18-1
Waiting Lines
CHAPTER
18
Waiting Lines
18-2
Waiting Lines
Disney World

Waiting in lines does not add enjoyment

Waiting in lines does not generate revenue
Waiting lines are non-value added occurrences
18-3
Waiting Lines
Waiting 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
18-4
Waiting Lines
Implications of Waiting Lines

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
18-5
Waiting Lines
Queuing Analysis
Figure 18.1
Cost
Total
cost
=
Customer
waiting cost
+
Total cost
Capacity
cost
Cost of
service
capacity
Cost of
customers
waiting
Service capacity
Optimum
18-6
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)
18-7
Waiting Lines
Elements of Queuing System
Figure 18.2
Processing
order
Arrivals
Waiting
line
Service
System
Exit
18-8
Waiting Lines
Queuing Systems
Figure 18.3
Multiple channel
Channel: A server in
a service system
Multiple phase
18-9
Waiting Lines
Poisson Distribution
Figure 18.4
0.25
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
8
9
10 11 12
18-10 Waiting Lines

Patient


Waiting customers grow impatient and leave the line
Jockeying


Customers enter the waiting line and remain until
served
Reneging


Waiting line Models
Customers may switch to another line
Balking

Upon arriving, decide the line is too long and decide
not to enter the line
18-11 Waiting Lines
Waiting Time vs. Utilization
Average number on
time waiting in line
Figure 18.6
0
System Utilization
100%
18-12 Waiting Lines
System Performance
Measured by:
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
18-13 Waiting Lines
Queuing Models: Infinite-Source
1.
2.
3.
4.
Single channel, exponential service time
Single channel, constant service time
Multiple channel, exponential service time
Multiple priority service, exponential service
time
18-14 Waiting Lines
Priority Model
Processing
order
1
3
Arrivals
Arrivals are assigned
a priority as they arrive
2
1
1
Waiting
line
Service
System
Exit
18-15 Waiting Lines
Finite-Source Formulas
Table 18.6
Service factor
Average number waiting
Average waiting time
Average number running
Average number being served
Number in population
T
X
T U
L  N (1  F)
L(T  U ) T(1  F)
W

NL
XF
J  NF(1  X )
H  FNX
N  J  L H
18-16 Waiting Lines
Finite-Source Queuing
Not waiting or
being served
Waiting
Being
served
J
L
H
U
W
T
JH
F
J  LH
18-17 Waiting Lines


Other 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
18-18 Waiting Lines
Queuing
QAP9
Managing Queues by Business Rules
18-19 Waiting Lines
Waiting Line Management
DWL5
Disney Fast Pass Results/Distributing Queues
18-20 Waiting Lines
Pilot Queue System
DWL6
Fast Pass at Disney’s Animal Kingdom—Statistics
18-21 Waiting Lines
Other Queue Perception Improvers
DWL7
Disney World—Traditional Queue Improvement Methods