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Hospital Pharmacy 275
PEER-REVIEWED ARTICLE
Queuing Theory and
Customer Satisfaction: A Review
of Terminology, Trends, and
Applications to Pharmacy Practice
Ronald Anthony Nosek, Jr., MS* and James P. Wilson, PharmD, PhD†
Hospital Pharmacy
Volume 36, Number 3, pp 275–279
2001 Facts and Comparisons
PEER-REVIEWED ARTICLE
W
aiting in lines or
“queues” seems to be an
American pastime.
Think about the many
times you had to wait in line in the last
month or year and the time and frustra-
tion that was associated with those
waits. Whether we are in line at the gro-
cery store checkout, the barbershop, the
stoplight, or in the pharmacy, “waiting
our turn” is part of our everyday life.
Queuing theory is the formal study
of waiting in line and is an entire disci-
pline within the field of operations
management. The purpose of this arti-
cle is to give the reader a general back-
ground into queuing theory and queu-
ing systems, its associated terminology,
and how queuing theory relates to cus-
tomer satisfaction. Also, past and pre-
sent applications of queuing technology
and what pharmacies can do to manage
patient or customer queues more effec-
tively will be discussed. Finally, auto-
mated queuing technology will be
described.
Queuing theory utilizes mathemat-
ical models and performance measures
to assess and hopefully improve the
flow of customers through a queuing
system.
1–3
Queuing theory has many
applications and has been used exten-
sively by the service industries. Queu-
ing theory has been used in the past to
assess such things as staff schedules,
working environment, productivity,
customer waiting time, and customer
waiting environment. In pharmacy,
queuing theory can be applied to assess
a multitude of factors such as prescrip-
tion fill-time, patient waiting time,
patient counseling time, and pharmacist
and technician staffing levels. The
application of queuing theory may be
of particular benefit in pharmacies with
high-volume outpatient workloads
and/or those that provide multiple
points of service, such as those in the
Abstract — Queuing theory is the formal study of waiting in line and is an
entire discipline in operations management. This article will give the reader a
general background into queuing theory, its associated terminology, and it
relationship to customer satisfaction. Queuing theory has been used in the past
to assess such things as staff schedules, working environment, productivity,
customer waiting time, and customer waiting environment. In pharmacy, queu-
ing theory can be used to assess a multitude of factors such as prescription fill-
time, patient waiting time, patient counseling-time, and staffing levels. The
application of queuing theory may be of particular benefit in pharmacies with
high-volume outpatient workloads and/or those that provide multiple points of
service. By better understanding queuing theory, service managers can make
decisions that increase the satisfaction of all relevant groups — customers,
employees, and management.
Key Words — customer satisfaction; queuing
Hosp Pharm — 2001;36:275–279
*Pharmacy Department, The National Naval Medical Center, Bethesda, Maryland, 20889;
ranosek@bethesda.med.navy.mil (Ronald A. Nosek, Jr., LCDR, MSC, USN is an active duty pharma-
cist in the United States Navy. At the time of writing this article he was attending the University of
Texas as a full time student in Navy’s Duty Under Instruction program); †Assistant Professor, Pharma-
cy Practice and Administration Division, The University of Texas College of Pharmacy, Austin, TX;
wilsonj@mail.utexas.edu. Address correspondence to Dr. James P. Wilson, Pharmacy Practice and
Administration Division, PHR 2.212 – Mail Code A1930, Austin, TX 78712;
wilsonj@mail.utexas.edu.
The opinions or assertions herein are the private views of the authors and are not to be construed
as official or reflecting the views of the U.S. Department of the Navy or the Department of Defense.
276 Volume 36, March 2001
Queuing Theory: A Review
Department of Veterans Affairs (VA),
Department of Defense (DoD), univer-
sity health systems, and managed care
organizations. Problematic queuing
systems (ie, long lines) can lead to the
customer’s perceptions of excessive,
unfair, or unexplained waiting time—
resulting in significant detrimental
effects on the customer’s overall satis-
faction with the service transaction.
4
QUEUING SYSTEMS
AND TERMINOLOGY
On the surface it may seem like
queuing is just simply waiting in a line.
To most customers, the waiting experi-
ence is all that matters. However, wait-
ing in line is just a part of the overall
queuing system. A queuing system
(also known as a processing system)
can be characterized by four main ele-
ments: the arrival, the queue discipline,
the service mechanism, and the cost
structure.
