The document describes a simulation of a Shell gas station, convenience store, and air pump located in Cincinnati, Ohio using Arena software. Data was collected on arrival patterns and service times. The simulation models customer flow between the gas station, food mart, and air pump based on probabilistic distributions. Key metrics like customers leaving due to long queues, total revenue, resource utilization, and wait times will be analyzed to identify opportunities to improve the Shell's operations.

1. Simulation of Shell
Using Rockwell Automation – Arena
Submitted By:
Akul Mahajan
M12420424

2. Introduction
The main aim of this project is to simulate the working of Shell located at 3337 Clifton
Ave, Cincinnati, OH 45220. The shell serves as a major service provider for the residents
who live near Clifton. It mainly comprises of a filling station for refueling vehicles, an air
filling station and a Food Mart which houses many items ranging from groceries,
packaged foods to utility items. The simulation process provides us with a real-time
understanding and analysis of the processes involved in the working of the Shell, based
on which recommendations will be provided for efficient utilization of resources and
reducing the Queue Wait time for customers. The simulation model on the Shell in this
report has been completed using Rockwell Automation’s software Arena Version
14.50.00002.
Operational Details
Theshell is operationalfrom6 A.M.to 11 P.M.on all7 daysof theweek. Thevarious
components at the shell are:
 GasStation: Therearefilling boothslocated atthe shell, whichthe customers
can use to re-fuel their vehicles. This process is self-service, the customers
can fill up their vehicles on their own make the payment using credit and
debit cards, after which they can leave the system or utilize other services
that are provided.
 Air Filling Station: At the Air Filling Station, the customers can fill the vehicles
of their tires according to the air pressurespecified for their vehicles. This is
a free service provided by the station.
 Food Mart: The Mart houses many items of utility such as clothes, food
items, an ATM, a coffee machine. The Food Mart is a major source of
revenue. It has two parallel billing desks but no self-check out counters. The
billing desk has resources based on the shifts of the staff. In general, there is
one operational desk from 6 A.M to 11 P.M, two operational desks from11
P.M. to 7 P.M. and one operational desk from 7 P.M to 11 P.M.

3. Data Collection
As a startto the project, I collected inter-arrivaltimes for the various components
in the system, on different hours of the days and on different days of the week in
order to makethe systemas robustas possible. The following statistics were
collected:
Filling StationAttributes
1. Fuel Demand: Itrepresents the quantity of fuel in gallons and differs from
customer to customer.
2. Time taken for Refueling.
3. Time taken for making the payment.
4. Queue Length beyond which the customers prefer to leave.
Food Mart Attributes
1. Parking Time: The time taken by customer to park their vehicles and enter
the mart.
2. Coffee Making Time: One of the heavily utilized resources in the martis the
coffee machine, which can queue up during peak hours.
3. Shopping Time: Time taken by the customer to fetch the items that are to
be bought.
4. Billing Time: The food mart has two parallel desks for billing, which are
operational based on schedules. The Billing Time is the time taken for
making the payment by the customer after the customer is ready for final
checkout.
Air Filling StationAttributes
1. Air Filling Time: The time taken by the customer to fill up the tires, after
which the customer leaves the system.
Model Assumptions
1. There is no break time for the resources.
2. The scheduling rule is Ignore, as in whenever a new customer comes in they
will attend the customer first.
3. Time taken in routes is assumed to be zero.

4. Data Fitting and Distributions
Arrival Rate
The arrival rates follow a non-stationary Poisson distribution with mean
values divided by hourly periods havebeen tabulated below.
Interval AverageNumber of Arrival
6 A.M. to 7 A.M. 9
7 A.M. to 8 A.M. 27
8 A.M. to 9 A.M. 14
9 A.M. to 10 A.M. 23
10 A.M. to 11 A.M. 36
11 A.M. to 12 P.M. 86
12 P.M. to 1 P.M. 126
1 P.M. to 2 P.M. 113
2 P.M. to 3 P.M. 90
3 P.M. to 4 P.M. 54
4 P.M. to 5 P.M. 81
5 P.M. to 6 P.M. 90
6 P.M. to 7 P.M. 99
7 P.M. to 8 P.M. 72
8 P.M. to 9 P.M. 59
9 P.M. to 10 P.M. 32
10 P.M. to 11 P.M. 13
Metrics Measured by the system.
1. Customers Left for all the 16 periods i.e. from6 A.M. to 11. P.M, when the
intervals are divided hourly.
2. Total Customers Left
3. Total Customers who utilized the Air Filling Service.
4. Total Revenue
5. AverageQueue Wait Time for Filling Station (Refueling)
6. Scheduled Utilization for Filling Station
7. Scheduled Utilization for Food Mart
8. AverageQueue Wait time for Food Mart

