Managing Waiting Lines
Learning Objectives
•
•
•
•
Describe how queues form.
Apply Maister's two “laws of service.”
Discuss the psychology of waiting.
Describe the essential features of a queuing
system.
• Explain the equivalence of Poisson arrival
rates and exponential time between arrivals
Lines and Waiting
“Every day I get in the queue, that waits
for the bus that takes me to you …”
Pete Townshend, Magic Bus
Where the Time Goes
In a life time, the average
American will spend-SIX MONTHS
Waiting at stoplights
EIGHT MONTHS
Opening junk mail
ONE YEAR
Looking for misplaced 0bjects
Unsuccessfully returning
TWO YEARS
phone calls
FOUR YEARS
FIVE YEARS
SIX YEARS
Doing housework
Waiting in line
Eating
Cultural Attitudes
• “Americans hate to wait. So business is
trying a trick or two to make lines seem
shorter…” The New York Times, September 25, 1988
• “An Englishman, even when he is by
himself, will form an orderly queue of
one…” George Mikes, “How to be an Alien”
• “In the Soviet Union, waiting lines were
used as a rationing device…” Hedrick Smith, “The
Russians”
Waiting Realities
• Inevitability of Waiting: Waiting results
from variations in arrival rates and service
rates
• Economics of Waiting: High utilization
purchased at the price of customer waiting.
Make waiting productive (salad bar) or
profitable (drinking bar).
Laws of Service
• Maister’s First Law:
Customers compare expectations with perceptions.
• Maister’s Second Law:
Is hard to play catch-up ball.
• Skinner’s Law:
The other line always moves faster.
• Jenkin’s Corollary:
However, when you switch to another other line,
the line you left moves faster.
Remember Me
• I am the person who goes into a restaurant, sits
down, and patiently waits while the wait-staff does
everything but take my order.
• I am the person that waits in line for the clerk to
finish chatting with his buddy.
• I am the one who never comes back and it amuses
me to see money spent to get me back.
• I was there in the first place, all you had to do was
show me some courtesy and service.
The Customer
Psychology of Waiting
• That Old Empty Feeling: Unoccupied time goes
slowly
• A Foot in the Door: Pre-service waits seem longer
that in-service waits
• The Light at the End of the Tunnel: Reduce
anxiety with attention
• Excuse Me, But I Was First: Social justice with
FCFS queue discipline
• They Also Serve, Who Sit and Wait: Avoids idle
service capacity
Approaches to Controlling Customer Waiting
• Animate: Disneyland distractions, elevator
mirror, recorded music
• Discriminate: Avis frequent renter
treatment (out of sight)
• Automate: Use computer scripts to address
75% of questions
• Obfuscate: Disneyland staged waits (e.g.
House of Horrors)
The Art of Service Recovery
“To err is human; to recover, divine”
•
•
•
•
•
•
•
Measure Cost of Lost Customer
Listen Carefully
Anticipate Need for Recovery
Act Fast
Train Employees
Empower the Frontline
Inform Customers of Improvement
Essential Features of Queuing Systems
Renege
Calling
population
Arrival
process
Balk
Queue
configuration
Queue
discipline
Service
process
Departure
No future
need for
service
Arrival Process
Arrival
process
Static
Dynamic
Random
arrivals with
constant rate
Random arrival
rate varying
with time
Facilitycontrolled
Accept/Reject
Price
Appointments
Customerexercised
control
Reneging
Balking
Relative frequency, %
Distribution of Patient Interarrival Times
40
30
20
10
0
1
3
5
7
9 11 13 15 17 19
Patient interarrival time, minutes
Temporal Variation in Arrival Rates
Percentage of average daily
physician visits
Average calls per hour
3.5
3
2.5
2
1.5
1
0.5
0
1 3 5 7 9 11 13 15 17 19 21 23
Hour of day
140
130
120
110
100
90
80
70
60
1
2
3
Day of week
4
5
Poisson and Exponential Equivalence
Poisson distribution for number of arrivals per hour (top view)
1
Arrival
2
Arrivals
0
Arrivals
1
Arrival
One-hour
interval
62 min.
40 min.
123 min.
Exponential distribution of time between arrivals in minutes (bottom view)
Queue Configurations
Multiple Queue
Single queue
Take a Number
Enter
3
4
8
2
6
10
12
11
5
7
9
Queue Discipline
Queue
discipline
Static
(FCFS rule)
Dynamic
Selection based
on individual
customer
attributes
selection
based on status
of queue
Number of
customers
waiting
Round robin
Priority
Preemptive
Processing time
of customers
(SPT rule)
Relative frequency, %
15
10
5
0
1
11
21
31
Minutes
41
Relative frequency, %
Relative frequency. %
Outpatient Service Process Distributions
15
10
5
0
1
11
21
31
Minutes
15
10
5
0
1
11
21
31
Minutes
41
41
Service Facility Arrangements
Service facility
Server arrangement
Parking lot
Self-serve
Cafeteria
Servers in series
Toll booths
Servers in parallel
Supermarket
Self-serve, first stage; parallel servers, second stage
Hospital
Many service centers in parallel and series, not all used by each patient
Topics for Discussion
• Suggest some strategies for controlling variability in service
times.
• Suggest diversions that could make waiting less painful.
• Select a bad and good waiting experience, and contrast
the situations with respect to the aesthetics of the
surroundings, diversions, people waiting, and attitude of
servers.
• Suggest ways that management can influence the arrival
times of customers.
• What are the benefits of a fast-food employee taking your
order while waiting in line?
Interactive Exercise
The class breaks into small groups with at
least one international student in each
group, if possible. Based on overseas
travel, each group reports on
observations of waiting behavior from a
cultural perspective.
Eye’ll Be Seeing You
• How are Maister’s First and Second Laws of
Service illustrated?
• What good and bad features of a waiting process
are evident?
• How should Dr. X respond to Mrs. F’s letter?
• How could Dr. X prevent future incidents?
• Should customers be rewarded for offering
constructive criticism?
Pronto Pizza
• Draw a process flow diagram and identify the
bottleneck operation.
• Calculate the expected waiting time in the order
preparation queue. Compare this value with your
simulation result.
• Use the ServiceModel computer simulation
software and the Pronto.pkg file to determine the
number of drivers that minimizes the total cost of
salaries and guarantee discounts.
Pronto Pizza (cont.)
• Based on your simulation recommended staffing
level, what is the probability of paying off on the
guarantee?
• What do you think of this service guarantee
policy?
• What other design or operating suggestions could
improve Pronto Pizza’s performance and customer
service?