. In this slide, queue theory is applied to enhance the service of a bank in lines. For this, firstly a queue model (M/M/C): (GD/∞/∞) is selected to find out efficiency of the servers, number of service facilities, when (days of the week) customers can typically be expected to arrive,amount of time customers has to spend to get the desired service, length of the queue, how much time the customers have to wait before the service starts, how much time the customers have to wait in the bank, human psychology (frustration). After that, the optimal number of counter is calculated to improve the operational efficiency. At last, we calculate the optimal service rate and service efficiency.

1. PROJECT ON
“APPLICATION OF QUEUE MODEL TO ENHANCE
BANK SERVICE IN WAITING LINES”
PROJECT SUPERVISOR:
KAZI ARIF-UZ-ZAMAN
ASSISTANT PROFESSOR
DEPT. OF INDUSTRIAL ENGINEERING
AND MANAGEMENT
KUET.
ASSIGNED BY:
MD. RAHAMAT ULLAH, 0911004
S.M. ISHTIAQ PARTHO, 0911025
DEPT. OF INDUSTRIAL ENGINEERING
AND MANAGEMENT
KUET.

2. WHAT IS THE
• Queue - a line of people
QUEUING THEORY?
or
vehicles waiting for something.
• Queuing Theory- Mathematical
study of waiting lines, using
models to show results, and
show
opportunities
within
arrival, service, and departure
processes.

3. PROJECT GOAL
In this paper, queue theory is
applied to enhance the service of
a bank in lines. For this, firstly a
queue model (M/M/C): (GD/∞/∞)
is selected to find out efficiency
of the servers.

4. KEY WORDS
Queuing model, optimal
number
of
server,
service rate, first come
first serve, (M/M/C):
(GD/∞/∞) model.

5. OBJECTIVES OF THE PROJECT
• Finding out the efficiency of the servers.
• Signifying the number of service facilities.
• When customers can typically be expected to arrive.
• The amount of time customers has to spend to get the desired service.
• The length of the queue (Waiting line).
• How much time the customers have to wait before the service starts.
• Human psychology (frustration, balking, impatience).
• the optimal number of counter is calculated to improve the
operational efficiency.

6. SIGNIFICANCE OF QUEUING
MODELS
• Queuing Models Calculate the best number of servers to minimize
costs.
• Queue lengths and waiting times can be predicted.
• Improve Customer Service, continuously.
• When a system gets congested, the service delay in the system
increases.
• A good understanding of the relationship between congestion and
delay is essential for designing effective congestion control for queuing
system.
• Queuing Theory provides all the tools needed for this analysis.

7. TERMINOLOGY AND
NOTATIONS
• M=Number of servers
• Pn= probability of exactly “n” customers in the system.
• N= number of customers in the system.
• Ls= expected number of customers in the system
• Lq= expected number of customers in the queue.
• Ws= waiting time of customers in the system
• Wq= waiting time of customers in the queue.
• λn= The mean arrival rate of new customers are in systems.
• µn= The mean service rate for overall systems when “n” customers are in systems.
• The mean arrival rate is constant for all n, this is denoted by λ and the mean service
rate per busy server is constant for all n≥1, is denoted by µ. And when n ≥M that is
all z servers are busy, µ=sµ. Under this condition,
• The expected inter-arrival time is 1/λ
• The expected service time is 1/µ.
• The utilization factor for the service facility is ρ= λ/Mµ.

8. METHODOLOGY AND PROPOSED
• Formula 1 [Adding another
MODEL
server to the system during
busy
days
(Comparative
analysis of adding an extra
counter)]
• Formula 2
[Improving the
service rate by serving the
customer
quick
(increase
service rate)]

9. FORMULA 1 [ADDING ANOTHER SERVER TO THE
SYSTEM DURING BUSY DAYS (INCREASE
SERVER)]
PROPOSED MODEL: (M/M/C): (GD/∞/∞) MODEL:
•

10. •

11. Case study of a local bank
[Service time per day is 10:00 to 1:00 and 3:00-4:00.total 240 minutes.]
Bank data of customer count for one month
Week No.
Sunday
Monday
Tuesday
Week 1
140
114
132
Wednesda Thursday
y
146
156
Week 2
120
123
199
145
150
Week 3
199
171
159
120
130
Week 4
150
180
149
107
110
Total
609
588
639
518
546
Average
152.25
147
159.75
129.5
136.5

