In operation research this is one of the intresting area which having lot of applications to apply in our real life. it can be used for both the service and manufacturing industry.

1. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
QUEUING ANALYIS
QUEUING ANALYSIS
ABINANTH M
Roll No: 15MF01
E-mail: abinanthsathya94@gmail.com
1

2. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Queuing theory definitions
• (Bose) “the basic phenomenon of queuing arises whenever a shared facility
needs to be accessed for service by a large number of jobs or customers.”
• (Wolff) “The primary tool for studying these problems [of congestions] is
known as queueing theory.”
• (Kleinrock) “We study the phenomena of standing, waiting, and serving, and
we call this study Queuing Theory." "Any system in which arrivals place
demands upon a finite capacity resource may be termed a queueing
system.”
• (Mathworld) “The study of the waiting times, lengths, and other properties of
queues.”
2

3. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
QUEUING THEORY
 Queuing theory deals with modeling and analyzing systems with queues of items and
servers that process the items.
 Queuing theory is the mathematics of waiting lines.
 It is extremely useful in predicting and evaluating system performance.
 Queuing theory has been used for operations research, manufacturing and systems
analysis.
 Traditional queuing theory problems refer to customers visiting a store, analogous to
requests arriving at a device.
QUEUING ANALYIS
3

4. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
• Capacity problems are very common in industry and one of the main drivers of
process redesign
– Need to balance the cost of increased capacity against the gains of increased
productivity and service
• Queuing and waiting time analysis is particularly important in service systems
– Large costs of waiting and of lost sales due to waiting.
Why is Queuing Analysis Important?
QUEUING ANALYIS
4

5. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Applications of Queuing Theory
• Telecommunications
• Traffic control
• Determining the sequence of computer operations
• Predicting computer performance
• Health services (eg. control of hospital bed assignments)
• Airport traffic, airline ticket sales
• Layout of manufacturing systems.
5

6. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Queuing System Costs
QUEUING ANALYIS
6
Total expected cost = waiting time cost + cost of providing service
Cost
Minimum
Total
Cost
Low Level
Of Service
High Level
Of Service
Optimal Service
Level
Cost of Waiting
Time
( time x value of time )
Cost of Providing
Service
( salaries + benefits )
Total Cost

7. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Waiting and Idle time costs
Cost of waiting customers Cost of idle service facility
• Indirect cost of business loss
• Direct cost of idle equipment or
person.
• Payment to be made to the
servers(engaged at the
facilities),for the period for
which they remain idle.
The optimum balance of costs can be made by scheduling the flow of units
or providing proper number of service facilities .
7
Courtesy : Google images/ sleeping

8. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Characteristics of a Queuing System
The queuing system is determined by:
• Arrival characteristics
• Queue characteristics
– Queue length (max possible queue length) – either limited or unlimited
– Service discipline – usually FIFO (First In First Out)
• Service facility characteristics
QUEUING ANALYIS
8
Courtesy: opnet ppt

9. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Arrival Characteristics
• Size of the arrival population – either infinite or limited
• Arrival distribution:
– Either fixed or random
– Either measured by time between consecutive arrivals, or arrival rate
– The Poisson distribution is often used for random arrivals
Poisson Distribution
• Average arrival rate is known
• Average arrival rate is constant for some number of time periods
• Number of arrivals in each time period is independent
QUEUING ANALYIS
9
probability
Arrival per unit time(λ)

10. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Poisson Distribution
λ = the average arrival rate per time unit
P(x) = the probability of exactly x arrivals occurring during one time period
Where : P ( X ) = probability of X arrivals
X = number of arrivals per time unit
λ = the average arrival rate
e = 2.7183 ( base of the natural logarithm )
Example:
If the average arrival rate per hour is two people ( λ = 2 ) , what is the probability of three (3)
arrivals per hour?
= 0.1804 ≈ 18 %
QUEUING ANALYIS
10

11. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Little’s Law
• Very simple law that works from a Case Western Reserve University professor Dr. Little
• For a given arrival rate, the time in the system is proportional to average time spent in the
system
N =  T
where
N: average no. of customers in the system
: Customer arrival rate (per unit time)
T: average time in the system per customer (response time)
Example:
Server satisfies input request in average of 100 msec. Input rate is about 100 requests/sec.
What is the mean number of requests at the server?
Mean number at server = arrival rate x response time
= (100 requests/sec) x (0.1 sec)
= 10 requests
QUEUING ANALYIS
11

12. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Service Facility Characteristics
1. Configuration of service facility
• Number of servers (or channels)
• Number of phases (or service stops)
2. Service distribution
• The time it takes to serve 1 arrival
• Can be fixed or random
• Exponential distribution is often used.
Exponential Distribution
μ = average service time
t = the length of service time (t > 0)
P(t) = probability that service time will be greater than t
P(t) = e- μt
QUEUING ANALYIS
.25
.20
.15
.10
.05
.00
P
R
O
B
A
B
I
L
I
T
Y
0 30 60 90 120 150 180 210
seconds
THE PROBABILITY
A CUSTOMER
WILL REQUIRE
THAT SERVICE
TIME
12

13. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Behavior of Arrivals
Most queuing formulas assume that all arrivals stay until service is completed
Balking refers to customers who do not join the queue
Reneging refers to customers who join the queue but give up and leave before completing
service
Jockeying- When a customer shifts from one queue to another.
Jockeying can be discouraged by placing
barricades such as magazine racks and
impulse item displays between waiting lines
Queue Discipline
QUEUING ANALYIS
13

14. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Queuing Theory Variables
• Lambda ( λ ) is the average arrival rate of people or items into the service system. It can
be expressed in seconds, minutes, hours, or days.
• Mu ( μ ) is the average service rate of the service system. It can be expressed as the
number of people or items processed per second, minute, hour, or day.
• Rho ( ρ ) is the % of time that the service facility is busy on the average. It is also known
as the utilization rate.
• Mu ( M ) is a channel or service point in the service system. Examples are gasoline
pumps, checkout counters, vending machines, bank teller windows.
• Phases are the number of service points that must be negotiated by a customer or item
before leaving the service system.
QUEUING ANALYIS
14

15. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Measuring Queue Performance
• Pn is the probability of exactly n customers in system
• Po or ( 1 – ρ ) is the percentage of time that the service facility is idle.
• L is the average number of people or items in the service system both waiting to be served and currently
being served.
• Lq is the average number of people or items in the waiting line ( queue ) only !
• W is the average time a customer or item spends in the service system, both waiting and receiving
service.
• Wq is the average time a customer or item spends in the waiting line ( queue ) only.
• Pw is the probability that a customer or item must wait to be served.
QUEUING ANALYIS
15

16. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Kendall Notation 1/2/3(/4/5/6)
Six parameters are
• First three typically used, unless specified
1. Arrival Distribution
(M for Poisson, D for deterministic, and G for general)
2.. Service Distribution
(M for Poisson, D for deterministic, and G for general)
3. Number of servers (PARALLEL SERVICE)
4. Total Capacity (infinite if not specified) [max no. of customers]
5. Population Size (infinite)
6. Service Discipline (FCFS/FIFO)
QUEUING ANALYIS
16

17. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Models with example
Name
(Kendall Notation)
Example
Simple system
(M / M / 1)
Customer service desk in a store
Multiple server
(M / M / s)
Airline ticket counter
Constant service
(M / D / 1)
Automated car wash
General service
(M / G / 1)
Auto repair shop
Limited population
(M / M / s / ∞ / N)
An operation with only 12 machines that might break
QUEUING ANALYIS
17

18. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Single Server Queuing System (M/M/1)
Queue
Arrivals
λ= arrival rate
server
Dispatching
discipline
w = mean # items waiting
Tw = mean waiting time
Departures
Ts = mean service time
ρ = utilization
R mean # items residing in the system
Tr = mean residence time
QUEUING ANALYIS
EXIT
18

19. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Service Channels
• Single channel queuing system
• Multi channel queuing system
• Single channel multi phase system
• Multi channel multi phase system
17

20. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
 Situation
– Patients arrive according to a Poisson process with intensity  ( the time
between arrivals is exp() distributed.
– The service time (the doctor’s examination and treatment time of a patient)
follows an exponential distribution with mean 1/ (=exp() distributed)
 The Emergency can be modeled as an M/M/c system where,
c=the number of doctors
 Data gathering
  = 2 patients per hour
  = 3 patients per hour
Example Hospital
QUEUING ANALYIS
20

21. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Operating Characteristics for M/M/1 Queue
1. Average server utilization
2. Average number of customers waiting
3. Average number in system
4. Average waiting time
5. Average time in the system
6. Probability of 0 customers in system
7. Probability of exactly n customers in system Pn = (λ/μ )n P0
QUEUING ANALYIS
21

22. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
• Interpretation
– To be in the queue = to be in the waiting room
– To be in the system = to be in the Emergency (waiting or under treatment)
Summary of Results – Government Hospital
Characteristic One doctor (c=1) Two Doctors (c=2)
 2/3 1/3
P0 1/3 1/2
(1-P0) 2/3 1/2
P1 2/9 1/3
Lq 4/3 patients 1/12 patients
L 2 patients 3/4 patients
Wq 2/3 h = 40 minutes 1/24 h = 2.5 minutes
W 1 h 3/8 h = 22.5 minutes
QUEUING ANALYIS
22

23. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
M/M/1 Example I
Traffic to a message switching center for one of the outgoing communication lines arrive in a
random pattern at an average rate of 240 messages per minute. The line has a transmission
rate of 800 char/ second. The message length distribution (including control characters) is
approximately exponential with an average length of 176 characters. Calculate the following
principal statistical measures of system performance, assuming that a very large number of
message buffers are provided:
(a) Average number of messages in the system
(b) Average number of messages in the queue waiting to be transmitted.
(c) Average time a message spends in the system.
(d) Average time a message waits for transmission
(e) Probability that 10 or more messages are waiting to be transmitted.
(f) 90th percentile waiting time in queue.
QUEUING ANALYIS
23

24. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
M/M/1 Example I (cont.)
 Performance E[s] = Average Message Length / Line Speed
= {176 char/message} / {800 char/sec}
= 0.22 sec/message
 Average service rate  = 1 / 0.22 {message / sec}
= 4.55 message / sec
 Average arrival rate  = 240 message / min
= 4 message / sec
 % of time service busy  =  E[s] =  / 
= 0.88
QUEUING ANALYIS
24

25. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
M/M/1 Example I (cont.)
(a) Average number of messages in the system L =  / (1 - )
= 7.33 (messages)
(b) Average number of messages in the queue waiting to be transmitted Lq= 2 / (1 - )
= 6.45 (messages)
(c) Average time a message spends in the system. W = E[s] / (1 - )
= 1.83 (sec)
(d) Average time a message waits for transmission Wq =  × E[s] / (1 - )
= 1.61 (sec)
(e) Probability that 10 or more messages are waiting to be transmitted.
P [11 or more messages in the system] = 11 = 0.245
(f) 90th percentile waiting time in queue pq(90) = W ln{(100-90) }
= W ln(10)
= 3.98 (sec)
QUEUING ANALYIS
25

26. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Therefore:
μ = 30
λ = 20
M = 1
Single-Channel / Single-Phase Model
• A clerk can serve thirty customers per
hour on average.
• Twenty customers arrive each hour on
average.
APPLICATION - 2
26
QUEUING ANALYIS

27. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
M/M/1 queue model
27



1
Wq
W
L
Lq

28. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
The Average Number of Customers in the System
The Average Number Just Waiting in Line
The Average Customer Time Spent in the System
The Percentage of Time the System is Busy
Single-Channel / Single-Phase Model
28
QUEUING ANALYIS

29. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Software packages
General
• RESQ
• QNA
• PANCEA
Manufacturing applications
• CAN-Q
• MANUPLAN
• MVAQ
29

30. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM 30
QUEUING ANALYIS

31. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM 31
QUEUING ANALYIS

32. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM 32
QUEUING ANALYIS

33. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Multi-server /single queue
Queue
Arrivals
λ= arrival rate
Dispatching
discipline
server0
server1
Server n
…..
QUEUING ANALYIS
33

34. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Multi-server /Multiple queues
server0
server1
Servern
-1
……….
Queue
Arrivals Queue
Queue
QUEUING ANALYIS
34

35. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Multi-Channel Single-Phase Systems
This system is a single waiting line serviced by more than one server.
It assumes:
an infinite calling population
a first-come, first-served queue discipline
a Poisson arrival rate
negative exponential service times
Additional Parameters
M = number of servers or channels
Mμ = mean effective service rate for the facility
QUEUING ANALYIS
35

36. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Multi-Channel Single-Phase Systems
Application Example
A bank has three loan officers on duty, each of whom can serve four customers
per hour. Every hour, ten loan applicants arrive at the loan department and join a
common queue. What are the system’s operating characteristics?
= .045 = 4.5%
The probability that the service facility is idle:
QUEUING ANALYIS
36

37. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Application Example Continued
L = 3.515625 + 2.5 ≈ 6.0
The average number of customers in the system:
QUEUING ANALYIS
37

38. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Lq = 6 – [10/4] = 3.5
W = 6/10 = .60 hours ( 36 minutes )
Wq = 3.5 / 10 = .35 hours ( 21 minutes )
L = 6
The average number of customers in the queue:
The average time a customer spends in the system:
The average waiting time in the queue:
The probability that all the system’s servers are currently busy:
or
Application Example Continued
QUEUING ANALYIS
38

39. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Finite Calling Population Model
Application
A shop has fifteen (15) machines which are repaired in the same order in which they fail. The
machines fail according to a Poisson distribution, and the service times are exponentially
distributed. One (1) mechanic is on-duty. A machine fails on average,
every forty (40) hours. The average repair takes 3.6 hours.
N = 15 machines
λ = 1/40th of a machine per hour = .0250 machine per hour
μ = 1/3.6th of a machine per hour = .2778 machine per hour
39
QUEUING ANALYIS

40. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Finite Calling Population Model
N = size of the finite calling population
Probability that the system is empty:
Average length of the queue
= 6.16%
40
QUEUING ANALYIS

41. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Average number of customers (items) in the system:
L = Lq + ( 1 – Po ) = 3.63 + ( 1 - .0616 ) = 4.57 machines
Average waiting time in the queue:
( N – L ) λ
Lq
Average time in the system:
W = Wq + ( 1 / μ ) = 13.94 + ( 1 / .2778 ) = 17.54 hours
Wq = = 13.94 hours
Finite Calling Population Model
41
QUEUING ANALYIS

42. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Priority Servers
• Packets form priority classes (each may have several flows)
• There is a separate FIFO queue for each priority class
• Packets of lower priority start transmission only if no higher priority packet
is waiting
• Priority types:
– Non-preemptive (high priority packet must wait for a lower priority packet
found under transmission upon arrival)
– Preemptive (high priority packet does not have to wait …)
Courtesy: http://www.athenasc.com/probbook.html
42

43. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Priority Queuing
• Packets are classified into separate queues
– E.g., based on source/destination IP address, source/destination TCP port, etc.
• All packets in a higher priority queue are served before a lower priority
queue is served
– Typically in routers, if a higher priority packet arrives while a lower priority
packet is being transmitted, it waits until the lower priority packet completes
Courtesy: http://www.athenasc.com/probbook.html
43

44. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Behavioral Considerations
• Customer willingness to wait depends on what is perceived as reasonable.
• Waiting lines that are always moving are perceived as less painful.
• Customer willingness to wait is higher if they know that others are also waiting their turn.
• Customers should be permitted to perform the services that they can easily provide for
themselves
• Well projected waiting times allow customers to adjust their expectations and therefore
their aggravation.
• If customers are kept busy, their waiting time may not be construed as wasted time
QUEUING THEORY
44
QUEUING ANALYIS
Courtesy : google images/ queue

45. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
Suggestions for Managing Queues
1. Determine an acceptable waiting time for your customers
2. Try to divert your customer’s attention when waiting
3. Inform your customers of what to expect
4. Keep employees not serving the customers out of sight
5. Segment customers
6. Train your servers to be friendly
7. Encourage customers to come during the slack periods
8. Take a long-term perspective toward getting rid of the queues
45

46. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
REFERENCES
• Applied Management Science for Decision Making, 1e © 2010 Pearson Prentice-Hall, Inc.
Philip A. Vaccaro , PhD
• www.slideshare.com “ QUEUING THEORY” by Anil Kumar, Avatar Singh
• “Modeling and Analysis of Manufacturing Systems”, by Ronald G Askin
• “ Operations Research” by Dr. D.S.Hira, Er. Prem Kumar Gupta
• http://www2.uwindsor.ca/~hlynka/queue.html
• OPNET Hybrid Simulation and Micro Simulation
– See Case Studies papers in
http://secure.opnet.com/services/muc/mtdlogis_cse_stdies_81.html
46

47. COURSE CODE. PAGE
FLEXIBLE MANUFACTURING SYSTEM
Department of Mechanical EngineeringFaculty: VIJAYANAND.V
10-Feb-17 15MN24
CLASS.
ME: IE & CIM
THANK YOU
QUEUING ANALYIS
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