Applied research. Optimization of the Shuttle Services

OPTIMIZATION OF THE
SHUTTLE SERVICE
Instructor: Prof. Farnaz Ganjeizadeh
ENGR 6800 Applied Research in Engineering Management
Spring 2016
Date 05/25/2016
Prepared by
Ramon Rios Rodriguez
Swathini Matheswaran
Deepan Raj Karthikeyan

Optimization of the Shuttle Service

2

ABSTRACT
The increment in waiting times for the shuttle service at XXX has gained much attention.
With this in mind, the purpose of this project is to demonstrate the root causes of the queue in
this service and eliminate them by applying different techniques. The project intends to find out
the passenger’s arrival rate and the percentages of lateness for the shuttle buses by collecting all
the possible data. Provided that, to see the time line deployed, define activities, and allocate
durations MS PROJECT software will be used to follow the performance and progress of the
project that is measured and evaluated with the help of a tracking Gantt chart. After that, to find
out the increment in population per year, linear trend forecasting method is applied to get an
approximate number in increment people per year. Furthermore, Queuing Theory will help to
find the root causes of the queue length in the different pick up locations with its static approach.
Finally, the dynamic mode is also applied by using ProModel Software and simulates the shuttle
service to verify the calculations obtained in the Queuing Theory. Moreover, the shortest
distance is found from point A to point B by using the network model named “the shortest route
technique”. Finding the nearest path from the origin or location A and then the next-nearest path
to minimize the total distance and optimize the time in the system too is what this technique
does. Finally, scheduling of resources technique is used to allocate all of them with an accurately
schedule. The proposed project will have a significant impact on XXXX Shuttle Services as it
will optimize the system and open up a new simulation model for any future doubts in queuing
times with any route.


3

ACKNOWLEDGEMENT
We
would
like
to
take
this
opportunity
to
thank
Professor
Farnaz Ganjeizadeh
for

intellectual
support,
advice,
guidance,
and
all
her
time
invested
during
the
course
of
this

project.


4

Table of Contents
ABSTRACT 2
1 INTRODUCTION 6
2 METHODOLOGIES/APPROACHES 6
2.1 Gantt Chart 7
2.2 Forecasting 7
2.3 Queuing Theory 7
2.4 Pareto Charts 8
2.5 Shortest Route 8
2.6 NPV 8
3 LITERATURE REVIEW 9
4 SELECTED METHODS 10
4.1 Surveys and Data Collection 10
4.2 Gantt Chart 10
4.3 Linear Trend Forecasting 10
4.5 ProModel Simulation 12
5 ANALYSIS 12
5.1 Surveys and Data Collection 12
5.2 Gantt Chart 13
5.3 Linear Trend Forecasting 13
5.5 ProModel Simulation 16
6 DEPLOYMENT AND EXAMPLES 18
7 CONCLUSION 19
8 FUTURE WORK 19
9 INDIVIDUAL CONCLUSIONS 19
9.1 Swathini 20
9.2 Ramon 20
9.3 Deepan 20
REFERENCES 23
APPENDIX 25


5

List of Tables and Figures
NPV Equation 1 9
Table 1. Performance Measures M/M/2 15
Table 2. Performance Measures M/M/1 16
Table 3. Grey Buses Summary 17
Table 4. Failed Passengers Arrivals 17
Table 5. Passengers Summary 17
Figure 1. Simple Queue System 11
Figure 2. Shortest Route for Grey Bus 18
Figure 3. M/M/1 31


6

1. INTRODUCTION
One of the world’s leading health science universities, the University of XXXX, dates its
founding to 1864, when South Carolina surgeon Hugh Toland founded a private medical school
in San Francisco (XXXX History, N.D). For 50 years, from transportation, housing, childcare,
and more, the businesses of Campus Life Services have touched everyone, at every campus
location.
The shuttle service is the biggest operation under campus life services and thousands of
people use the service to commute to work or school. The shuttle service is divided in 16
different routes (See appendix 1) that go to the different campuses in San Francisco and SFGH
(San Francisco General hospital). A survey results showed that the busiest routes are: grey route
that goes from A to B Campus, red route from A to C, blue route from A to D Campus, and gold
route that goes from A Campus to SFGH (San Francisco General Hospital) (Appendix 2 table 6).
Out of these routes, the most used one for commute is the grey route since approximately 40% of
the total riders commute everyday.
For the grey route, both locations have an uncontrollable incremental in the queue every
hour. Passengers are getting frustrated because they don’t get on time to their work, schedules,
meetings, class, etc. Thus, this project is conducted based on this route.
2. METHODOLOGIES AND APPROACHES
In this part, all the methodologies that apply to eliminating the queue were considered.
There are thousands of methods that may apply to this, but for the purpose of the project Gantt
chart, queuing theory, simulation using ProModel software, linear trend forecasting, Pareto