The arrival is the way in which a
customer arrives and enters the system
for service. Whenever customers arrive
at a rate that exceeds the processing
system rate, a line or queue will form.
Arrivals may come in singly or in
batches; they may come in consistently
spaced or in a completely random man-
ner. A potential customer can also leave
if, on arrival, he or she finds the line too
long—this is called balking.
The queue discipline is the rule for
determining the formation of the line or
queue and the order in which jobs are
processed. There may only be one line
and jobs are processed First-In, First-
Out or FIFO. Others may have more
than one line to give certain customers
priority such as express lanes in grocery
stores.
The service mechanism describes
how the customer is served. It includes
the number of servers and the duration
of the service time—both of which may
vary greatly and in a random fashion.
The service time may be similar for
each job or it could vary greatly.
The cost structure specifies the
payment made by the customer and the
various operating costs of the system.
Other elements that impact the queue
structure and performance include the
number of service stations and the
number and speed of servers.
2,5
THE IMPORTANCE OF
QUEUING MANAGEMENT
Pharmacy, like other service-ori-
ented industries, functions in an
increasingly competitive environment.
Speed of service has been shown to
provide businesses a competitive
advantage in the marketplace.
4
In addi-
tion, the literature reveals several stud-
ies documenting customer dissatisfac-
tion with long waiting times and indi-
cates that this is a pervasive problem in
pharmacy practice and a common
source of anxiety and dissatisfaction
among customers and, in many cases,
pharmacists.
6
Speed of delivery is being empha-
sized increasingly and can be partly
attributed to increased competition and
the value a customer places on his or
her time. We live in a society who has
come to expect film development and
eyeglasses to be ready in an hour or
less. A brief story told from the cus-
tomer’s perspective will help to further
illustrate this point:
I just arrived at my local pharma-
cy to get a new prescription filled and
to pick up a few other things. There is a
line of four people at the register and
another six people sitting in the waiting
area. By the time I get to the counter to
hand the cashier/technician my pre-
scription, 5 minutes have passed. I ask
how long the wait will be and I am told
30 to 40 minutes. I go about my shop-
ping and return to the pharmacy 35
minutes later. Again, there are people in
line at the register and it takes me
another 5 minutes to find out that my
prescription is not ready. Feeling weary
and somewhat frustrated, I have a seat
in the waiting area. As I sit there, I
watch people come and go and wonder,
“Wasn’t I here before that guy?” At last
my name is called! I pay the cashier
and my pharmacy encounter is com-
plete. However, I don’t feel good about
it. Why did I have to wait so long? Did
others get special priority over me?
Maybe another pharmacy will service
my needs better? Am I a satisfied cus-
tomer?
QUEUING APPLICATIONS
IN SERVICE INDUSTRIES
Queuing management has been
applied very successfully in many ser-
vice-oriented industries. L. L. Bean, a
large telemarketer and mail-order cata-
log house for high-quality sporting
goods and apparel, used queuing theory
to optimize staffing levels — resulting
in an estimated $500,000 per year sav-
ings.
7
The Department of Motor Vehi-
cles in Virginia and Arizona used queu-
ing technology to virtually eliminate
long lines and greatly improve cus-
tomer satisfaction. In addition, they
were able to significantly improve
employee morale and reduce operating
costs.
8–10
Queuing models have also been
used to plan staffing levels in an outpa-
tient hospital laboratory department
and a centralized appointment depart-
ment in Lourdes Hospital in Bingham-
ton, New York. Queuing models were
used to identify an optimal configura-
tion of capacity and staffing levels for
both departments. The lengthy delays
in answering telephone calls in the cen-
tralized appointments department were
completely eliminated by rearranging
work shifts of current employees.
11,12
The Virginia Mason Medical Center in
Seattle, Washington used queuing theo-
ry and other classic quality manage-
ment principles to drastically reduce
patient waiting time for appointments
(42 days to 13), emergency room triage
time (45 minutes to 15), and increased
staff morale.
13
Queuing theory has been used
extensively in the banking industry to
increase business by careful placement
of merchandising materials while at the
Hospital Pharmacy 277
same time alleviating both the actual
and perceived amount of time a cus-
tomer spends waiting in line.
