation systems can lead to lower commuting costs for residents, thereby increasing intercity
travel and fostering development of local and regional businesses. Rural community leaders must
identify pressing issues of rural transportation systems before strategic plans are developed. Best
practices and case studies may be used as a guideline for future transportation systems, while
recognizing the need for local, provincial, federal, and stakeholder support. Policy leaders must
recognize the need for rural transportation systems to better plan for the future.”1
1.1Canada’sMajorChallenges Canada’s senior citizens use public transportation more than any other age group in Canada according to
Transport Canada (2009), and roughly 25% of Canada’s population will be 65 or older by the year 2031.2
This gives rise to the need for rural public transportation, especially considering the increasing
proportion of senior citizens in rural communities.3 One of the greatest challenges facing ageing
communities is providing access to healthcare for elderly citizens that are unable to drive,4 as well as
other essential services. Personal automobiles are very common in rural communities, obviating the
need for public transit. However, many senior citizens become unable to drive as they get older, which
could create the need for sustainable public transit in rural areas. It may be obvious that community
leaders and developers should begin designing and implementing rural transit systems, but these
1 Kevin Majkut, “Rural Transportation Issues and Strategies,” Knowledge Synthesis, Monieson Centre (2011), 1. 2 Transport Canada, “Sustainable Transportation in Small and Rural Communities,” Case Studies in Sustainable Transportation, Issue 61 (June 2009), 1. 3 Ibid. 4 Michael Kostiuk, “Rural Transit Symposium for Eastern Ontario and Western Quebec,” http://web.ncf.ca/fd978/transgeo/Rural%20Transit%20Symposium%20Nov%2019%202009.pdf (Accessed January 10, 2011).
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systems can be very expensive.5 In contrast with urban transit routes, rural transit routes will span long
distances and carry few passengers. In most cases it is simply not economically feasible,6 especially
since rural public transit is not federally funded or considered an essential service in Canada.7 For these
reasons, rural communities like Durham County have been better off using “on‐demand” transit services
such as van pools and taxis.8
Another challenge faced when trying to implement rural transit systems is Government policy. There
can be large amounts of bureaucracy, even with small communities, which can significantly slow or halt
the design or implementation process. As communities get larger, bureaucracy has a tendency to grow
and imposes more formal rules and regulations.9 In addition to municipal Governments, regional
Governments must also be consulted, making the process even more extensive. However, even with
the challenges of increasing bureaucracy, it is indeed possible and feasible to implement rural transit
systems. The Canadian Urban Transit Association (CUTA) is also helping with this effort by pursuing
federal funding for public transit across Canada. This would not only reduce the bureaucracy
surrounding public transit, but would provide funding at a national level – similar to the US – for public
transit projects.10
1.2TemplatesforImprovement
Different communities will most likely face different challenges with rural transit. Some may wish to
develop an entirely new transit system while others may want to evaluate and improve upon an existing
5 Majkut, 2.
6 Region of Durham Planning and Works Departments, “Transportation Master Plan,” Regional Municipality of Durham, (2004), 35. 7 Kostiuk. 8 Region of Durham Planning and Works Departments, “Transportation Master Plan,” Regional Municipality of Durham, (2004), 35. 9 Transport Canada, 2. 10 Kostiuk.
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transit network. Communities could also work together to increase efficiency by combining transit
systems. Regardless of the plans of rural community leaders, there seem to be three different ways to
develop rural transit systems based on how communities use their resources.
This paper will focus on three templates that can act as decision support for rural community leaders
looking to improve or create rural public transit systems. The first will apply to communities where
there is currently an “on‐demand” transit system in place, meaning that trips are scheduled on a daily
basis to satisfy demand. The template will provide an algorithm for efficient route selection, helping
community leaders routinely choose an optimal combination of trips per day. The second template is
intended for community leaders who wish to analyze and improve their existing routine transit system.
For the purposes of this paper, a routine public transit system is one where the same route is repeated
to satisfy demand – most commonly known as a bus route. The template will help community leaders
analyze existing routine routes and generate alternate routes until an optimal route is found. The final
template is intended to increase the efficiency of an entire region’s transit network by combining
resources. This could be accomplished for a rural transit system by sharing buses across county lines
and integrating transit systems to serve the greatest number of people. The third template can be
viewed as a second phase from a higher level, whereas the first phase would be designing transit
systems in different communities using either of the first two templates. The following three sections
will explain how each of the three templates work and provide case studies outlining and validating their
application.
2.0Template1–On‐DemandTransit Rural communities that currently use on‐demand transit, such as chartered services or first come first
served call in services, schedule new transit routes on a daily basis. Developing optimal routes based on
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daily demand can make a big difference when trying to serve the greatest number of people. This
template offers a decision‐making process that helps community leaders develop daily routes based on
demand and priority of passengers, and a process summary is shown in Figure 2.1.3.
2.1Method
The first step when designing an on‐demand daily transit route is to gather information for the number
of trips for the following day. This should be done on a first come first served basis, so whoever calls
first gets priority for a trip earlier in the day. Although priority should be on a first come first served
basis, communities may wish to further prioritize calls in terms of travel type. For example, the last
caller in the day who wishes to visit the hospital would have priority over the first caller in the day who
wishes to visit the park. Each requested trip from one point to another point will be called a vertex, and
traversals between vertices (the empty trips) will be called edges and are assumed to be the shortest
possible distance between two vertices. It is also worth noting edges begin at the end point of one
vertex and end at the starting point of the following vertex, unless the traversal following the empty trip
is a return trip within that vertex. A sample travel route is visualized in Figure 2.1.1, with each vertex
having a starting point, V1, and an end point, V2, where V is any given vertex.
Figure 2.1.1 – Sample Travel Route
Depot
D1, D2
B1, B2
E1, E2
C1, C2
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The next step is to plot vertices on an interactive map of the community, most commonly found in a
Geographic Information System (GIS). A GIS is an interactive geographic image of any area that can be
manipulated at the user’s request. One of the most user friendly and readily available versions of this
software is Google Earth and can be downloaded for free. After the vertices are plotted, the distances
between the starting and end points for each vertex should be measured using a measuring tool in the
GIS software. Starting with the location of the depot – where the bus will be leaving from – the Sweep
method (Gillet and Miller, 1974) can then be used to generate an initial daily route. The Sweep method
works by extending a straight line in any direction and rotating in either direction, adding the next
scheduled stop every time a vertex starting point is intersected by the line. If a vertex contains a return
trip, only the first of two trips will be added to the schedule until the sweep method selects the vertex
for a second time during its second rotation; this should give the passenger enough time for his or her
visit.
The Two‐Opt procedure (Flood, 1956, and Croes, 1958) can subsequently be used on the initial route to
find an optimal route with a shorter overall distance. Although the distance between starting and end
points of vertices will remain the same, the distance of edges can change based on the order in which
vertices are visited. Figure 2.1.2 shows an example of a single iteration of the Two‐Opt procedure,
where two edges (highlighted in red) are eliminated and a new route (noted by a dashed line) is formed
in their absence. This iterative approach is repeated for each potential Two‐0pt move until the best
option – the one with the shortest distance – is selected.
