Simulation study of the BART station at Embarcadero in San Francisco using Arena. The model compares the wait time for passengers at the station for multiple scenarios analyzed within.

1. BART Station Simulation at Embarcadero, SFO
using Microsoft Arena
1st
December, 2017
Preethi Jayaram Jayaraman
BANA, Class of 2017
M12420360

2. CHAPTER 1:
INTRODUCTION
SYNOPSIS:
This project submission is intended to showcase Simulation concepts learnt during the coursework for
BANA 7030 Fall 2017 and apply them to a working model of a real-world situation using Microsoft Arena.
Arena provides options to extend the run length of the simulation to as per the modeler’s choice and run
multiple replications of the model so that statistical analyses can be performed. The outputs obtained
from Arena’s simulation model were analyzed and read into the Arena Process Analyzer module to
perform comparisons in the model performance across multiple scenarios. The comparisons helped make
recommendations to the system modeled.
PROBLEM STATEMENT:
For this project, the problem statement chosen was one that simulates the BART Station in San Francisco
during the peak hours of 4 PM to 8 PM during a weekday. The chosen peak time reflects the busiest day
in the train station. Hence, the waiting time and number of passengers in the system calculated by the
model will reflect the footfall in the station during the peak time. The simulation was run for 5 days and
30 replications of the model were performed to evaluate statistical significance of the outputs obtained
from Arena.
ABOUT THE BART:
The BART Station in San Francisco is a primary mode of transportation for people who live in the Bay area.
The BART started its service as early as September 11, 1972 and has since remained among the major
forms of commute across San Francisco, East Bay and South Bay. The BART 2017 Factsheet published that
“Embarcadero and Montgomery stations are the busiest in the BART system. In FY16, over 180,000 trips
were made to or from these stations each weekday. During peak commute hours, nearly 70,000 people
ride through the Transbay Tube in each direction.”. The BART currently runs across 45 stations with an
average of 724 trains dispatched per weekday. An average trip length for a passenger spans over 14.4
miles for an average passenger fare of $3.80. 3.24 billion riders in FY2016 recorded a total of 128.5 million
trips in FY 2016.
The Figure below (Fig. 1) shows the map of the BART system in the Bay area.

3. RELEVANCE OF THE PROBLEM STATEMENT:
Clearly, the BART system faces its largest passenger traffic at the peak times. While the BART schedule
accommodates for the peak in passengers by increasing the frequency of trains, peak times also record
the most congestion in the platform. By simulating the Embarcadero train station, I want to evaluate the
average number of passengers waiting in the station and their average waiting time during the peak hours
on a weekday. I also want to identify if there are any bottlenecks in the system and compare scenarios
that would make the model work closer to reality.
ASSUMPTIONS:
1. Number of Passengers at arrival: I assumed the following probability distribution for the
number of passengers that arrive at a time into the station.
# of Passengers that enter together Probability Distribution
1 35%
2 30%
3 15%
4 10%
5 10%

4. This assumption was made because many of the peak time riders work near the Financial District
in SF and leave work together. They enter the BART together and then then fork away to travel
on their respective train lines.
2. Passengers with tickets: I’ve also assumed that 40% of the peak time riders have a ticket
(or a monthly pass) and so the rest of the passengers would queue up at the Ticketing machine to
refill their (Clipper) card or buy a ticket.
3. Direction of Travel: I’ve further assumed (with the knowledge of the number of train lines
that travel towards the East Bay), that 65%of the peak rider travel towards the East bay, while the
rest travel towards the Peninsula.
4. Choice of Train line: I used the following logic to assign a probability that’ll assign each
passenger with an intended direction of travel. I calculated the ratio of trains that travel to Dublin
Pleasanton (30%) over all trains that travel to the Easy bay during the peak hour period earlier
defined. I assumed that with 30% probability, peak riders will want to travel to Dublin Pleasanton.
Using this logic, I assigned the below probability distribution for the travel routes of the riders.
Direction – East bay Probability Direction – South Bay Probability
Dublin Pleasanton 30% 24th
Street 9%
Richmond 22% Millbrae 26%
Pittsburg Bay Point 20% Daly City 41%
Warm Springs South Fremont 18% SF Airport 24%
Others 10%
5. This simulation model does not account for the passengers who left the system after waiting a
while for the BART. It assumes that whoever enters the BART station leaves the station only by
boarding the train
6. Passengers who transfer from another train are also not specially accounted for. They are
considered equivalent to a new passenger who enters the system
7. No breakdown time of any of ticketing kiosks/ train lines are considered. Subsequently, no delays
as a result of breakdowns are considered in the system

