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

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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.


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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.


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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 4.4 Queuing Theory 11 4.5 ProModel Simulation 12 4.6 Shortest Route 12 5 ANALYSIS 12 5.1 Surveys and Data Collection 12 5.2 Gantt Chart 13 5.3 Linear Trend Forecasting 13 5.4 Queuing Theory 14 5.5 ProModel Simulation 16 5.6 Shortest Route 18 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


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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


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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


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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


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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)


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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)


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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).


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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


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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).


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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


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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


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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!=

1𝜇 1 − 𝜌!

Mean waiting time in the queue 𝑊! = 𝑊 −

1𝜇=

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.


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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 −1𝜇 =

𝜌𝜇 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)


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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.


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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


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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.


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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


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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


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according to their schedule. I think adding/buying more Shuttle Buses or Increasing the shuttle

capacity both are same, which proves the needed.


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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/S0305054816300612.

Nagatani, T., & Naito, Y. (2011, July 6). Schedule and complex motion of shuttle bus induced by

periodic inflow of passengers. Retrieved from: http://www.sciencedirect.com.proxylib.csueastbay.edu/science/article/pii/S0378437116000194.

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: http://www.sciencedirect.com.proxylib.csueastbay.edu/science/article/pii/S18777

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


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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


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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)


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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