7

charts, net present value or NPV, and shortest route technique with their applications were being
taken into consideration for the following reasons:
2.1 Gantt Chart
The main purpose of the Gantt chart is to assess the duration for the optimization of the
shuttle system project. It will help to establish the order in which tasks need to carry out before
the completion of the project, to find the critical path, and if the case, to level and/or crash
activities to complete the project on time.
2.2 Forecasting
Forecasting is the process of predicting the future events whose actual outcomes have not
been observed yet (Gahirwal & Murli, N.D). In this project, forecasting will help to predict the
future of people in XXXX University that will ride the shuttle for the next 5 years and adjust the
project for the same length. The selection of the method depends on many factors, such as the
relevance and availability of historical data, the time period of the forecast, etc. To have high
performance, XXXX University focuses on robust demand forecasting techniques and process,
which leads to better passenger satisfaction and responses. Hence, time series linear trend
forecasting is the best fit for the purpose of the project.
2.3 Queuing Theory
Queuing is the process of moving passengers in a sequence to specific service according
to the passenger needs (Render & Hanna, 2012). In the XXXX shuttle service; passengers arrive
at the queue waiting for being served or boarding the bus to go to their destination. This theory is


8

to find out the waiting time of the passengers in the queue; waiting time of the passengers in the
system; how many passengers are in the queue, how many passengers in the system, utilization
of the servers, and the different arrivals probabilities that help to find the optimal solution to
reduce the queue. Hence, queuing theory can be applied.
2.4 Pareto Charts
The Pareto chart can be used to analyze the different behaviors of the shuttle arrival times
and passengers’ arrival rates. Also, it can be identified where exactly the problem is and why is
the cause, in other words, finding out the root causes of the main problem.
2.5 Shortest Route Technique
The shortest route technique can be used to identify the shortest distance from one point
to another point in the different shuttle locations. The existing routes in the service may not be
the optimal, so the optimal routes can be found by applying this technique.
2.6 Net Present Value (NPV)
A few projects can be presented in the optimization of the shuttle service, thus the net
present value will compare the money invested with the different cash flow per year or period. A
positive and greater NPV means the better project and quicker return.
The calculation of the NPV can be seen in Eq. 1 where:
NPV = (Cash inflows from investment) – (cash outflows or costs of investment)


9

Formally, the net present value is simply the summation of cash flows (C) for each period (n) in
the holding period (N), discounted at the investor’s required rate of return (r) (What is NPV and
How Does It Work, N.D.).
3. LITERATURE REVIEW
A review of literature indicates that the most effective methodology is The Queuing
Theory to attack the direct root causes of the queue (Yu & Sule, 2014). Another review stated
that the modified circle map model is the best method to find out the causes of delays in the
shuttle industry (Nagatani & Naito, 2011). These delays could be inflow time per passengers to
board the bus, traffic, and other circumstances that might happen. Another review showed that
the method of logistic regression is applied when surveys are in place and need to find out if the
shuttle service is worth it or not (Cao & Wang, 2016). Another review showed that the
optimization model of passenger transportation structure is based on resource constraints that are
built and using Fuzzy comprehensive evaluation method (Yanli & Yuee, 2016). The passenger
transportation structures before and after optimization are calculated. Through the comparison
and analysis bases the effectiveness of optimization model is estimated. Finally, the use of
dynamic programming model for minimizing the total travel time resulting with the set of
preferred tactics are deployed along with the increase of the direct transfers which reduces the
waiting time making the public-transit system more attractive (Yuval & Avishai, 2016)
(Appendix 11).
(Eq. 1)


