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18-1 Waiting Lines
William J. Stevenson
Operations Management
8th edition
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CHAPTER
18
Waiting Lines
McGraw-Hill/Irwin
Operations Management, Eighth Edition, by William J. StevensonCopyright 2005 by The McGraw-Hill Companies, Inc. All rights reserved.
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Disney World
Waiting in lines does not add enjoyment
Waiting in lines does not generate revenue
Waiting lines are non-value addedoccurrences
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Waiting Lines
Queuing theory: Mathematical approach to theanalysis 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 addedoccurrences
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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 Lines
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18-6 Waiting Lines
Queuing Analysis
Optimum
Cost of
service
capacity
Cost of
customers
waiting
Total costCost
Service capacity
Total
cost
Customer
waiting cost
Capacity
cost= +
Figure 18.1
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18-7 Waiting Lines
System 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)
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18-8 Waiting Lines
Elements of Queuing System
Arrivals ServiceWaiting
line
Exit
Processing
order
System
Figure 18.2
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Queuing SystemsMultiple channel
Multiple phase
Figure 18.3
Channel: A server in
a service system
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Poisson Distribution
0
0.05
0.10.15
0.2
0.25
0 1 2 3 4 5 6 7 8 9 10 11 12
Figure 18.4
18 11 W L
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Waiting 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
18 12 W i i Li
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18-12 Waiting Lines
Waiting Time vs. Utilization
System Utilization
Av
eragenumbe
ron
tim
ewaitinginline
0 100%
Figure 18.6
18 13 W i i Li
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System Performance
1. Average number of customers waiting
2. Average time customers wait3. System utilization
4. Implied cost
5. Probability that an arrival will have to wait
Measu red by:
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1. Single channel, exponential service time2. Single channel, constant service time
3. Multiple channel, exponential service time
4. Multiple priority service, exponential service
time
Queuing Models: Infinite-Source
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Priority Model
Arrivals ServiceWaiting
line
Exit
Processing
order
System
11231
Arrivals are assigned
a priority as they arrive
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18-16 Waiting Lines
Finite-Source FormulasX T
T U
L N F
W L T UN L
T FXF
J NF X
H FNX
N J L H
(1 )
( ) (1 )
(1 )
Average number being served
Service factor
Average number waiting
Average waiting time
Average number running
Number in population
Table 18.6
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18-17 Waiting Lines
Finite-Source Queuing
Not waiting or
being servedWaiting
Being
served
J L H
U W T
F
J H
J L H
18 18 Waiting Lines
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18-18 Waiting Lines
Other Approaches
Reduceperceived 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
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Queuing
QAP9
Managing Queues by Business Rules
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Waiting Line Management
DWL5
Disney Fast Pass Results/Distributing Queues
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Pilot Queue System
DWL6
Fast Pass at Disneys Animal KingdomStatistics
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Other Queue Perception Improvers
DWL7
Disney WorldTraditional Queue Improvement Methods