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Figure 2.1.2 – Two‐Opt Move for Initial Route
The Two‐Opt procedure should reduce the distance travelled for the route, therefore decreasing the
total time required for the trip. However, if the optimal route still does not satisfy the time constraints
(i.e. the bus only operates for eight hours per day), then vertices should be removed one by one based
on priority until the constraints are satisfied. The Sweep method and Two‐Opt procedure should be
performed every time a vertex is removed. Removed vertices should be put on a waiting list for the
following day and given higher priority when making the following day’s travel route.
As previously mentioned, priority can be based on travel type. It might make sense to give hospital visits
top priority before adding people from the previous day’s waiting list and abiding by a first come first
served guideline for all other trip requests.
Figure 2.1.3 – On‐Demand Transit Process Flowchart
Plot locations of
vertices and measure
edges between them
On-Demand Transit
Generate initial daily route using Sweep
Method starting from the depot
Interactive map of community
(GIS)
Gather information
for number of trips
the following day
(distance, location)
Optimize initial route by using Two-Opt Method (see Figure
2.1.2)
Execute travel route
Depot
D1, D2
B1, B2
E1, E2
C1, C2
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2.2CaseStudy:PrinceEdwardCountySpecializedTransit
Prince Edward County (PEC) is a municipality in Southern Ontario and is located in between Kingston and
Toronto, Ontario. The population of the municipality is approximately 25,000, with a population density
of 24.3/km2, and an area of about 1,000 km2. A map of the community is seen in Figure 2.2.1. Quinte
Access is an on‐demand specialized transit systems that serves PEC, Quinte West, and Brighton, Ontario
with four buses and five vans. It is intended for people who are physically or mentally challenged, or
seniors who need transportation assistance. For simplicity, this case study focuses on the use of one
vehicle and assumes that only one passenger is picked up at a time. It also assumes that the vehicle will
operate for eight hours per day and travels at an average speed of 37 km/h, which is the recorded
average speed of the Quinte Access transit system.
Figure 2.2.1 – Prince Edward County
Daily demand was simulated including both one way and return trips throughout PEC, as shown in
Figure 2.2.2. In order of decreasing priority, travel types included hospital, waiting list, pharmacy,
groceries, and recreation. In the case of more than one travel type, priority was awarded based on the
order of calls placed. As can be seen in Figure 2.2.2, there was one passenger put on a waiting list from
the previous day.
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Figure 2.2.2 – Simulated Trip Demand
Trips were plotted using Google Earth as seen in Figure 2.2.3, with one way trips denoted by a red line
and return trips having a green line. The yellow pushpins with the number one indicate the starting
point for each vertex, and the number two pushpins show the end points. Starting with the green
pushpin icon near Picton, which represents the depot, the Sweep method was used by extending a
straight line upwards and rotating it to the left, adding a new vertex every time a starting point for a
new vertex was crossed. For return trips, the second trip was added by continuing the rotation of the
extended line until all return trips had been satisfied.
Figure 2.2.3 – Trips Plotted in Google Earth
Route Return Trip?
One Way Distance (km)
Travel Type Order of Call
Priority
1 No 5.8 Hospital 2 12 No 12.7 Hospital 3 23 Yes 9 Waiting List 1 44 No 11.4 Pharmacy 5 55 No 7.1 Groceries 4 66 Yes 41.2 Hospital 7 37 No 8.5 Recreation 6 78 Yes 33.4 Recreation 8 8
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Figure 2.2.4 compares the initial route using the Sweep method with the results from the Two‐Opt
procedure, which used the Sweep results as a starting point. As expected, the total distance was
decreased by using the iterative Two‐Opt procedure, as well as the total hours required for the trip –
calculated by dividing total distance by the average speed of 37 km/h. However, the 10.4 hour
requirement for all trips meant that one or more vertices or trips must be removed in order to satisfy
the capacity constraint of an eight hour working day. Starting with the trip with the lowest priority,
vertex number eight was removed and the Sweep method and Two‐Opt procedures were once again
calculated as seen in Figure 2.2.5.
Figure 2.2.4 – Sweep Method vs. Two‐Opt Procedure
Sweep Method Two-Opt ProcedureRoute Distance Empty Trip Travel Type Route Distance Empty Trip Travel TypeDepot 0 12.8 N/A Depot 0 12.8 N/A
7 8.5 16.8 Recreation 7 8.5 Recreation4 11.4 7.8 Pharmacy 1 5.8 12 Hospital6 41.2 37.8 Hospital 8 33.4 7.8 Recreation5 7.1 20 Groceries 2 12.7 15.8 Hospital3 9 12 Waiting List 3 9 29.4 Waiting List2 12.7 0 Hospital 5 7.1 19.0 Groceries1 5.8 12 Hospital 4 11.4 7.8 Pharmacy8 33.4 17.3 Recreation 6 41.2 17.3 Hospital6 41.2 30.1 Hospital 8 33.4 5.5 Recreation3 9 5.5 Waiting List 3 9 5.4 Waiting List8 33.4 15.7 Recreation 6 41.2 39.7 Hospital
Depot 0 N/A Depot 0 N/A
Total Distance 400.62 Total Distance 385.24Total Hours 10.8 Total Hours 10.4
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Figure 2.2.5 – Sweep vs. Two‐Opt after Removing Vertex Eight
Although the total time required was reduced to 8.3 hours, this was still greater than the maximum
constraint of an eight hour work day. Therefore, one more vertex with the next lowest priority – vertex
number seven – had to be removed. The removal of vertex seven led to a travel route that satisfied all
constraints, as can be seen in Figure 2.2.6. The total time for the trip was reduced to 7.9 hours, making
it a feasible transit route for the day. If only one vehicle were available, vertices seven and eight would
be put on the waiting list for the following day and given a higher priority. Otherwise, the same
procedure could be used to fill travel capacity for the next vehicle.
Figure 2.2.6 – Sweep and Two‐Opt after Removing Vertex Seven
Sweep Method Two-Opt ProcedureRoute Distance Empty Trip Travel Type Route Distance Empty Trip Travel TypeDepot 0 12.8 N/A Depot 0 0.6 N/A
7 8.5 16.8 Recreation 1 5.8 10.2 Recreation4 11.4 7.8 Pharmacy 2 12.7 15.8 Pharmacy6 41.2 37.8 Hospital 3 9 29.4 Hospital5 7.1 20 Groceries 5 7.1 19 Groceries3 9 12 Waiting List 4 11.4 7.8 Waiting List2 12.7 0 Hospital 6 41.2 7.8 Hospital1 5.8 41.6 Hospital 7 8.5 13.4 Hospital6 41.2 30.1 Hospital 3 9 19.0 Hospital3 9 9.0 Waiting List 6 41.2 39.7 Waiting List
Depot 0 N/A Depot 0 N/A
Total Distance 333.9 Total Distance 308.05Total Hours 9.0 Total Hours 8.3
Sweep Method, Followed by Two-Opt ProcedureRoute Distance Empty Trip Travel TypeDepot 0 0.6 N/A
1 5.8 10.2 Recreation2 12.7 15.8 Pharmacy3 9 29.4 Hospital5 7.1 19 Groceries4 11.4 7.8 Waiting List6 41.2 14.3 Hospital3 9 19.0 Hospital6 41.2 39.7 Waiting List
Depot 0 N/A
Total Distance 292.65Total Hours 7.9
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This type of planning process for on‐demand transit can become more complicated if people need to be
picked up or dropped off at certain times, however, this would simply act as an additional constraint
during the planning process. Another variation to this type of transit system could be picking up more
than one passenger at a time. In this case, trips could simply be combined during the planning process,
which would mean slightly longer travel times for some passengers, but probable increases in efficiency
with more passengers served.