10

4. SELECTED METHODS
In this chapter, brief descriptions of the all the selected methods for this project are
explained in detail. There are the explication of five primary approaches used and the explication
of the collection of data.
4.1 Surveys and Data Collection
To start the research of this project, random surveys were performed and data were
collected against them. Surveys are used to find out what are the needs of the passengers and
what are their biggest concerns regarding the shuttle system.
Another strategy was to take the time for the arrival passenger per hour. This helped to
identify what is the arrival distribution, such as binomial, normal, Poisson, exponential, etc.
4.2 Gantt Chart
Gantt chart was selected because it visually depicts what tasks are to be done at what
point in our project in order to move forward. These charts help us to:
• Track the project schedules and any additional information about the tasks.
• Have a clear view of the relationships of the various tasks and the dependency of the
completion of another task to meet the project completion.
• Figure out if the project needs any additional resources if it is not completed on time.
4.3 Time Series – Linear Trend Forecasting
When the arrival time of the shuttle is treated as time series, trend estimation can be used
to make and justify the statements regarding drift in the data (Koopman & Ooms, 2016).


11

Passenger
population

Queue
Service

Determining the trend of the population of riders per year exhibits an increasing or
decreasing order and depending upon these results; forecasting can be done for next 5 years. It is
useful in making decisions on whether to buy more buses or not or increasing the bus frequency
for that schedule time.
4.4 Queuing Theory
The major project’s aim is to minimize the waiting time in the queue of the passengers.
The queuing theory and its formulas will help to find out the root causes and attack to reduce the
long waiting lines and the passengers in the system (Render & Hanna, 2012). The shuttle service
is restricted to use one of the common scheduling algorithms with a single queue model:
FCFS (First Come First Serve): The passengers are served in the order of their arrival,
without any partiality or priority (Render & Hanna, 2012).
Single Queue (SQ): In figure 1, the passengers wait until the next schedule shuttle
arrives.
Arrival Departure
Figure 1: Simple Queue System


12

4.5 Simulation Using ProModel Software
Another method is Pro Model simulation. By modeling the important elements of the
shuttle system, leaders can experiment with different operating strategies and designs to achieve
optimal performance for this service (What’s New in ProModel 2011, 2015).
4.6 Shortest Route Technique
The shortest route method is useful to find the optimal path in any route by choosing the
nearest one. This leads to reduction in shuttle traveling time and the waiting time for the
passengers.
5. ANALYSIS
After the selection of methods, the results and analysis of the different approaches are
described in this section. Analysis of the outcomes of every method used is analyzed and the best
option will be presented.
5.1 Surveys and Data Collection
The optimization of the shuttle service began with the collection of all the possible data.
First, the study was conducted to a survey, where 5,000 people per question were interviewed.
The results as expected were: 5000 people use the shuttle service, where 4,000 use it every day.
3,500 people are concerned when the bus gets full before they get on board and 1,500 when the
bus is late (Appendix 3).


13

Staff at XXXX provided collection of tardiness for all the year 2015 for the grey route.
The allowed late time per route is 5 to 10 minutes as a max and these results showed that for 7
months the grey route in general (including all) were late over the allowed time (Appendix 3).
Collection for the passengers’ arrival rate was also in place. Thus, the arrival rate for this
route is also calculated by plotting in a chart the time and number of passengers and then
comparing it with the different distributions, such as binomial, Poisson, and Exponential. In
conclusion, the passenger arrival rate is Poisson distribution of 1.58 passengers per minute
(Appendix 4).
5.2 Gantt Chart
The total of different activities and allocated times are listed in MS Project using the
Gantt chart. A Gantt chart, commonly used in project management, is one of the most popular
and useful ways of showing activities (tasks or events) displayed against time. To summarize, a
Gantt chart shows what (activities) and when (the schedule) has to be done (What is Gantt chart,
2012). After the Gantt chart was tracked, the total project time was 38 days starting on
04/11/2016 and finishing on 06/01/2016 without any delay in the different activities, so the need
to crash activities or level resources was not necessary (Appendix 5).
5.3 Linear Trend Forecasting
In order to have more precisely results in the shuttle system and get a longer project life
cycle, linear trend forecasting technique is used to predict an approximation of the increasing
population of riders in the system. "Linear trend forecasting works well for the most basic of
operations management and supply issues, for example, analyzing population over time to