12. Bank data of customer
count for one month
Average number of customer
160
140
120
100
80
152.25
147
159.75
129.5
136.5
60
40
20
0
Sunday
Monday
Tuesday
Day of the week
Wednesday
Thursday

13. Graphical representation of effect of
adding an extra counter for Sunday
number of counter vs waiting time of customers
in minute
Waiting time of customers, ws
30
25
20
15
26.58
10
9.5
5
3.27
1.75
4
5
0
2
3
number of server, s

14. Graphical representation of effect of
adding an extra counter for Monday
number of counter vs waiting time of customers in
minute
waiting time of customers
16
14
12
10
8
15.123
6
4
5.624
2
2.356
1.448
4
5
0
2
3
number of server,s

15. Graphical representation of effect
of adding an extra counter for
Tuesday
Waiting time of customers, ws
number of counter vs waiting time of customers in
minute
100
90
80
70
60
50
40
30
20
10
0
96.664
33.923
9.217
2
3
2.911
4
5
number of server, s

16. Graphical representation of effect of
adding an extra counter for
Wednesday
number of counter vs waiting time of customers in
minute
Waiting time of customers, ws
5
4.5
4
3.5
3
2.5
4.992
2
1.5
2.387
1
1.612
1.456
4
5
0.5
0
2
3
number of server, s

17. Graphical representation of effect of
adding an extra counter for Thursday
number of counter vs waiting time of customers in
minute
Waiting time of customers, ws
8
7
6
5
4
7.074
3
2
3.025
1.754
1
1.481
4
5
0
2
3
number of server, s

18. PROBLEM FORMULATION
• It has been seen in the research that If waiting time increases then
frustration level increases with this. In the scenario utilization factor
is as high as 0.39 to 0.48 during busy days of the bank. It is clear that
high utilization rate is not helping to reduce customer’s waiting time in
queue. On high utilization factor customers have to wait more time in
system as like as 26.58, 15.123, 96.664, 4.992, 7.074 minutes
respectively from Sunday to Thursday. It seems that there is a problem
in the operations which if not noticed could reduce business of bank.

19. RESULT AND DISCUSSION OF
FORMULA 1
• The comparative analysis of adding an extra counter to the
system and improving the service rate have shown in the above
figures.
• when one more counter is added (s=3) the waiting time in
system reduces significantly to 9.5, 5.624, 33.923, 2.387, 3.025
minutes respectively from Sunday to Thursday. However, it can
be seen that adding one more counter (s=3) does significantly
change the waiting time of the system except for Tuesday. Using
four counter for Tuesday significantly changes waiting time from
33.923 (when s=3) to 9.217.
.

20. From this analysis, the
optimum number of counter
for the week Optimum number Utilization factor
Day of the days are listed below
Sunday
of counter
3
0.30
Monday
3
0.29
Tuesday
4
0.24
Wednesday
2
0.39
Thursday
2
0.41

21. FORMULA 2 [IMPROVING THE SERVICE
RATE BY SERVING THE CUSTOMER
QUICKLY (INCREASE SERVICE RATE)]
 On another experiment, it has been found by meeting
with the customers in waiting line that before they arrive
at the bank they are mentally prepared for waiting 8 to 10
minutes in the bank for getting their service. From this
point of view, for Wednesday and Thursday there is no
need for adding an extra counter.

22. SERVICE RATE VS. WAITING TIME OF
CUSTOMERS IN MINUTE
service rate vs. waiting time of customers in minute
100
Waiting time of customers, ws
90
80
70
60
50
96.664
40
30
20
28.43
14.12
10
8.73
5.98
0
0.7
0.73
0.76
service rate
0.79
0.82

23. Result and discussion
• The second way of reducing the waiting time in line is by
improving the service rate. The above figure (8) indicates the
ultimate effect of improving the service rate. From the
comparative analysis, it can be seen that on Tuesday, if the
service rate is improved from .70 to .76 then waiting time
reduces to 96.664 to 14.12 (82.554minutes) without
adding an extra counter thus adding no extra cost.

24. psychological View [Frustra

25. CONCLUSION
The efficiency of commercial banks is improved by the following three
measures:
• the queuing number
• the service stations number and
• the optimal service rate
which are investigated by means of queuing theory. By the example, the
results are effective and practical. The time of customer queuing is
reduced. The customer satisfaction is increased. It was proved that this
optimal model of the queuing is feasible.

26. QUESTIONS?

27. THANK
YOU!