This document presents a queuing theory analysis of customer wait times at a Burger King location during peak evening hours. Data was collected on customer arrival patterns and service times. The data was fitted to distributions in Arena simulation software. The initial model showed average wait times of over 15 minutes. Proposed solutions like adding a self-serve soda fountain and digital queue displays were modeled and reduced average wait times by 4-10 minutes and decreased the number of customers in the system.

1. Modeling and Simulation Lab
Queuing Theory for
Presentation by :-
Rajat Goyal(2014UME1504)
Pawan Yadav(2014UME1488)
Sagar Kartik Dharmendra(2014UME1456)
Presented to:
Dr. Gunjan Soni

2. WHY BURGER KING ????
Huge foot fall in the Peak Hours Proper Utilization of Restaurant’s resources
Location : GT CENTRAL
Rush hours : 6:30 – 8:30 pm
The evening hours experiences almost 1000 customers at the shop

3. In the rush hours the average waiting time of the customer reaches up to 15 minutes
at the cash counters itself..………!!!!!!!!!!!!
With competition being nearby itself, efficiency must be worked upon

5. • There are no breaks for the workers during the time when the model is
running. Every counter has a single server.
• Only one customer from each group place an order and even that is only
once. No repetition in order is observed.
• Group of 4 customers or exceeding are averaged as group of five based on
data.
• There is no intermixing in queue of different cash counters and service
counters as observed in minimum cases.
• The time is assumed to be same for both cash counters and also at service
counters.
• The ice cream ordered by a person dining is taken at the ice cream counter
separately.

6. PROBLEM LAYOUT

10. Data
Collection
Input
Analyzer
Modelling Simulation
Result
Interpretation
Finding the
Distribution
• Data Entry
• Curve
fitting
Finding the
Distribution
• Data Entry
• Curve
fitting
Multiple
iteration on the
basis of
entered Data
Interpret the
data (output)
to put in form
of Physical
Model
ARENA –STUDENT VERSION

11. DATA COLLECTION
Time of data collection: 6:30-8:30 pm
No. of visits made: 5
DATACOLLECTION
Relative arrival time of customers with
group size for both take away counter and
dine in counters.
Service time at cash counters for a set of
customers.
Service time at food counters for same set
of customers.
Sitting time also of same group.
Service time at ice cream counter.

12. DATA SAMPLES
Group size Stop watch time(mins) Time in seconds
2 0:00 0
3 0:13 13
1 1:25 85
3 2:08 128
1 5:15 318
1 5:35 335
3 7:17 437
2 7:25 445
2 8:32 512
ORDER START ORDER END ORDER TIME
MIN SEC TIME IN SEC MIN SEC TIME IN SEC SEC
3 40 220 6 16 376 156
18 38 1118 27 51 1671 553
25 40 1540 26 26 1586 46
32 6 1926 39 4 2344 418
33 51 2031 36 32 2192 161
35 58 2158 37 1 2221 63
41 27 2487 44 50 2690 203
Data of Arrival
Sample of Data of Cash Counter (also similar for food counter service and the Take
away service)

13. DATA FITTING TO DISTRIBUTIONS
Raw data collected was modified as shown below in tabular form:
FREQUENCY TABLE FORMATION FOR ARRIVAL OF PEOPLE IN GROUP OF 2
TIME INTERVAL (sec) MEAN VALUE FREQUENCY
0-100 50 23
100-200 150 8
200-300 250 5
300-400 350 0
400-500 450 1
500-600 550 0
600-700 650 1
700-800 750 1

14. DATA FITTING TO DISTRIBUTIONS
Frequencies of different interval were arranged in text file and
distribution for each data file was plotted to find the required
expression.

15. DATA FITTING TO DISTRIBUTIONS
• The expression obtained with a least square error is: 20 + EXPO(85.4).

16. ARRIVAL OF ONE PERSON 50 + EXPO(158).
ARRIVAL OF THREE PERSON 50 + EXPO (200)
ARRIVAL OF MORE THAN FOUR
PERSON
TRIA( 50, 95.8, 1.15e+003).
CASH COUNTER SERVICE RATE TRIA(62,117,238)
FOOD COUNTER SERVICE RATE NORM(264,189).
IDLE TIME IN SITTING TRIA( 50, 200, 1.15e+003).
SITTING TIME FOR MEAL TRIA (450, 582, 2.25e+003).
ICE CREAM COUNTER/ TAKE AWAY
ARRIVAL RATE
25 + EXPO(116).
TIME IN TAKE AWAY/ ICE CREAM
COUNTER
NORM (71.2, 36.6)
DATA FITTING TO DISTRIBUTIONS

17. ARENA
MODEL

18. RUN SETUP
• Simulation run for 2
hours
• Total no. of
replication were 20
for most appropriate
result

19. SIMULATION

20. RESULTS
BY ENTITY

21. RESULTS
BY QUEUE

22. ARENA
MODEL

23. RESULTS
Total average number of seats occupied in a system is 40
while number of person prefers ice cream or take away the
order is 53.

24. NOW WE PROVIDE THE INTERPRETATION AND
POSSIBLE SOLUTION……….

25. Increase the customer
productivity by decreasing
time at cash counters.
Increase the labor
productivity by
increasing the
resource utilization
factor.
FINALLY….REDUCTION
IN QUEUE LENGTH
INTERPRETED SOLUTION
Automated Soda
Fountain Machine

26. INTERPRETED SOLUTION
Digital Display Queue Management
System for order status
• Decrease the crowd and for instantaneous acknowledgement of order
delivery to the customer.
• Decrease the overall service time and queue length at the service counters.

27. INTERPRETED SOLUTION
INCREMENT IN BURGER
MACHINE
REDUCTION IN SERVICE TIME
Approximate cost : Rs 7,00,000

28. INTERPRETED SOLUTION
Get your order here app
• Will increase the potential of customer
• Lead to mass expansion of Burger King

29. IMPROVED MODEL
ADDITIONAL DECISION
FOR COKE COUNTER
COKE
COUNTER

30. CHANGES PROPOSED
Expression 20 + EXPO(31).
Resource Self Serviced
Action Seize Delay Release
Customer Preference 70%
Improved Cash Counter Service
Expression
NORM(120, 40.5)
Improved Food Counter Service
Expression
NORM(180,160)
Self service soda fountain Machine
Digital Display Queue Management System

31. PROCESS ANALYZER OUTPUTS
• The number out is increased to 233.
• Average customers in system is decreased to 60
BY ENTITY

32. CHANGES PROPOSED
BY QUEUE

33. STATISTICAL COMPARISION
Cash Counter
1
Cash Counter
2
Food Counter
1
Food Counter
Actual Model 544 438 1466 1378
Proposed
Model
259 183 1115 787
Time
decrement
4 Minutes 45
Seconds
4 Minutes 15
Seconds
5 Minutes 52
Seconds
9 Minutes 52
Seconds
Cash Counter
1
Cash Counter
2
Food Counter
1
Food Counter
Actual Model 4.6 3.4 10.7 9.4
Proposed
Model
2.1 1.4 8.2 5.4
•Waiting Time( in seconds)
•Waiting Queue( in numbers)

34. STATISTICAL COMPARISION
RESOURCE UTILIZATION
0
0.2
0.4
0.6
0.8
1
1.2
Resource 1 Resource 2 Resource 3 Resource 4 Resource 5
Actual Model
Proposed Model

35. BY USER SPECIFIED
Number of customer occupying a sit is increased by 5 persons.
STATISTICAL COMPARISION

36. THANK YOU..!!!

37. QUSETIONS AND ANSWERS