14

predict future demand” (Linear Trend Forecasting, 2009). Like all the linear equations, this
method also uses a linear regression equation: y=427x+4154.6 and 𝑅!
=. 999974. (Appendix 6)
Where:
• y: is the number of passengers to be calculated.
• m: is the slope of the line, which equals the change in the y value divided by the change in the
x value. 
• x: is the given data point or the dependent variable, in this case, it is passengers per hour.
In the final analysis for forecasting, the results showed that it would be an increase of
40% for the next 5 years of riders (Appendix 6). Therefore, this increase in real numbers means
that from 361 riders for the hours of 7am-12pm in 2015, in 2019 will be 509 passengers for the
same hours. In other words, this project’s life cycle will be over 5 years.
5.4. Queuing Theory
In the actual system, passengers arrival rate is greater than the service rate, ρ =
!
!
> 1, so
this means, queuing theory cannot be applied to this system because it is an infinite increment in
the queue. Thus, the first action to take was to increase the capacity by adding a 30 passengers
bus and apply queuing theory to find out the utilization of the servers, passengers waiting times,
and passengers in the queue.
The system is using a model of arrival distribution/service distribution/number of servers
open or, in other words, M/M/1 (Appendix 7 Fig. 3). Thus, after analyzing this, the M/M/2 is
applied to compare the differences in the models. Formulas in table 1 were applied to find the
different variables. The results were very critical because the utilization ρ was below 40% per
server, which means the servers are not utilized properly and basically are running empty with


15

just a few passengers on board. The waiting time of passengers Wq decreased dramatically from
long waiting times to 5.36 seconds in the queue and 35.36 seconds in the system. The probability
of 0 passengers in the system is high 56% and the probability >5 passengers in the system is 0%
(Appendix 8).
Table 1: Performance Measures for model M/M/2
Utilization rate 1 − 𝜋! = 1 −
!!!
!!!
=
!!
!!!
Mean number of customers in the
system
𝐿 =
2𝜌
1 + 𝜌!
Mean time to go through the system
𝑊 =
2𝜌
𝜆 1 − 𝜌!
=
1
𝜇 1 − 𝜌!
Mean waiting time in the queue
𝑊! = 𝑊 −
1
𝜇
=
𝜌!
𝜇 1 − 𝜌!
queue
𝐿! = 𝜆𝑊! =
2𝜌!
1 − 𝜌!
The model of M/M/2 is not the solution to the problem, so the application of the model
M/M/1 is applied again with the new added bus. The formulations for this model are written
below in table 2. Results were a lot better since utilization is 79% per server, the number of
passengers in the queue Lq= 1.43 or 2 passengers per minute, the waiting time or Wq= 54.77
seconds or about a minute, and the waiting time in the system or Ws= 84.77 seconds (Appendix
9). The probability of having more than 20 passengers waiting is 1%, which is very low.
Apparently this is the optimal solution however, more calculations need to be done to verify
these results.


16

Table 2: Performance Measures for model M/M/1
Utilization rate 1 − 𝜋! = 1 − 1 − 𝜌 = 𝜌
system
𝐿 =
𝜌
1 − 𝜌
Mean time to go through the system
𝑊 =
𝜌
𝜆 1 − 𝜌
=
1
𝜇 1 − 𝜌
Mean waiting time in the queue
𝑊! = 𝑊 −
1
𝜇
=
𝜌
𝜇 1 − 𝜌
queue
𝐿! = 𝜆𝑊! =
𝜌!
1 − 𝜌
5.5 Simulation using ProModel
ProModel simulation will help to verify the outcome of the queuing theory because the
outcome of which is less accurate than the outcome of the simulation. Thus, more optimal results
can be obtained.
First, the layout of the service was drawn and the code for the simulation was built
(Appendix 12). Then, the outcome came out with utilization per shuttle of 84.4%, 84.2%, 83.8%,
and 83.2% for the grey shuttles 1-4 respectively. (Table 3)