14
Finally,
queuing theory has been applied to
computer simulation models to help
with business decisions and prob-
lems.
15,16
CUSTOMER SATISFACTION
AND CONSUMER BEHAVIOR
In general, customer satisfaction is
multifactorial and is considered a part
of overall consumer behavior model.
Consumer behavior evolves over time
and is influenced by many factors. Sev-
eral key factors that greatly influence
satisfaction include consumer’s expec-
tations, attitudes, and intention about
the service provided.
Expectations are the consumer’s
anticipated beliefs about a product or
service prior to the interaction. Atti-
tudes consist of the consumer’s evalua-
tions, emotional feelings, and action
tendencies toward a product or service
that has developed over time. Intentions
are the decisions the consumer makes
about future actions toward the firm
producing the product or service.
Together, these factors influence the
future behavior or the actual future
action taken by the customer.
For the most part, these factors are
intangible so it is the perceived perfor-
mance rather than the actual perfor-
mance that is more critical to customer
satisfaction. The main goal of queuing
management is to maximize the level of
customer satisfaction with the service
provided. Therefore, the primary issue
in queuing management and customer
satisfaction is not the actual amount of
time a customer waits for service, but
the customer’s perception about that
wait and the associated level of satis-
faction. A highly satisfied customer
will be very likely to provide repeat
business and spread the positive experi-
ence by word of mouth (advertising),
resulting in increased revenues and
profitability. Conversely, a dissatisfied
customer will most likely not provide
repeat business and will be more than
willing to share his or her bad experi-
ence with whoever will listen. This will
have an obvious negative impact on
profits and revenues.
1–4
CUSTOMER SATISFACTION
AND WAITING TIME
Customer satisfaction has been
defined as the difference between the
customer’s perceptions of the experi-
ence and his or her expectations, which
is many times based on past experience.
Although it is possible to manage and
decrease actual waiting time and to
some extent to manage customer
expectations about customer satisfac-
tion, managing the customer’s percep-
tion of the queuing experience can be
the vital element in satisfaction with the
service interaction.
4
The measurement
of customer satisfaction as it relates to
waiting time is highly qualitative and
subjective, and the relationship is gen-
erally inverse in nature (ie, in general,
as waiting time decreases, satisfaction
increases). This relationship was fur-
ther expanded by Maister who, in 1985,
postulated that satisfaction is dependent
on customer perception and customer
expectation.
4
Numerous scientific studies, jour-
nal articles, and text books have been
published describing the relationship
between customer satisfaction, waiting
time, and consumer behavior.
1–25
For
example, one study examined customer
attitudes toward waiting times in the
hotel and restaurant industry and found
that over 70% of all respondents were
clearly concerned about waiting times.
In fact, those most concerned about
waiting times were generally more
willing to pay more to avoid waiting in
line and believed that quality is worth
waiting for. The results of this survey
indicate that queues do affect the satis-
faction level of customers and their
willingness to spend. In addition, this
study also suggests that there is a point
where a lengthy wait begins to affect
the customer’s perception of quality.
17
Another study examined patient
satisfaction with outpatient pharmaceu-
tical services at a large university hos-
pital. This study reported that of the
patients who received prescriptions
from university physicians and did not
fill them at the university pharmacy,
21% went elsewhere to have their pre-
scription filled because of the long
waiting time, even though prescription
prices were less expensive through the
university system.
18
Similarly, another
study conducted in a large Veterans
Affairs hospital reported that pharmacy
redesign improved patient satisfaction
because of a 50% decrease in patient
waiting time.
6
Finally, another article
describes the relationship between
waiting time and satisfaction in the con-
text of social justice or injustice, as the
case may be.
19
QUEUING THEORY IN
PHARMACY
Queuing theory and its application
has gotten very little attention from
pharmacy operations management;
however, pharmacy practice could ben-
efit by understanding and applying
some of the concepts of queuing theory.
A publication, Operations Man-
agement for Pharmacists, briefly dis-
cusses queuing theory and customer
wait-time management. The authors
appropriately acknowledged that the
advanced mathematical models used in
queuing theory were beyond the scope
of the book. Unfortunately, the only
suggestion offered by the authors for
managing perceived waiting time is to
distract the customer by providing
entertainment, refreshments, or com-
fortable conditions, such as television
and coffee in the waiting area.