5. CHAPTER 2:
DATA COLLECTION, MODEL ELEMENTS, FITTING DISTRIBUTIONS TO DATA
DATA COLLECTION:
The model developed for this project required data to be collected for the passenger arrival times,
ticketing process and train arrival times. I fitted distributions to the data collected over twenty minutes at
the train station entry and the Ticket kiosk. I also fitted distributions to the train arrivals data based on
the BART schedule during the peak hours for each of the train lines.
MODEL ELEMENTS:
Figure 2 is a flow-chart of the entire simulation model at the Embarcadero station. Based on the below
flow chart, the simulation model was built and then data was collected.
Fig 2. Flow chart of the proposed model
In the model flow chart proposed, the passenger arrives at the station. If the passenger has a ticket, he/she
heads directly to the station to wait for the train. If the passenger doesn’t, then they head to the station
after they purchase the ticket. Once the respective train arrives at the station, the passenger boards the
train and leaves the station.
FITTING DISTRIBUTIONS TO DATA:
The raw data collected for each of the elements in the model recorded the inter-arrival times between
each of the passengers at entry, the process time at the Ticketing Kiosk and the inter-arrival time between
different train lines. Distributions for the data were fitted using Arena’s Input Analyzer.

6. I. Passenger Arrival Times
II. Ticketing Process time

7. III. Dublin- Pleasanton Line:
IV. Richmond

8. V. Pittsburg – Bay Point

9. VI. Others
VII. 24th
Street

10. VIII. Millbrae
IX. Daly City

11. X. SF Airport

12. CHAPTER 3:
MODELING
SIMULATION MODEL BUILDING:
The model built to simulate the BART station was based on the flowchart in Fig.2. As a passenger arrives
into the BART station, a decide module with a probability of 0.4 of passengers having tickets, separates
passengers into ones that have tickets and others that don’t. After the passengers that don’t tickets buy
one (they go through a process module to buy the ticket), these passengers along with the ones that
already had tickets go through a Decide module that separates passengers based on their Direction of
travel. Passengers go to the East Bay with a probability of 0.65. Once this bifurcation is done, passengers
go through an additional decide module that decides which train line they want to take. At this point,
passengers wait till the train arrives at the Station. Once the train comes in, they take the train and exit
the system. This last section was completed using Hold and Signal modules. Each train line was given a
specific signal value that will be flashed by the Signal module when the train arrives at the station. When
the signal value is flashed, the Hold module releases the passengers that have been waiting for the train,
up till a maximum limit of passengers who can board the train. This limit is set using variables within the
Hold module, 9 of which are created for this purpose.
The entire simulation follows the below steps:
1. Passenger enters the Station
2. Passenger buys a ticket, if he/she doesn’t have one
3. Passenger goes to the respective platform based on where he wants to travel – East/ South Bay
4. Passengers wait for the Train
5. Train arrives at the Station
6. Passenger boards the train and leaves the Station
Fig 3: Passenger-side of the Simulation

13. Each of the train lines have their own Hold and Signal
modules. Figure 3 and 4 show the passenger and the train
side of the simulations respectively.
Fig 4: Train side of the Simulation
The modules used in the Arena simulation based on the above steps are now explained.
1. Passenger enters the Station
A Create module was used to create a Passenger arriving at the Station. A new entity type called
Passenger is created along with this module. The rate at which the passenger arrives at the station
was determined using the Input Analyzer. As this simulation captures the peak time at the station,
a probability distribution was used to determine the number of entities per arrival. An expression
called ‘Pass’ was created for this with a value, DISCRETE(0.35,1,0.65,2,0.8,3,0.9,4,1,5).
A decide module then decides if the passenger has a ticket or not. For this decide module, a
probability of 0.4 is used for passengers who have a ticket as they enter the station.