17

Table 3: ProModel Grey Shuttles Summary
The failed passengers outcome showed that a total of zero failed arrivals was during the
simulation process. This means that all the passengers find a seat in the bus in from 7 am-12 pm.
(See table 4).
Table 4: ProModel Failed Passengers Arrivals
The summary of passengers in table 5 shows that the waiting time in the system per
passenger or Ws is 5.05 min, the waiting time in the queue per passenger or Wq is 3.56 min, the
moving time or travel time is 30 min, and the average of entry is 475 passengers in 5 hours.
Table 5: ProModel Passengers Summary
After all, the optimal solution was found with the queuing theory method and it is
verified by ProModel. So the optimal solution is: Add a 30-passengers shuttle and change the
frequency from 20 minutes to 15 minutes is the right solution because the queue will be reduced
dramatically from over 20 minutes waiting in the queue and an average of 5 people left for not
enough capacity now the Wq is 3.56 minutes and failed arrivals is 0.


18

5.6 The Shortest Route
The shuttle system starts from Mission Bay Campus or point A, when passengers start
boarding the bus and ends in the destination Parnassus Campus or point B when the last
passenger gets off the bus. The actual time of the passengers is 35 minutes to go to the next
location.
The results of the shortest route technique showed that the optimal path for the grey route
in time is only 25 minutes (Fig 2 red path). Modifying the old route of 35 minutes to the new one
of 25 minutes, the waiting passengers time will be even less and the optimization of the service is
also improved (Appendix 10).

Figure 2: Shortest Route For Grey Bus
6. DEPLOYMENT AND EXAMPLES
The optimization of the shuttle service at XXXX project is to be used in all shuttle
services and apply to any route. In the near future, if XXXX has delays problems in any route
and unhappy customers because of the capacity of the buses or the schedule, this project can be


19

used with the right calculations of the arrival rates, service rate, and schedule times to solve these
problems.
Also, this project is not limited to use for USCF shuttle service, it can be used for any
transportation service that has schedule pick up times and follows a specific route. Again, the
arrival rates and service rates need to be adjusted for any particular situation.
7. CONCLUSION
This article documented the survey results of passengers that ride in the XXXX
University shuttle service. These surveys and data collected showed evidence that the demand
was greater than the capacity and a solution needed to be done.
It was introduced customized shuttle as the way to reduce the waiting time of the
passengers by taking them from Mission Bay to Parnassus and back riding in the Grey route
through the City of San Francisco as the case study. The analysis of the customized shuttles
indicates that in order to reduce the waiting time of the passenger, the service should be designed
in essential ways to serve customers.
Based on time series, linear trend forecasting helped to find out the project life cycle.
Also, queuing theory method helped to find out the root causes of the queue by defining
utilization of the buses, waiting times, number of passengers per hour, etc.
Finally, the study suggests that there is a strong potential for the deployment of adding
another shuttle bus for the peak hours of 7am-12pm and 4pm-7pm.


20

8. FUTURE WORK
After analyzed all the outcomes for the different approaches used, future work would be
the increment of the capacity by adding a grey bus to the three already existing in the service and
change the departing times from 20 minutes to 15 minutes. Doing so, the waiting time of the
customers in the queue or Wq=3.56 minutes which is minimal and failed arrivals is 0, thus the
goal has been achieved. Not only that, but the shortest route was found and 25 minutes back and
forth can be done by changing the route. Hence, assuming 4 minutes for loading and unloading
passengers a total of 29 minutes can be achieved. Also, after analyzing the Pareto chart for the
grey shuttle, when the shuttles are most of the time on time in the months of January, April, June,
July, and December; basically when everybody is on vacations because in other months people
are all on the road. For these particular months, limited shuttles will operate and when the peek
seasons come, a shuttle will be added to the routes and we can balance our budget.
9. INDIVIDUAL CONCLUSION
Swathini: In this paper, optimization of the shuttle services in XXXX was done using
forecasting and queuing model that is needed to serve the passengers. After running the model
using the data collected, we found that only few months in a year required more buses than
usual. More buses are required to run during these months to accommodate the passengers who
use XXXX shuttle services during the peak hours – 7AM – 12PM. In order to make a decision,
the data where forecasted for the next 5 years and found that the count of the passengers
increased every year causing more wait time. For XXXX University, waiting time of the
passenger should be less as it is being used by the students, patients and staffs. To avoid
passenger waiting time an optimal solution is provided where the shuttle can run most frequently