3.0Template2–EvaluatingExistingPublicTransit Rural communities with existing transit systems may wish to evaluate their systems in order to validate
or improve their overall network. This template shows how an existing transit system can be evaluated
with the collaboration of community leaders and GIS technicians. This template is also useful for
communities in the planning stages of developing a new routine transit system, who currently have no
routine transit system in place.
3.1Method
The process flowchart found in Figure 3.1 shows the steps required to evaluate an existing routine
transit system and/or develop new routes for routine transit in a rural community.
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Figure 3.1 – Three Stage Decision‐Making Process11*
*See Appendix B for detailed flowcharts for each of the three stages.
Similar to Template 1, GIS can be used to help analyze the existing network and provide a baseline for
improvement. Points of interest, such as hospitals, grocery stores, and other areas that are important to
local residents, are plotted on a GIS map of the community with the help of GIS technicians. The entire
community is split into grid cells measured 400m by 400m, since 400 metres is considered a reasonable
walking distance to a bus stop (Lam and Morrall, 1982). Next, scores are assigned to each grid cell based
on points of interest, their relative importance, and the population within a specific grid cell; this gives
the accessibility score for each grid cell. Grid cells with high accessibility scores represent areas in the
11 Majkut, Kevin, “Developing a Rural Public Transportation Network,” Thesis, (2011), 29.
Data Gathering and Analysis
•Meet with Community Team to Define Objective of Transit System
•Give KML Files with Point of Interest Locations to GIS Technician
•Receive Excel Spreadsheet with Grid Cell Information
•Give Survey to Rank Weights of Different Factors
•Receive Survey with Rankings
Model Development
•Determine Weights Based on Rankings
•Calculate Accessibility Scores using Grid Cell Spreadsheeet
•Plot Locations of Grid Cells with Highest Scores to Community Map
Route Generation and Testing
•Evaluate Scores for Existing Routes
•Develop New Routes using VRS or Other Methods
•Compare Different Routes to Find Optimal Route
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community that should be given priority for routine bus stops. For example if an existing routine transit
system does not have a bus stop in a grid cell with a high score, one should be placed in order to satisfy
the needs of citizens.
3.2CaseStudy:NorthHastingsPublicTransit
The Rural Overland Utility Transit (TROUT) is a routine public transit system that serves North Hastings
(Figure 3.2.1) and Highlands East in Ontario. The transit system has a daily route within the city of
Bancroft, and also has additional routine stops all across North Hastings on different weekdays. This
case study focuses on the routine transit within the city of Bancroft, its evaluation, and suggestions for
improvement. The method in Section 3.1 is applied to the transit system in order to complete the
analysis.
Figure 3.2.1 – North Hastings Map12
The first step in the process was to meet with the leaders of the TROUT bus system and define the
objective of the transit system. This was defined as serving as many citizens as possible with a quality
12 North Hastings, www.north‐hastings.com, (Accessed February, 2012).
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transit system throughout North Hastings. The next step was to define points of interest within the
community that contribute towards accessibility for local residents. For the purpose of this paper,
accessibility is defined as the appeal of a certain area based on its importance to people. For example,
an area with a hospital, grocery store, and pharmacy would have high accessibility, since it would have
three major points of interest that appeal to members of the community. The following points of
interest were defined by leaders of the TROUT system: hospitals, schools, pharmacies, grocery stores,
parks, retirement residences, banks, retail locations, seniors’ clubs, and restaurants. These ten point of
interest categories were objectively ranked using a utility scoring tool (Figure 3.2.2), which allowed
community leaders to rank different combinations of points of interest within a specific area. Multi‐
Objective Utility Analysis (MOUA) (de Neufville, 1990) was then used in collaboration with Excel Solver’s
linear programming tool to find the weights – or relative importance – for each point of interest.
Figure 3.2.2 – Utility Scoring Tool
The results of MOUA showed that hospitals, pharmacies, and banks were the three most important
points of interest when considering accessibility. The next step involved plotting points of interest as
well as existing bus stops in a GIS system; Google Earth was used for this case study. After all points
were plotted, the file containing location information was sent to Hastings GIS technicians to split the
area into 400m by 400m grid cells and return a Microsoft Excel spreadsheet with location and bus stop
Combination Hospitals Schools Pharmacies Grocery Stores Parks Retirement Residences Banks Retail Seniors' Clubs Restaurants = Utility1 1 1 0 0 1 1 1 0 0 0 = ?2 0 1 1 1 1 1 1 0 1 0 = ?3 0 1 1 0 1 1 1 0 1 1 = ?4 1 0 1 0 0 0 1 0 1 0 = ?5 0 0 1 1 0 0 1 1 0 1 = ?6 1 0 1 0 1 0 1 1 0 0 = ?7 1 0 0 0 0 0 1 1 1 1 = ?8 1 0 0 1 0 0 0 0 0 1 = ?9 1 1 1 0 1 1 0 0 1 1 = ?
10 0 1 0 0 1 1 1 1 1 0 = ?11 0 0 0 1 0 1 0 1 1 1 = ?12 0 1 1 0 1 0 1 0 1 1 = ?13 1 0 0 1 1 0 0 1 0 0 = ?14 0 1 1 0 1 1 1 0 0 0 = ?15 1 0 1 0 0 1 1 1 0 1 = ?16 0 1 1 0 1 0 1 1 1 1 = ?17 1 1 0 1 1 1 1 0 1 0 = ?18 1 1 1 0 0 1 0 0 0 1 = ?19 0 1 1 1 1 1 1 1 1 1 = ?20 1 1 1 1 0 1 1 0 1 1 = ?
MAX 1 1 1 1 1 1 1 1 1 1 = 100
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information per grid cell. Once the spreadsheet was received, weights for each point of interest and the
relative population per grid cell were used to calculate accessibility scores. Population was calculated
based on the number of houses per grid cell, and multiplied by the average number of residents per
household as per the Statistics Canada Community Profile.
Accessibility scores were calculated for each grid cell by adding the weights together for points of
interest that were present, adding one, and then multiplying by the total population. For example, if the
weights for a hospital and a restaurant were 15 and 10, respectively, then a grid cell with one hospital
and a population of 100 would have an accessibility score of (15+1)x100 = 1600. If the population were
zero in the same scenario, the accessibility score would be zero. The reason for adding one before
multiplying by population is to recognize grid cells with high populations but no points of interest. For
example, a grid cell with no points of interest but a population of 2000 would receive a score of 2000 as
opposed to zero.