14. At this point, two assign modules are used, one for passengers who entered the BART with tickets and
one for passengers who bought a ticket at the BART station. Attribute, ‘Had Ticket’ marks the passengers
with 1 for ones who had a ticket on arrival and 0 for ones that bough the ticket at the Station, and
attribute, ‘Arrival Time’ records the arrival time TNOW for each passenger.
2. Passenger buys a ticket, if he/she doesn’t have one
The ‘Buy a Ticket’ Seize Delay release module used a resource, Ticket Kiosk. There are 5 Ticket Kiosks
at the BART station in Embarcadero that the passengers can use. Also, the process of buying a ticket
takes a customer some time, which is given by an expression calculated using the Input Analyzer.

15. 3. Passenger goes to the respective platform based on where he wants to travel – East/ South Bay
Passengers’ decision to travel to the East or the South Bay is determined using a Decide module
with 0.65 probability that the passenger wants to travel to the East Bay. This is an assumption of
the model made as a majority of the peak riders commute to the East Bay.
Followed by this decision, the passengers’ decision of the train line is made using two separate
decide modules, one for the East Bay train and another for the South Bay trains. The probability
distribution used for this decision is mentioned earlier in the assumptions section.

16. 4. Passengers wait for the Train
Passengers for each of the trains (5 towards the East bay and 4 towards the South Bay) wait in 5
independent hold modules. The limit for the number of passengers who can board the train when
it arrives at the station is mentioned by the variable defined in the Limit field in the Hold module.
9 different queues for each of the train lines is defined in the Hold module.

17. Similarly, 4 such modules were created for the
South Bay bound trains with unique Signal
values and individual queues.
5. Train arrives at the Station
A create module was used to have a train entity enter into the system. The frequency at which the
train arrives at the station is defined by the expression that was generated using the Input Analyzer.
A screenshot of two of the train entities (East Bay bound, and South Bay bound) is shown below. A
total of nine such entities were created, one for each line.

18. The create module is followed by a Signal module that flashes the signal value, which appropriately
releases all the Passenger entities held in the Hold module. One Signal module for each of the 9 train lines
was created with corresponding Signal values.
6. Passenger boards the train and leaves the Station
Once the train arrives at the station, before the passenger leaves the station, another decide module was
used to split the passengers again into ones that had tickets and others that did not, so that the overall
waiting time for these passengers can be calculated. This was done using the two record modules shown
below.

19. The Record module is followed by the Dispose modules for both passenger and one for each of the 9 train
lines.
Below is a screenshot of all the queues in the system.

20. RUN SETUP:
The simulation was run during the peak hours of a weekday for 5 days. The model was replicated for 30
runs so that statistical analyses could be performed. A screenshot of the run setup for the model is shown
below.

21. QUEUE ANIMATION:
Below is a snapshot of the Queue animation of the train station simulation. The box on the left shows the
number of passengers waiting to get a ticket issued, while the boxes on the right show the number of
passengers waiting to board the trains. The text boxes show the number of tickets issued and the number
of trains that arrived at the Embarcadero station, picked up passengers and exited the station.

22. CHAPTER 4:
RESULTS AND INTERPRETATION
Arena posts the results of the simulation after a model successfully runs to completion. The Category
Overview reports that gets generated has information in sections about the Entity, Queue, Resource and
User specified variables. This system of BART simulation run for peak hours (4 to 8 PM) for 5 days recorded
an average of 3,089 passengers that were serviced during this period.
ENTITY RELATED OUTPUTS
At the entity level, outputs such as Number of Passengers who used the BART and their total time in the
system are key. As this simulation was run for 30 days, Arena generates the outputs and provides the half-
width, minimum and maximum for each output metric.
A passenger waits for an average of 19.39 +/- 2.94 minutes for a BART at the Embarcadero station. On an
average, the total time spent by a passenger for the BART is 21.91 +/- 2.95 minutes.
The Number outputs show us that over 5 weekdays in a week 2344 +/- 17 passengers used the BART. The
number of trains that serviced these passengers are also mentioned in the attached output figure.

23. QUEUE
The queue related outputs show the waiting time for each process and train and the average number of
people waiting at every queue.
The figure above shows that on an average people wait for 21 +/- 5 minutes for a ticketing kiosk to be
available. Adding an additional ticket kiosk resource could reduce this queue time and reduce the overall
waiting time for passengers. On an average, a passenger who wants to board the Dublin Pleasanton line
waits 7.65 +/- 0.07 minutes for the train. Similarly, the figure shows the average wait time for all such
passengers.