21

during the peak hours using the backup shuttles where it would be economical to the University
instead of buying new shuttles or it can also be done by increasing the capacity of the shuttles
with a limit of 40 passengers per trip. With the decrease in waiting time, XXXX shuttle services
can provide a great level of satisfaction to the passengers.
Ramon: All the selected methods were well presented and adding a bus according to our
calculations was the right solution. However, money wasn’t considered, so if an analysis with
financial models is presented, may not be the right solution just adding a bus. Another thing, if
we increase the capacity of the buses by adding one bus, is the same thing as adding a bigger
bus. Right now, there aren’t bigger buses than 30 passengers, but this might be a solution and the
extra resources wouldn’t need, but investment would. A 60 passengers bus is approximate
$350,000 with a life of 12 years. I don’t know if it’d worth it or not because the analysis has to
be made, but we can have it as a consideration if this project is execute.
Deepan: According to me this article is review and documented the survey of shuttle passengers
of XXXX University. Using the survey we forecasted the demand of more shuttle service. Using
the queuing theory we customized the shuttle service in the way to reduce the passenger waiting
time of XXXX students and staff by taking their Mission Bay and Parnassus route of the Grey
bus.
Based on the Time series – Linear trend Forecasting we forecasted the survey results. So, Based
on all these study suggests that there should be an additional shuttle service to reduce the waiting
time for the passengers, which will be helpful for both students and staffs to do their work


22

according to their schedule. I think adding/buying more Shuttle Buses or Increasing the shuttle
capacity both are same, which proves the needed.


23

REFERENCES
XXXX History. (n.d) Retrieved May 15, 2016, from: https://www.XXXX.edu/about/history-3
Gahirwal, M., Mrs., & Murli, V. (n.d.). Inter Time Series Sales Forecasting. Retrieved from:
http://arxiv.org/pdf/1303.0117.pdf
Render, B., Stair, R. M., & Hanna, M. E. (2012) Quantitative analysis for management. (Waiting
Lines and Queuing Theory Models, page 499-532) Upper Saddle River, NJ: Pearson
Prentice Hall 2012. Print.
What is NPV and How Does It Work? (n.d.). Retrieved May 15, 2016, from:
http://www.propertymetrics.com/blog/2015/06/11/what-is-npv/
Yu, M., & Sule A. (2014, May 13). Strategic queuing behavior for individual and social
optimization in managing discrete time working vacation queue with Bernoulli
interruption schedule. Retrieved from:
http://www.sciencedirect.com.proxylib.csueastbay.edu/science/article/pii/S03050548163
00612.
Nagatani, T., & Naito, Y. (2011, July 6). Schedule and complex motion of shuttle bus induced by
periodic inflow of passengers. Retrieved from:
00194.
Cao, Y., & Wang J. (2016, February 10). The Key Contributing Factors of Customized Shuttle
Bus in Rush Hour: a Case Study in Harbin City. Retrieved from:
Yanli Ma., & Yuee Gao. (2016, February 10). Passenger Transportation Structure Optimization
Model Based on User Optimum. Retrieved from:
http://www.sciencedirect.com/science/article/pii/S1877705816002642
Yuval Hadas., & Avishai (Avi) Ceder. (2010, June 7). Optimal Coordination of Public-Transit
Vehicles Using Operational Tactics Examined by Simulation.
Retrieved from:
http://www.sciencedirect.com/science/article/pii/S0968090X10000586


24

10. Koopman, J., & Ooms, M. (n.d.). Forecasting economic time series using unobserved
components time series models. Retrieved May 14, 2016, from:
https://www.gwu.edu/~forcpgm/SiemJanKoopman-final-2010UCForecasting.pdf
What's New in ProModel 2011. (2015). Retrieved May 15, 2016, from:
https://www.promodel.com/Products/ProModel
What is a Gantt chart? (2012). Retrieved May 15, 2016, from http://www.gantt.com/
Linear Trend Forecasting. (2009). Retrieved May 15, 2016, from:
https://www.kbmanage.com/concept/linear-trend-forecasting


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APPENDIX
1. Shuttle Service 16 different routes
2. Table 6. Busiest routes and destinations
Shuttle Grey Red Blue Gold
Routes
Mission bay –
Parnassus –
Mission Bay
Mission Bay –
MCB – 16th
Bart
– MCB – Mission
Bay
Mission Bay –
Mt. Zion –
Parnassus –
SFGH – Mission
Bay
Mission Bay –
SFGH –
Parnassus – MT.
Zion – Mission
Bay
Service 3 times per hour 2 times per hour 4 times per hour 4 times per hour
Frequency 20 minutes 15 minutes 15 minutes 15 minutes


26

0

1000

2000

3000

What
color
is
the

route
you
usually

ride?