Grid cells with the highest scores were plotted using Google Earth; the top 30 results were selected. As
seen in Figure 3.2.3, the yellow pushpin icons represent existing bus stops while the green pushpins
denote grid cells within the top 30 but not currently in the transit network. It is quite clear that
potential stops such as 12 and 13 are too far out of the way to accommodate, however, zooming in on
the central Bancroft route shows some more viable options for improvement. Figure 3.2.4 shows the
existing bus route through Bancroft as well as existing and potential stops with their assigned scores.
The majority of the existing bus stops are within the top 20 accessibility scores, and the most important
grid cells already have existing bus stops. This shows that the TROUT system has been well designed,
but the green pushpins (unused grid cells) could still potentially be used to increase the overall score of
the route.
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Figure 3.2.3 – Top 30 Accessibility Scores and Current Bus Stops
Figure 3.2.4 – Top Ranked Grid Cells within Bancroft Transit Area
Calculating the Total Route Score per Distance (TRSD) for a bus route is as simple as adding up the
accessibility scores for all grid cells travelled during the course of a trip and dividing by the total
distance. The TRSD for the existing transit route can be found below in Figure 3.2.5. The first column
labelled “Bus Stop” shows the number of bus stops in the system and the following two columns show
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the Rural Accessibility Score (RAS) rank and score for the particular grid cell. It is easy to see that there
are five bus stops within the highest ranked grid cell and the TRSD for the existing route is 5757.
Figure 3.2.5 – Comparing Different Routes
The existing route is shown in Figure 3.2.6.
RAS Rank Score RAS Rank Score RAS Rank Score1 1 20440 1 20440 1 204402 1 20440 1 20440 2 95133 1 20440 1 20440 3 56104 1 20440 1 20440 4 51185 1 20440 1 20440 5 30556 2 9513 2 9513 6 11887 2 9513 2 9513 7 11358 2 9513 2 9513 8 8989 3 5610 3 5610 10 60110 3 5610 3 5610 11 39911 4 5118 4 5118 19 9412 5 3055 5 3055 23 8213 6 1188 6 1188 39 5314 7 1135 7 1135 9 71515 8 898 8 898 25 7216 10 601 10 601 16 9817 11 399 11 399 20 8618 19 94 19 9419 23 82 23 8220 39 53 39 5321 9 71522 25 7223 16 9824 28 7025 20 86
Total Score: 48132 49226 49156Total Distance: 8.36 km 9.57 km 8.32 kmDuration: 52 mins 65 mins 44 minsTRSD: 5757 5144 5908
Bus Stop
Route 1 Route 3
Existing Alternate 2Alternate 1
Route 2
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Figure 3.2.6 – Existing Bancroft Route
Two alternate routes were created to compare with the existing transit system. The first can be seen in
Figure 3.2.7, which adds five stops to the existing transit system based on proximity and rank. Figure
3.2.5 shows that Alternate Route 1 produces a higher total score, but a lower overall TRSD. This is
because the ranks of the additional routes were fairly low compared with the distance they added to the
route. It is also worth noting that Alternate 1 exceeds the route time for the existing route by 13
minutes.
Alternate Route 2 removes bus stops that occur within the same grid cell, as previously mentioned, and
adds four additional bus stops. Figure 3.2.8 shows a comparison between the existing route with five
stops within the highest ranked grid cell and Alternate Route 2 with one stop in the same grid cell.
Reducing the number of stops will decrease overall travel distance thereby increasing the TRSD. This is
acceptable since all five stops are less than 400 metres apart; therefore, one bus stop will be a
reasonable walking distance from any point within the grid cell. The results in Figure 3.2.5 show that the
TRSD for Alternate Route 2 is higher than the existing route. In addition, the total route time – even
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after adding four new stops – is eight minutes less than the existing route. Alternate Route 2 can be
seen in Figure 3.2.9.
Figure 3.2.7 – Alternate Route 1
Figure 3.2.8 – Existing Route vs. Alternate Route 2
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Figure 3.2.9 – Alternate Route 2
These results suggest that altering the existing route to include one bus stop per grid cell, as well as
adding four more bus stops, will increase the accessibility of the bus route by serving more people and
more points of interest. Adopting Alternate Route 2 will directly increase efficiency by eliminating
unneeded travel space, since repeated bus stops within the same grid cell will be deleted. This option
can also increase ridership, since a greater population and more points of interest will be served with
the new bus stops. As previously mentioned, this template can also be used to develop a brand new
transit system for a rural community. If that were the case, stops would simply be added to each grid
cell – one at a time – from highest to lowest rank until a desired route is developed. Keep in mind that
some grid cells may be ranked highly but far off the travel path; if so, be sure to skip to the next highest
grid cell in order to minimize total distance (and time) of the route. Remember, many alternatives
should be compared in order to find the optimal route.
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4.0Template3–ResourceSharing Sharing resources can greatly increase efficiency for rural transit systems and help reduce overall costs.
This template provides a useful algorithm that communities can use to integrate transit systems to
maximize operational efficiency for an entire region, and is reflected in Figure 4.1.2.
4.1Method
The primary algorithm used to solve this type of problem is Fleury’s Alrgorithm (Fleury, 1883), which
assists in the construction of an Eulerian Circuit connecting all travel destinations in an efficient manner.
An Eulerian Circuit is one in which every required edge is travelled exactly once and the start and end
nodes are the same. An example of an Eulerian Circuit is shown in Figure 4.1.1 (Circuit 1), since each
required edge (or trip) is travelled exactly once and the start and end nodes are both A. Circuit 2 in
Figure 4.1.1 is not an Eulerian Circuit since the trip from A to B is travelled twice, and the start and end
nodes are not the same. Using this method can greatly decrease wasted travel time for transit routes,
which can increase the number of destinations and the quantity of people served.
Figure 4.1.1 – Eulerian vs. Non‐Eulerian Circuits
A B
C D
Required Trips:
A B = 1
C A = 1
D C = 1
A D =1
A B
C D
Circuit 1 Circuit 2
Path:
A‐B‐A‐D‐C‐A
Path:
A‐B‐C‐A‐B‐D‐A‐D‐C
Path:
A‐B‐A‐D‐C‐A
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Once the number of required trips within a network has been determined, Fleury’s Algorithm can be
used to manually find an Eulerian Circuit. First, any node can be chosen to be the starting point for the
trips. Secondly, another node should be chosen to travel to next, and a dark line should be drawn
between the two nodes as a reminder to not traverse it again. This process is repeated until all edges
are traversed and the final trip ends at the starting node. In addition, the following guidelines should be
followed to make the process as easy as possible:
As many nodes as possible should be traversed before repeating a particular trip;
“Empty trips,” such as the trip from B to A in Figure 4.1 (Circuit 1), should be used as late as
possible; and
Never repeat a required trip unless there is no other choice.
Once an Eulerian Circuit is derived, constraints must be applied to determine how many vehicles are
required to satisfy all trips in the network. For example, a time constraint of eight hours – reflecting
working hours in the day – can be used as the capacity constraint per vehicle. In addition, the required
time to travel from one destination to the next must be considered in order to determine when vehicle
capacity has been reached. Starting with the first point in the Eulerian Circuit, the transit developer can
add trips until capacity for each vehicle is reached. By the end of the Eulerian Circuit, the developer will
have an individual schedule for each vehicle in the network while minimizing the total number of
vehicles used. The following case study shows how this process can be used to create an efficient
schedule for transferring patients to and from hospitals in different cities.
