Management of Waiting Lines & Implication

Management of Waiting Line

1. McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
1818
Management ofManagement of
Waiting Lines

2. 18-2
Learning ObjectivesLearning Objectives
Explain why waiting lines form in systems
that are underloaded.
Identify the goal of queuing (waiting-line)
management.
List the measures of system performance
that are used in queuing.
Discuss the assumptions of the basic
queuing models presented.
Solve typical problems.

3. 18-3
Disney WorldDisney World
Waiting in lines does not add enjoyment
Waiting in lines does not generate
revenue
Waiting lines are non-value added occurrences

4. 18-4
Waiting LinesWaiting Lines
Queuing theory: Mathematical approach to
the analysis of waiting lines.
Goal of queuing analysis is to minimize the
sum of two costs
Customer waiting costs
Service capacity costs
Waiting lines are non-value added
occurrences

5. 18-5
Cost to provide waiting space
Loss of business
Customers leaving
Customers refusing to wait
Loss of goodwill
Reduction in customer satisfaction
Congestion may disrupt other business
operations
Implications of Waiting LinesImplications of Waiting Lines

6. 18-6
Queuing AnalysisQueuing Analysis
Optimum
Cost of
service
capacity
Cost of
customers
waiting
Total cost
C
o
s
t
Service capacity
Total
cost
Customer
waiting cost
Capacity
cost
= +
Figure 18.1

7. 18-7
System CharacteristicsSystem Characteristics
Population Source
Infinite source: customer arrivals are
unrestricted
Finite source: number of potential
customers is limited
Number of observers (channels)
Arrival and service patterns
Queue discipline (order of service)

8. 18-8
Elements of Queuing SystemElements of Queuing System
Arrivals ServiceWaiting
line
Exit
Processing
order
System
Figure 18.2

9. 18-9
Queuing SystemsQueuing Systems
Multiple channel
Multiple phase
Figure 18.3
Channel: A server in
a service system

10. 18-10
Poisson DistributionPoisson Distribution
0
0.05
0.1
0.15
0.2
0.25
0123456789101112
Figure 18.4

11. 18-11
Waiting line ModelsWaiting line Models
Patient
Customers enter the waiting line and remain until
served
Reneging
Waiting customers grow impatient and leave the
line
Jockeying
Customers may switch to another line
Balking
Upon arriving, decide the line is too long and decide
not to enter the line

12. 18-12
Waiting Time vs. UtilizationWaiting Time vs. Utilization
System Utilization
A
v
e
r
a
g
e

n
u
m
b
e
r

o
n

t
i
m
e

w
a
i
t
i
n
g

i
n

l
i
n
e
0 100%
Figure 18.7

13. 18-13
System PerformanceSystem Performance
1.Average number of customers waiting
2.Average time customers wait
3.System utilization
4.Implied cost
5.Probability that an arrival will have to wait
Measured by:

14. 18-14
1.Single channel, exponential service time
2.Single channel, constant service time
3.Multiple channel, exponential service
time
4.Multiple priority service, exponential
service time
Queuing Models: Infinite-SourceQueuing Models: Infinite-Source

15. 18-15
Priority ModelPriority Model
Arrivals ServiceWaiting
line
Exit
Processing
order
System
11231
Arrivals are assigned
a priority as they arrive

16. 18-16
Finite-Source FormulasFinite-Source Formulas
X
T
TU
LN F
W
LTU
NL
TF
XF
JNF X
HFNX
NJLH


 





 


(1)
( )(1)
(1)
Average number being served
Service factor
Average number waiting
Average waiting time
Average number running
Number in population
Table 18.6

17. 18-17
Finite-Source QueuingFinite-Source Queuing
Not waiting or
being served
Waiting
Being
served
J L H
U W T
F
JH
JLH




18. 18-18
Other ApproachesOther Approaches
Reduce perceived waiting time
Magazines in waiting rooms
Radio/television
In-flight movies
Filling out forms
Derive benefits from waiting
Place impulse items near checkout
Advertise other goods/services

19. 18-19
Video: Queue Management IVideo: Queue Management I

20. 18-20
Video: Efficiency Obj.Video: Efficiency Obj.

21. 18-21
Video: Queue Management IIVideo: Queue Management II