What
color
is

the
route
you

usually
ride?

0

2000

4000

6000

1
2
3
4
5

How
many
times
per

week
do
you
use
the

shuttle
service

How
many

times
per
week

do
you
use
the

shuttle
service

0

2000

4000

Late
Full

What
do
you
like

least
out
of
the

shuttle
service?

What
do
you

like
least
out

of
the
shuttle

service?

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%

Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec

%Late

Months
2015

Tardiness
Chart
Grey
Bus

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

3. Surveys and data collected
0

2000

4000

6000

Yes
No

Do
you
commute
in

the
XXXX
shuttle?

Do
you

commute
in

the
UCSF

shuttle?


27

4. Poisson distribution


28

5. Gantt chart


29

5. Gantt chart (continue)


30

6. Forecasting Charts
320

340

360

380

400

420

Forecasted
Value

Month

Forecasted
Value
(7AM
-‐
12PM)

y
=
362.31e0.0076x

300

320

340

360

380

400

420

440

460

FORECASTED
VALUES

YEAR

FORECASTING
FOR
2016

y
=
427x
+
4154.6

R²
=
0.99974

0

1000

2000

3000

4000

5000

6000

7000

8000

2015
2016
2017
2018
2019

FORECASTED
VALUE

YEAR

Forecasted
Value
(7AM
-‐
12PM)


31

7. M/M/1
Fig. 3
8.QM solutions for proposed M/M/2
Waiting lines results:


32

8.QM solutions for proposed M/M/2 (continue)
Table of Probabilities:
Sensitivity of the numbers of servers
Chart of Probabilities


33

9. QM Solutions for proposed M/M/1
Service Solutions
Table of probabilities
Chart of Probabilities


34

10. QM results for shortest route


35

11. Summary of the literature review.
Reference Topic Method Strength Weakness
Miaomiao
Yu &
Attahiru
Sule Alfa
May 13,
2014
Strategic queuing
behavior for individual
and social optimization
in managing discrete
time working vacation
queue with Bernoulli
interruption schedule
Queuing
Theory with
Bernoulli
Mixed strategy for
individual
optimization and
long planning
No transition rate
diagram for the
observable queues.
Insufficient
assessment.
Takashi
Nagatani
& Yuichi
Naito. 6 of
July 2011
Schedule and complex
motion of shuttle bus
induced by periodic
inflow of passengers
Nonlinear
Map,
Simulation
The dynamic model
for the shuttle bus
with the periodic
inflow of passengers
in terms of the
nonlinear map.
Insufficient
Scenario Analysis
Yang Cao
& Jian
Wang,
2016
The Key Contributing
Factors of Customized
Shuttle Bus in Rush
Hour: a Case Study in
Harbin City
The method
of Logistic
Regression,
Nagelkerke
R square
The advantage of
logistic regression is
a kind of curve
model of
classification
variable and
Insufficient
Scenario Analysis


36

multiple factors.
Yanli Ma
& Yuee
Gao, 2016
Passenger
Transportation
Structure Optimization
Model Based on User
Optimum
Probability
distribution
function for
optimizatio
n, Matlab
and Fuzzy
Compressiv
e Method
Evaluation method
and the comparison
of these results
demonstrated the
effectiveness of
optimization model.
Inadequate
explanation for the
evaluation model
Yuval
Hadas &
Avishai
(Avi)
Ceder,
2010
Optimal Coordination
of Public-Transit
Vehicles Using
Operational Tactics
Examined by
Simulation
Simulation
and a
Dynamic
Programmi
ng
Operational
Tactics
Comparison of
Global & Local
optimization and
Simulation &
Dynamic
Programming
optimization results
in an effective and
efficient model
Insufficient
Assessment


37

12.12. ProModel Code.


38

12.ProModel Code (Continue)
13. ProModel Layout

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