Page | 25
Figure 4.1.2 – Resource Sharing Process Flowchart
4.2CaseStudy:PrinceEdwardLennoxAddingston(PELA)HospitalTransfers
The PELA community – located between Kingston and Toronto, Ontario – is approximately 3,800 square
kilometres with a population of roughly 70,000 and is classified as a rural region.13 The community also
has a large proportion of senior citizens who require medical attention more frequently than the
younger demographic.14 The PELA community has 14 hospitals in the region (Figure 4.2.1), with inter‐
facility patient transfers occurring between all hospitals. A geographic representation can also be found
in Figure 4.2.2.
Figure 4.2.1 – Hospitals in the PELA Community
1. Brockville General Hospital Brockville 2. Hotel Dieu Hospital Kingston 3. Kingston General Hospital Kingston 4. Lennox and Addington County General Hospital Napanee 5. Perth and Smiths Falls District Hospital Perth 6. Perth and Smiths Falls District Hospital Smiths Falls 7. Providence Continuing Care Centre Brockville 8. Providence Continuing Care Centre Kingston 9. Quinte Healthcare Corporation Bancroft 10. Quinte Healthcare Corporation Belleville 11. Quinte Healthcare Corporation Picton
13 Zhao, Samson, “Healthcare Inter‐Facility Transportation Problem,” Thesis, (2010). 14Ibid.
Find Eulerian Circuit
using Fleury’s
Algorithm (See
Figure 4.1.1)
Resource Sharing
Apply time constraint (working hours per day) and solve by
adding one vehicle at a time
Excel file with number of trips and distances
Gather information
for number of trips
and distances
between locations
Execute travel route (output total number of vehicles required
and schedules)
Page | 26
12. Quinte Healthcare Corporation Trenton 13. Royal Ottawa Health Care Group Brockville 14. Wisemans Private Hospital Perth
There are currently no efficient means of transporting patients from one hospital to another, and
emergency ambulance vehicles are used for these trips. Emergency vehicles are very expensive to
operate and using them in this manner can actually increase the risk for residents; for example, if
someone had a heart attack and there were no ambulances available due to hospital transfers, that
person may die. The remainder of this section compares the existing transportation system with an
improved system based on Fleury’s Algorithm and the use of an Eulerian Circuit. The fourteen hospitals’
identities as well as their required trips per day have been disguised for confidentiality; however, they
still accurately reflect demand for a given day.
Figure 4.2.2 – PELA Community Map15
15 South East Local Health Integration Network,
http://www.southeastlhin.on.ca/Page.aspx?id=108&ekmensel=e2f22c9a_72_184_btnlink, (Accessed February, 2012).
Page | 27
The data presented in Figure 4.2.3 shows the travel times from one hospital to another, as well as the
number of required trips in a given day. This data was used to create a set of trips assuming an eight
hour working day for any ambulance driver and each ambulance was only responsible for the trips for
their own hospital. Although each ambulance would only be responsible for their own trips, it was
assumed that if an ambulance arrived at a hospital with a patient that needed a ride to their hospital,
they would accommodate the patient. Routes were generated one at a time until each ambulance’s
time constraint of eight hours was filled, moving from left to right across the lower grid in Figure 4.2.3
until all trips were satisfied.
Figure 4.2.3 – Travel Data
In total, 56 ambulances were required across the region to satisfy demand. A summary of the number
of ambulances required at each hospital can be found in Figure 4.2.4 and the detailed routes for each
Origin Destination Hospital (Times)Hospital A B C D E F G H I J K L M N
A - 45 68 90 125 70 120 95 132 130 65 60 130 156B 45 - 30 60 115 55 110 90 105 115 55 52 112 135C 68 30 - 53 128 45 125 108 115 130 48 50 115 145D 90 60 53 - 96 35 92 95 80 90 40 42 88 120E 125 115 128 96 - 65 52 90 50 10 65 68 47 25F 70 55 45 35 65 - 45 116 50 66 12 15 48 85G 120 110 125 92 52 45 - 185 10 49 52 50 12 33H 95 90 108 95 90 116 185 - 180 165 136 132 176 180I 132 105 115 80 50 50 10 180 - 45 50 47 13 28J 130 115 130 90 10 66 49 165 45 - 63 60 46 17K 65 55 48 40 65 12 52 136 50 63 - 10 38 85L 60 52 50 42 68 15 50 132 47 60 10 - 40 82
M 130 112 115 88 47 48 12 176 13 46 38 40 - 30N 156 135 145 120 25 85 33 180 28 17 85 82 30 -
Origin Destination Hospital (Trips)Hospital A B C D E F G H I J K L M N
A - 4 2 2 2 1 2 0 0 1 3 0 2 1B 4 - 4 4 0 0 0 0 1 0 6 1 4 0C 1 6 - 9 0 0 0 1 0 2 2 0 2 2D 3 1 8 - 1 0 1 0 0 0 0 0 0 0E 0 1 0 0 - 1 0 2 0 0 4 0 0 1F 1 2 0 0 2 - 0 0 2 1 2 0 1 0G 0 0 2 1 0 0 - 1 0 0 0 0 0 0H 3 1 0 0 2 3 0 - 1 1 0 0 1 0I 0 3 0 2 1 0 1 3 - 2 2 0 0 1J 2 0 2 2 1 1 0 0 0 - 3 1 0 0K 6 2 1 3 0 0 0 0 0 0 - 0 2 1L 1 0 5 0 0 0 0 0 1 0 0 - 0 0
M 2 3 1 0 1 1 0 0 1 0 7 0 - 0N 0 2 2 0 1 2 1 0 0 1 1 0 2 -
Page | 28
ambulance can be found in Appendix C. Keep in mind that demand for the following day will be
different, and will probably require different numbers of ambulances at each hospital, not to mention
the ambulances required for emergency services.