5. Fuel Demand at Gas station
Billing Time at Food Mart

6. Time at Coffee Machine
Shopping Time at Food Mart

7. Parking Time distribution
Air Filling Time

8. Arena Model for the Shell
The following modules have been incorporated in the model:
1. Car Arrival(Create Module): Itis the create module fromwhere the entities
enter into the system. The create module follows a non-stationary Poisson
Process for its arrival schedules.
2. Air or Fuel or Food (Decide Module): This module splits the entities in the
systemfromwhere60% go to the Filling station for refueling, 35% go
towards the Food Mart, and 5% for Air filling.
3. Buy Fuel (Decide Module): When entities enter this decide module, they
observethe queue length, if it is greater than 6 they decide to leave the
system. As it was observed during peak hour times people leave the
system, if the queue is too long.

9. 4. Customers Left by Periods (Record Module): This module counts the
number of customers that have left the systemfor various time intervals
and records them into a set.
5. Customers Left (Record Module): This record module counts the total
number of customers who haveleft the systemfor all periods.
6. Car Leaves 1 (DisposeModule): The entities which haveleft the systemexit
at this point.
7. Demand Assign (Assign Module): This assigns a demand to the entities for
their refueling needs according to this distribution 11 * BETA(1.34, 1.06).
According to this distribution an attribute of demand is assigned to each
entity.
8. Filling Time (Process Module): This is a Seize Delay Release Module which
has the capacity of 8 parallel filling booths. The time taken by the entities
for refueling and billing is calculated as Demand*1.6 + UNIF(1,2) .

10. 9. Revenue Count (Assign Module): This module calculates the total revenue
generated fromthe filling station and increments the Total Revenue
variable after entities are done with the refueling and billing. This helps in
determining the total revenue at the end of the cycle of run.
10. Need Air Refill (Decide Module): This splits the entities after they are done
with the refueling process, where60% decideto refill their tires and 40% of
the entities exit the systemafter this. We haveincorporated two entries to
the air filling station, as the entities might chooseto come to Shell justfor
Air Filling or they might choose to refill their tires after the refueling
process.
11. Air Station (Process Module): This is a seizedelay release module where
two resources arein parallel. The filling time taken by the entities is given
by the distribution TRIA (1.49, 2.19, 4).
12. Total Air Refill (Record Module): This module calculates the total number
of entities that have used air filling service. Itmakes sense to incorporate
this module as it gives a clearer picture of how many people are using the
free resource, if they are not utilizing it, it doesn’t makesense to include
the free servicewhich might not increasethe customer satisfaction and be
a sourceof additional maintenance for the management.
13. Parking (Delay Block): This block incorporates the parking of the Shell into
the design, the entities entering the system and deciding to enter the food
mart will park their cars. Italso provides the feature of providing the
storageto help the animation for the delay caused in the parking. The
parking delay follows a UNIF (1,3) distribution.

11. 14. Assign Entity Picture (Assign Module): This module assigns a picture of a
person to the entities, to show up in the animation that the person has
parked his car and is now entering the food mart.
15. Coffee or Other Food Items (DecideModule): The food mart provides a
variety of services but one of the most heavily utilized is the coffee
machine, this decide module splits the entities fromwhereon 40% of the
entities decide to get a coffee and 60% decide to shop for other items such
as groceries and food items.
16. Coffee Machine (Process Module): This is a Seize Delay Module, where we
have a single resourcerepresenting the coffee machine. The time taken by
entities follows the distribution 3 * BETA(1.49, 1.23).
17. Food Shopping (Delay Block): This block represents that people are
shopping for food items. The Time taken follows the distribution 1 + WEIB
(2.08, 1.8).
18. Billing Process (Process Block): This SeizeDelay Release Module has two
resources working in parallel which represents the billing counters at the
mart. The time taken for billing follows the distribution 1 + WEIB(1.31,
1.81). Thestaffing at the billing desk is based on schedule, where1 person
is assigned from6 A.M. to 11 A.M., 2 resources from11 A.M. to 7 P.M. and
1 resourcethereafter.
19. Parking 2 (Delay Block): This represents the point whereentities exit the
food mart and go towards parking, fromwherethey can drive themselves
out of the system. The time taken in the process follows the distribution
UNIF(1,3).
20. Assign Entity Picture2 (Assign Module): This module changes the picture of
the person to the picture of a car in the animation.
21. Car Leaves2 (Disposemodule): The entities exit the systemat this point
after they are done with their respective processes in the system.