24. The figure above shows that on an average, there are 25 +/- 6 people waiting in line for the Ticket kiosk.
Though there are 5 kiosks available, this means that there is a queue of 5 +/- 1 people waiting for the kiosk
at all time during the peak hours. For the Dublin- Pleasanton train, on an average 3 people are waiting to
board the train. Similarly, the figure shows the number of passengers waiting for each train.
RESOURCE:
The only resource available in this model is a Ticketing Kiosk. There are 5 such kiosks whose outputs are
shown below.
The resource utilization metrics provided above shows the how much the resource is being used and if it
could be a potential bottleneck in the system. The utilization rate of the Ticket Kiosk in this model is
0.9673, which is very high for any resource. On an average, all the kiosks are busy during the peak hours.

25. USER SPECIFIED:
The user specified statistics collected in this system calculate the total time spent in the system of
passengers who had a ticket at entry and ones who bought a ticket at the station.
Clearly, the numbers from the table below indicate that any passenger who bought a ticket at the station
spent an average of 31.97 +/- 4.86 minutes at the station, whiles ones with tickets spent 7.09 +/- 0.05
minutes at the station.

26. CHAPTER 5:
ALTERNATE SCENARIOS AND IMPROVEMENTS
ALTERNATE SCENARIOS:
Alternate scenarios for this simulation model are considered by increasing the number of kiosks at the
train station – from 5 kiosks (base case) to 9 ticketing kiosks. Comparison of these 5 scenarios shows us
the expected reduction in average total time in the system and waiting time for all passengers.
Passenger Average Wait times and Total Time in System:
From the two charts below, we can see that the total time and the wait time for the passengers at the
station is the least when there are 9 kiosks available at the station. However, there is a large
improvement in waiting time when we increase the number of kiosk machines from 5 to 6, and this
increase isn’t stark when we increase one kiosk at a time from 6 onwards.

27. Resource Utilization:
From the resource utlization chart below, we can see the resource utlization of the kiosk falls from .967
to 0.550, which means that even during the peak times, 45% of 9 kiosks will not be used. Hence,
increasing the number of kiosks from 5 to 6 might serve the purpose and further improvement in the
waiting time might not be the best solution.
STATISTICAL ANALYSIS:
Fig: Passenger Total Time Output Statistics
From the igure above, we can see that for 5 kiosks, the passenger minimum average total time in system
is 18.97 +/- 2.95 minutes. Increasing the number of kiosks by 1, improves the average waiting time
(minimum) in system to 10.66 +/- 0.1953 minutes. This is the average waiting time confidence interval at
95% confidence interval.
Assuming that we wouldn’t care about knowing with certainity if the passenger wait time changes by
0.08 or 0.06 minutes, increasing the ticket kiosk resource by 1 serves the purpose.

28. CHAPTER 6:
CONCLUSION
The BART station at Embarcadero was modeled at simluated using Microsoft Arena in an attempt to
identify the operations at the station during the peak hours. The objective of the project was to reduce
the average waiting time for the passengers at the station, considering the current schedule of the BART
station.
Real world data was fed into the arena module after fitting distribution to various input data using
Arena’s Input Analyzer. After the model was built, different scenarios were considered by tweaking the
number of resources available in the system. This was done using the Process Analyzer and a statistical
analysis of the outputs were performed.
Increasing the number of kiosks at the Embarcadero station from 5 to 6 resulted in lesser average
waiting time for passengers from 19.4 minutes to 8.32 minutes on an average. This however resulted in
the scheduled utilization of resource to reduce from 96.7% to 81.6%.
The simulation of a train station is a complex problem involving many other factors. This model
simplifies many of these complexities by the assumption made during modeling. The model validity for
this problem can be assessed by changing the fixed inputs one at a time and checking how close the
problem resembles reality. This solution explores one modification among the many that can be
performed in this system. In future studies, other alternatives can be compared.

29. REFERENCES:
1. https://www.bart.gov/sites/default/files/docs/2017Factsheet_Map1.pdf
2. https://www.bart.gov/about/reports/ridership
3. https://www.bart.gov/about/history/history3
4. Simulation with Arena 6th Edition, W. David Kelton, Randall P Sadowski, Nancy B. Zupick