Figure 4.2.4 – Required Ambulances (Iterative Method)
Starting with Hospital K and using the method outlined in Section 4.1, an Eulerian Circuit was developed
as a starting point for route generation as follows:
K‐A‐B‐C‐D‐E‐F‐I‐G‐H‐J‐K‐N‐M‐K‐A‐B‐D‐C‐H‐F‐I‐E‐K‐D‐C‐N‐J‐L‐C‐B‐K‐A‐E‐H‐M‐F‐E‐K‐B‐D‐C‐J‐A‐N‐M‐K‐A‐B‐C‐
D‐G‐C‐D‐C‐J‐K‐M‐K‐D‐A‐C‐D‐A‐E‐H‐I‐N‐K‐M‐C‐B‐A‐M‐I‐H‐E‐N‐F‐K‐A‐G‐C‐B‐I‐H‐F‐J‐K‐D‐C‐B‐A‐F‐E‐K‐C‐D‐B‐
A‐G‐D‐C‐M‐K‐A‐D‐C‐B‐L‐I‐H‐F‐M‐E‐B‐D‐C‐N‐F‐B‐M‐K‐B‐C‐D‐A‐J‐F‐B‐M‐C‐M‐B‐A‐M‐A‐C‐B‐M‐A‐B‐M‐B‐C‐A‐
K‐M‐K‐L‐A‐K‐M‐K‐I‐B‐D‐H‐E‐K‐M‐N‐B‐K‐L‐C‐D‐I‐J‐E‐J‐C‐K‐M‐N‐C‐D‐I‐J‐C‐D‐I‐B‐K‐L‐C‐K‐M‐N‐B‐K‐L‐B‐K‐I‐D‐I‐
B‐K‐M‐N‐C‐F‐A‐D‐I‐K‐L‐C‐F‐K‐M‐N‐E‐J‐D‐I‐D‐J‐D‐J‐A‐H‐B‐H‐A‐H‐A‐H‐A‐K‐M‐N‐G‐I‐K
HOSPITAL AMBULANCE REQUIREMENT
A 5
B 5
C 5
D 3
E 3
F 2
G 3
H 6
I 6
J 4
K 4
L 2
M 4
N 4
Total 56
Page | 29
Ambulances were then filled in the order above until all trips were satisfied. The total number of
ambulances required to satisfy demand using this method were 37. The detailed routes for each
ambulance can be found in Appendix D. An unbelievable 19 fewer ambulances were required to satisfy
the exact same demand through resource sharing. In comparison, the number of required ambulances
at each hospital can be seen in Figure 4.2.5. In order to prepare for the following day’s demand,
ambulances would either have to be transferred from one hospital to another or reserve ambulances
could be present at larger hospitals to account for larger expected demand.
Figure 4.2.5 – Required Ambulances (Eulerian Circuit)
Using an Eulerian Circuit and Fleury’s Algorithm to satisfy demand through resource sharing increased
efficiency by 34% and would be expected to generate significant cost savings. In addition to operational
efficiency and costs, ambulances would be more readily available for emergency services to better serve
the community.
Hospital Ambulance Requirement
A 4
B 4
C 7
D 3
E 2
F 2
G 1
H 2
I 1
J 3
K 3
L 2
M 2
N 1
Total 37
Page | 30
5.0DiscussionandConcludingRemarks
Each of the three templates discussed in this paper offer rural community leaders decision‐making and
support tools that can be applied to foster development, dependent on the resources used and future
plans for transit growth. A brief summary of the three templates is seen below in Figure 5.1.
Figure 5.1 – Template Comparison
Template Purpose Users
On‐Demand Transit Develop daily transit schedules for changing demand.
Individual Communities.
Evaluating Existing Public Transit
Evaluate existing transit routes and make recommendations to increase accessibility.
Generate brand new transit system based on accessibility of community members.
Individual Communities.
Resource Sharing Maximize efficiency by sharing resources among different communities with existing transit systems, regardless of the template used.
Regional Communities.
The first two templates are ideal for rural community leaders looking to implement a new transit system
or improve upon an existing network. The first template would be applicable to a rural community
whose goal was to offer an efficient and effective means of public transportation through an on‐demand
system. This type of transit would be easily recognizable, since communities would receive calls and
offer transit on an as need basis. The second template would be ideal for rural communities wishing to
develop routine public transit, with the same routes occurring on a daily, bi‐daily, or even weekly basis.
This type of transit system is targeted towards communities with a high demand for routine transit to
work, grocery stores, or essential services, and is designed to satisfy demand on a regular basis.
The final template is intended to help different communities work together to share resources and
increase the efficiency of an entire region. This template could also be used by regional leaders to
Page | 31
increase the overall efficiency of their region. For example, the TROUT system has recently began a
transit route from Bancroft to Peterborough. Due to the length of the trip and the potential for a
smaller number of riders, this particular transit route will probably not be as profitable as the in town
Bancroft route discussed in Section 3.2. Resource sharing could lead to greater overall efficiency and
ridership if Peterborough’s transit system were to connect one of their existing rural routes with the
TROUT’s Peterborough route. This is just one example of how sharing resources can help a region as a
whole. One of the greatest challenges to this approach is the fact that each municipality or community
has its own budget and may frown upon lowering their bottom line while raising another community’s,
even though the net result is positive. However, a simple solution could be some sort of profit sharing
plan between the two communities.
In conclusion, the three templates discussed in this paper offer rural community leaders decision‐
making support to implement new transit systems or evaluate existing systems. Template three in
particular offers community leaders a tool that can drastically increase the efficiency of a region through
resource sharing. Increasing the presence of rural public transportation in North America will increase
accessibility for an ageing and growing population, as well as foster economic development in rural
areas.
Page | 32
6.0References
Ballou, R.H. and Agarwal, Y.K. “A Performance Comparison of several Popular Algorithms for Vehicle
Routing and Scheduling,” Journal of Business Logistics, 9(1), 51‐65. (1988).
Canadian Urban Transit Association. “Transit Vision 2040.”
<www.cutaactu.ca/en/publicationsandresearch/resources/CUTABook_Compressed_complete
.pdf>
Clarke, G. and Wright, J.W. “Scheduling of Vehicles from a Central Depot to a Number of Delivery
Points.” Operations Research, 12(4), 568‐581. (1962).
Croes, GA. “A Method for Solving Travelling Salesmen Problems.” Operations Research, 6, 791‐812.
(1958).
Fleury. “Deux problems de geometrie de situation.” Journal de Mathematiques
Elementaries. 257‐261. (1883).
Flood, MM. “The Travelling Salesman Problem.” Operations Research, 4, 61‐75. (1956).
GIS.com. “What is GIS?” <www.gis.com/content/what‐gis>
International Forum for Rural Transport and Development. “IRAP.” <www.ifrtd.org/en/issue.php?id=033>
Jaw, J., Odoni, A. R., Psaraftis, H. N., & Wilson, N. H. M. “A heuristic algorithm for the multi‐vehicle
advance‐request dial‐a‐ride problem with time windows.” Transportation Research, 20, 243–
257. (1986).
Kau, James B. “A Transportation Land Use Model for Rural Areas.” The Annals of Regional Science, 11(2),
41‐54. (1977).
Kidder, Ben. “The Challenges of Rural Transportation.”
<wrdc.usu.edu/files/publications/publication/pub__9373753.pdf>
Kostiuk, Michael. “Rural Transit Symposium for Eastern Ontario and Western Quebec.”
<web.ncf.ca/fd978/transgeo/Rural%20Transit%20Symposium%20Nov%2019%202009.pdf>
Land Use Modeling Workshop. “The State of the Practice in Land use Models.”
<www.oregon.gov/ODOT/TD/TP/docs/TMR/General/luwkshpproc.pdf?ga=t>
Lam, W. and J. Morrall. “Bus Passenger Walking Distances and Waiting Times: A Summer‐
Page | 33
Winter Comparison.” Transportation Quarterly, 36(3), 407‐421. (1982).
Lilien, Gary L., and Arvind Rangaswamy. “Marketing Engineering: Computer‐assisted Marketing Analysis
and Planning.” Trafford. (2004).
Litman, Todd. “Evaluating Public Transit Benefits and Costs.” Victoria Transport Policy Institute. (January
2011).
Lowry, Ira S. “A Model of Metropolis.” RAND Memorandum, RM‐4035. (1964).