12. Arena Module Flowchart
Animation

13. Statistical Analysis
As the main objective of simulating the working of the shell is to study how we
can make the functioning better based on the scheduling of the resources for
proper utilization, lesser number of people leaving the systemdue to queue
length and lessen the queue wait time. We first decide on the number of
replications needed that will reduce the half-width of these estimates and provide
us with a more accurate and precisevalue.
Hence, Initially I ran 10 number of replications to get an estimate of the half width
which later on can be used to get the number of replications that would be
required for the desired half width. The length of each replication is 17 hours.
Metric AverageValue 95% Half Width Relative Precision
Customers Left 125.80 18.38 0.146
Total Air Refill 360.70 13.42 0.037
Revenue 7776.30 131.38 0.016
AverageQueue
Wait Time Filling
Station
3.7648 0.16 0.042
AverageQueue
Wait Time Food
Mart
1.1739 0.43 0.367
Scheduled
Utilization Filling
Station
0.6462 0.01 0.015
Scheduled
Utilization Food
Mart
0.4865 0.02 0.041
Since the Relative Precision of AverageQueue Wait Time for Food Mart is the
highest we will make number of replications based on it. The desired Half width is
0.05 for this we will implement this formula to calculate the number of
replications. N = N0 * H0
2
/ H2
. Hence the desired number of replications come out
to be 740.

14. The new average values, respectivehalf-width and relative precision are:
Metric AverageValue 95% Half Width Relative Precision
Customers Left 116.66 <1.48 -
Total Air Refill 363.12 <1.14 -
Revenue 7855.79 21.23 0.0027
AverageQueue
Wait Time Filling
Station
3.6137 0.03 0.0083
AverageQueue
Wait Time Food
Mart
1.3674 0.06 0.043
Scheduled
Utilization Filling
Station
0.6404 0.00 -
Scheduled
Utilization Food
Mart
0.4948 0.00 -

15. Alternate Scenarios
Case 1:
Base Case – Number of Resources at Filling Station is 8 and number of resources
at Food Mart is 1 from6 A.M. to 11 A.M., 2 from11 A.M. to 7 P.M., 1 from7 P.M.
to 11 P.M.
Case 2:
1st
Alternate Case – Number of Resources at Filling Station is 9 and number of
resources atFood Mart is 2 from6 A.M. to 11 A.M., 3 from11 A.M. to 7 P.M., 2
from7 P.M. to 11 P.M.
Case 3:
Base Case – Number of Resources at Filling Station is 10 and number of resources
at Food Mart is 3 from6 A.M. to 11 A.M., 4 from11 A.M. to 7 P.M., 3 from7 P.M.
to 11 P.M.
Using Process Analyzer, wecomparethese scenarios entering the relevant
controls and responses to study which case is the best in terms of Queue Wait
and Utilizations.

16. Box and Whisker Plots for the outputs
Customers Left
Filling StationResourceUtilization

17. Average Queue Wait time for Filling Station
Food Mart Resource Utilization

18. Average Queue Wait time for Food Mart
Customers Left Divided by hourly Period Base Configuration

19. Customers Left Divided by hourly Period 1 Additional Resource Configuration

20. Conclusion
After running the models in PAN, a comparison between the models yields that as
we increasethe number of resources at the Filling Station and Food Mart, our
Queue wait time decreases drastically along with the resourceutilization as well.
The customers who leave the filling station due to Queue length havealso
decreased, the decreaseis paramountwhen weadd one additional resourceand
thereafter seems to get stable after we employ more people. Based on these
factors, I would recommend the 2nd
modelbeing a better configuration compared
to the basecase as the decrease in AverageQueue Wait Time is significant by just
hiring one more resourceat the Food Mart and Filling Station. The customers that
leave the systemdue to Queue Length can be considerably reduced this way and
will provide an additional sourceof revenuefor the system. A comparison
between the customers leaving the systemdivided by periods provides us with a
deeper understanding, wherewe see that the number of entities exiting the
systemdue to the busy queue has reduced drastically.