Majkut, Kevin. “Developing a Rural Public Transportation Network.” Queen’s School of Business. Thesis.
(2011).
Majkut, Kevin. “Rural Transportation Issues and Strategies.” Knowledge Synthesis for Monieson Centre,
Queen’s School of Business. (March 2011).
North Hastings. www.north‐hastings.com. (February 2012).
Quinte Access. <www.quinteaccess.org>
Region of Durham Planning and Works Departments. “Transportation Master Plan.” Regional
Municipality of Durham. (2004).
Rodrigue et al. “The Geography of Transport Systems.” Routeledge. (2009).
Sanchez, Thomas. “Rural Public Transportation: Using Geographic Information Systems to Guide Service
Planning.” Center for Urban Studies, Transportation Research Group. (June 2002).
Sarkar, Ashoke. “Rural Accessibility Planning: A Review.” Birla Institute of Technology and Science, Pilani.
(January 2008).
South East Local Health Integration Network.
http://www.southeastlhin.on.ca/Page.aspx?id=108&ekmensel=e2f22c9a_72_184_btnlink.
(February 2012).
Statistics Canada 2006 Census.
<www12.statcan.ca/census‐recensement/2006/rt‐td/index‐eng.cfm>
Transportation Research Board, National Research Council. “Assessment of the Economic Impacts of
Rural Public Transportation.” TCRP Report, 34. (1998).
Page | 34
Transport Canada. “Sustainable Transportation in Small and Rural Communities.” Case Studies in
Sustainable Transportation, 61. (2009).
Zhao, Samson. “Healthcare Inter‐Facility Transportation Problem.” Thesis. (2010).
Page | 35
AppendixA–RuralCommunitieswithPublicTransitSystems16 Deseronto Transit – Deseronto, Ontario
http://deseronto.ca/departments/deseronto‐transit
Deseronto’s transit system provides service to Deseronto, Belleville, Napanee, and Prince Edward
County. The service operates from Monday to Saturday and uses small buses to serve rural
communities.
Green Rider – Hantsport, Nova Scotia
http://www.greenrider.ca
This vanpool service has been running since 1981 and offers rural residents along a commonly travelled
route the opportunity to schedule rides to work and school. The service also transports people to
Halifax and Dartmouth.
Kings Transit – Berwick, Kentville, Wolfville, and County of Kings, Nova Scotia
http://www.kingstransit.ns.ca
This rural public bus system was established in 1981 and serves the above listed county and towns, who
jointly fund the service. In September 2007, the service was expanded to serve Hants County and parts
of Annapolis County.
16 Majkut, 6.
Page | 36
Kootenay Rideshare – Nelson, British Columbia
http://www.kootenayrideshare.com/index.html
This free service helps connect rural residents to share cars and save costs. The website includes
emissions calculators and the ability to form ridesharing groups.
Ottawa’s Rural Routes, OC Transpo – Ottawa, Ontario
http://www.octranspo1.com/community‐events/rural_communities
OC Transpo introduced service to rural communities in 2002, and now serves 13 communities in the
greater Ottawa area. The buses operate during peak hours to serve these small communities.
Specialized Transit – Prince Edward County, Ontario
http://www.pecounty.on.ca/government/rec_parks_culture/properties/transit.php
In 2007, this specialized transit system for elderly and disables citizens was developed. Riders must be
eligible and register through an application process. Trips are scheduled at least one day in advance and
serve social and health needs.
Trius Transit – Charlottetown, Prince Edward Island
http://www.triustransit.ca
This public bus system started in 2005 and serves Charlottetown, Cornwall, Stratford, and some county
lines. Ridership for the transit system is continuing to grow and revenues from transit fares are
offsetting the costs for the system.
Page | 37
AppendixB–DetailedFlowcharts
Meet with team
(define area,
factors, options,
team leaders
Acceptable?
(format, info)
Define
requirements
(area, grid size,
spreadsheet)
Create survey (factors, options,
random combinations)
Define inputs and outputs (GIS
Technician)
Create layers using KML or SHAPE
files (factor locations)
GIS
Server(s) Send files to GIS
Technician
Receive spreadsheet (GIS
Technician)
Model
Development
Data Gathering and Analysis
Yes
No
Send survey to team leader(s)
with instructions
Receive utility survey (team
leader(s))
Complete? (correct info)
No
Yes
Page | 38
Define variables for
calculation of
weights (N, Mn, r,
etc…)
Utility Survey
(utility scores)
Route
Generation
and Testing
Model Development
Yes
Calculation of weights process
Figure 3.1.2
Weights (spreadsheet or
output file)
Define variables for RAS and prepare data sheet / input
table (all grid cells)
Create program to calculate RASi and rank in descending
order
Input Formatting Required?
Accessibility scores in
descending order
No
Plot top 10-50 points in GIS
KML or SHAPE file with plotted
scores
Page | 39
Calculate value of
existing routes
(TRSD)
Total Route
Score(s)
Plan for
Implementation
Route Generation and
Testing
Compare potential/existing
routes and choose one with highest score
Existing Standard Routes?
Use iterative or VRS methods to calculate potential routes and
TRSD
KML or SHAPE file with plotted
scores
Yes No
KML or SHAPE file with plotted
scores
Maps and details for
potential routes
Page | 40
AppendixC–AmbulanceRoutes(IterativeMethod)
Ambulance Origin Destination Time
1 A B A C A D A
Time 45 45 68 68 90 90 406
2 B A B C B D B I B 0
Time 45 45 30 30 60 60 105 105 480
3 C B C D C H C K C 0
Time 30 30 53 53 108 108 48 48 478
4 D A D C D E D 0
Time 90 90 53 53 96 96 478
5 E B E F E N E 0
Time 115 115 65 65 25 25 410
6 F A F B F E F I F 0
Time 70 70 55 55 65 65 50 50 480
7 G C G D G 0
Time 125 125 92 92 434
8 H A H B H 0
Time 95 95 90 90 370
9 I B I D I E I 0
Time 105 105 80 80 50 50 470
10 J A J D J E J 0
Time 130 130 90 90 10 10 460
11 K A K B K D K M K D K 0
Time 65 65 55 55 40 40 38 38 40 40 476
12 L A L C L I L C L 0
Time 60 60 50 50 47 47 50 50 414
13 M A M E M F M I M 0
Time 130 130 47 47 48 48 13 13 476
14 N B N F N J N 0
Time 135 135 85 85 17 17 474
15 A B A C A E A 0
Time 45 45 68 68 125 125 476
16 B A B C B D B K B C B 0
Time 45 45 30 30 60 60 55 55 30 30 440
17 C B C D C J C 0
Time 30 30 53 53 130 130 426
18 D A D C D C D 0
Time 90 90 53 53 53 53 392
19 E H E K E K E 0
Time 90 90 65 65 65 65 440
20 F B F I F J F K F K F 0
Time 55 55 50 50 66 66 12 12 12 12 390
21 G C G 0
Time 125 125 250
22 H A H E H 0
Time 95 95 90 90 370
23 I B I D I G I J I 0
Time 105 105 80 80 10 10 45 45 480
24 J A J D J 0
Time 130 130 90 90 440
25 K A K D K M K N K 0
Time 65 65 40 40 38 38 85 85 456
26 L C L C L C L 0
Time 50 50 50 50 50 50 300
27 M A M K M K M 0
Time 130 130 38 38 38 38 412
28 N B N F N 0
Time 135 135 85 85 440
29 A E A K A 0
Time 125 125 65 65 380
30 B D B K B L B D B 0
Time 60 60 55 55 52 52 60 60 454
Page | 41
31 C B C D C J C 0
Time 30 30 53 53 130 130 426
32 D C D C D 0
Time 53 53 53 53 212
33 E K E K E 0
Time 65 65 65 65 260
34 G H G 0
Time 185 185 370
35 H A H F H 0
Time 95 95 116 116 422
36 I H I J I 0
Time 180 180 45 45 450
37 J K J L J K J 0
Time 63 63 60 60 63 63 372
38 K A K A K A K 0
Time 65 65 65 65 65 65 390
39 M B M K M K M K M 0
Time 112 112 38 38 38 38 38 38 452
40 N C N G N M N M N 0
Time 145 145 33 33 30 30 30 30 476
41 A G A G A 0
Time 120 120 120 120 480
42 B K B M B K B 0
Time 55 55 112 112 55 55 444
43 C D C K C M C 0
Time 53 53 48 48 112 112 426
44 H F H F H 0
Time 116 116 116 116 464
45 I H I K I 0
Time 180 180 50 50 460
46 J K J 0
Time 63 63 126
47 K A K 0
Time 65 65 130
48 M B M 0
Time 112 112 224
49 N C N 0
Time 145 145 290
50 A M A 0
Time 130 130 260
51 B K B M B 0
Time 55 55 112 112 334
52 C M C 0
Time 115 115 230
53 H J H 0
Time 165 165 330
54 I H I K I 0
Time 180 180 50 50 460
55 H M H 0
Time 176 176 352
56 I N I 0
Time 28 28 56
Page | 42
AppendixD–AmbulanceRoutes(EulerianCircuit)
Vehicle #1 Stops K A B C D E F I G
Arrival Times 8:00 9:05 9:50 10:20 11:13 12:49 13:54 14:44 14:54
Vehicle #2 Stops G H J K N M K A B D C
Arrival Times 8:00 11:05 13:50 14:53 9:25 9:55 10:33 11:38 12:23 13:23 14:16
Vehicle #3 Stops C H F I E K D
Arrival Times 8:00 9:48 11:44 12:34 13:24 14:29 15:09
Vehicle #4 Stops D C N J L C B K A
Arrival Times 8:00 8:53 11:18 11:35 12:35 13:25 13:55 14:50 15:55
Vehicle #5 Stops A E H M F
Arrival Times 8:00 10:05 11:35 14:31 15:19
Vehicle #6 Stops F E K B D C J
Arrival Times 8:00 9:05 10:10 11:05 12:05 12:58 15:08
Vehicle #7 Stops J A N M K A B
Arrival Times 8:00 10:10 12:46 13:16 13:54 14:59 15:44
Vehicle #8 Stops B C D G C D C
Arrival Times 8:00 8:30 9:23 10:55 13:00 13:53 14:46
Vehicle #9 Stops C J K M K D A C
Arrival Times 8:00 10:10 11:13 11:51 12:29 13:09 14:39 15:47
Vehicle #10 Stops C D A E H
Arrival Times 8:00 8:53 10:23 12:28 13:58
Vehicle #11 Stops H I N K M C B
Arrival Times 8:00 11:00 11:28 12:53 13:31 15:26 15:56
Vehicle #12 Stops B A M I H E
Arrival Times 8:00 8:45 10:55 11:08 14:08 15:38
Vehicle #13 Stops E N F K A G C B
Arrival Times 8:00 8:25 9:50 10:02 11:07 13:07 15:12 15:42
Vehicle #14 Stops B I H F J
Arrival Times 8:00 9:45 12:45 14:41 15:47
Vehicle #15 Stops J K D C B A F E K C
Arrival Times 8:00 9:03 9:43 10:36 11:06 11:51 13:01 14:06 15:11 15:59
Vehicle #16 Stops C D B A G D C
Arrival Times 8:00 8:53 9:53 10:38 12:38 14:10 15:03
Vehicle #17 Stops C M K A D C B L
Arrival Times 8:00 9:55 10:33 11:38 13:08 14:01 14:31 15:23
Vehicle #18 Stops L I H F M E
Arrival Times 8:00 8:47 11:47 13:43 14:31 15:18
Vehicle #19 Stops E B D C N F
Arrival Times 8:00 9:55 10:55 11:48 14:13 15:38
Vehicle #20 Stops F B M K B C D A
Arrival Times 8:00 8:55 10:47 11:25 12:20 12:50 13:43 15:13
Vehicle #21 Stops A J F B M C
Arrival Times 8:00 10:10 11:16 12:11 14:03 15:58
Vehicle #22 Stops C M B A M
Arrival Times 8:00 9:55 11:47 12:32 14:42
Vehicle #23 Stops M A C B M A
Arrival Times 8:00 10:10 11:18 11:48 13:40 15:50
Vehicle #24 Stops A B M B C A K M
Arrival Times 8:00 8:45 10:37 12:29 12:59 14:07 15:12 15:50
Vehicle #25 Stops M K L A K M K I B D
Arrival Times 8:00 8:38 8:48 9:48 10:53 11:31 12:09 12:59 14:44 15:44
Vehicle #26 Stops D H E K M N B
Arrival Times 8:00 9:35 11:05 12:10 12:48 13:18 15:33
Vehicle #27 Stops B K L C D I J E J C
Arrival Times 8:00 8:55 9:05 9:55 10:48 12:08 12:53 13:03 13:13 15:23
Vehicle #28 Stops C K M N C D I J
Arrival Times 8:00 8:48 9:26 9:56 12:21 13:14 14:34 15:19
Vehicle #29 Stops J C D I B K L
Arrival Times 8:00 10:10 11:03 12:23 14:08 15:03 15:13
Vehicle #30 Stops L C K M N B K L B K
Arrival Times 8:00 8:50 9:38 10:16 10:46 13:01 13:56 14:06 14:58 15:53
Page | 43
Vehicle #31 Stops K I D I B K M N
Arrival Times 8:00 8:50 10:10 11:30 13:15 14:10 14:48 15:18
Vehicle #32 Stops N C F A D I K
Arrival Times 8:00 10:25 11:10 12:20 13:50 15:10 16:00
Vehicle #33 Stops K L C F K M N E J D I D
Arrival Times 8:00 8:10 9:00 9:45 9:57 10:35 11:05 11:30 11:40 13:10 14:30 15:50
Vehicle #34 Stops D J D J A
Arrival Times 8:00 9:30 11:00 12:30 14:40
Vehicle #35 Stops A H B H A H
Arrival Times 8:00 9:35 11:05 12:35 14:10 15:45
Vehicle #36 Stops H A H A K M N G I
Arrival Times 8:00 9:35 11:10 12:45 13:50 14:28 14:58 15:31 15:41
Vehicle #37 Stops I K
Arrival Times 8:00 8:50