20
A literature search revealed few
published articles in the area of phar-
macy practice and queuing theory.
Donehew and colleagues used queuing
theory to address prescription queues
and work measurement assessment of
prescription fill times.
21
Similarly,
Boyce and colleagues sought to deter-
Queuing Theory: A Review
278 Volume 36, March 2001
mine the impact of a computerized
waiting time program on order turn-
around time in a hospital pharmacy.
22
Perhaps the most common and
useful application of queuing theory in
pharmacy operations is to reduce
patient waiting time and maximize staff
effectiveness. Lin and colleagues used
workflow analysis and times study to
identify factors leading to excessive
waiting times in an ambulatory phar-
macy at the University Hospital Inc.
(TUH), Cincinnati, Ohio.
23
In another
study, also by Lin, work measurement
and computer simulation were used to
assess the re-engineering of community
pharmacies to facilitate patient counsel-
ing.
24
Although queuing theory was
never mentioned in these articles, the
authors used many concepts similar to
queuing theory’s and their results could
be instrumental in designing queuing
applications for reducing patient wait-
ing time and improving staff utilization.
In a study by Moss, queuing theo-
ry was used to assess the relationships
among the number of pharmacy staff
members, prescription dispensing
process, and outpatient waiting times.
He used a mathematical queuing model
to estimate the probability of waiting
time exceeding a given value, when
prescription arrival and service rates
and number of servers are known. The
study revealed that the major factors
determining outpatient waiting time
were the arrival pattern of prescriptions
at the pharmacy, sequencing of work,
and percentage of staff at work.
25
Finally, Vemuri used computer
simulation with a queuing model to
assess patient waiting time in the outpa-
tient pharmacy at the Medical College
of Virginia. This study concluded that
the most significant factor contributing
to patient waiting times was the interac-
tion between pharmacy service
providers, specifically the typist and the
technician.
26
Many different mathematical
equations can be used to describe queue
formation and behavior; however, the
decision to choose one over the other is
beyond the scope of this article.
Although Moss
25
provided the mathe-
matical formula used in his research,
most queuing research applications are
now completed through some form of
computerization due to the complexity
of the models and the accessibility of
off-the-shelf software and personal
computers.
WHO MIGHT BENEFIT FROM
QUEUING APPLICATIONS?
It is true that many pharmacies do
not experience problems with queues.
However, there are many pharmacies
that do experience difficulties with
queue formation. For example, pharma-
cies that experience high-volume pre-
scription workload frequently have dif-
ficulty in managing workflow and wait-
ing times. This could also be true in
pharmacies that offer their customers
multiple points of service (ie, bank
teller design). Pharmacies such as those
in large managed care organizations,
university health systems, and those in
the VA and DoD typically fit this
description.
It is safe to say that the traditional
methods employed by pharmacies to
distract customers (eg, comfortable
waiting area, coffee, and television)
would be of limited benefit in pharma-
cies that fill in excess of 1,000 prescrip-
tions per day and have patient waiting
times that commonly exceed 1 to 2
hours.
Recently, however, automated
queuing technology has been success-
fully developed and applied in areas of
pharmacy practice that specifically
address customer waiting times. Prior
to this innovation, the most advanced
queuing applications to manage cus-
tomer waiting times in pharmacies was
a consecutive number ticketing system
commonly found in barber shops and
grocery stores.
QUEUING TECHNOLOGY
IN PHARMACY
Automated queuing technology
(AQT) is primarily utilized in the feder-
al sector and includes numerous phar-
macies in the DoD and the VA. Howev-
er, several prominent nonfederal phar-
macy organizations utilize AQT,
including the University of North Car-
olina, Medical College of Virginia,
Jewish Hospital in Cincinnati, and
Parkland Hospital in Dallas, just to
name a few.
27
Both the DoD and the VA
operate very busy outpatient pharmacy
departments, some filling in excess of
2,500 outpatient prescriptions and ser-
vicing over 1,000 patients daily.
Automated queuing systems are
typically PC based systems that can
track a multitude of useful information
that was previously very difficult to
quantify for pharmacy managers. Phar-
macies utilizing AQT can easily track
variables such as customer arrival and
departure time, patterns of arrival, pre-
scription fill time, waiting time, and
individual staff member productivity.
In addition, AQT can track numerous
points of service and different service
categories (ie, certain patients may get
priority service or can be used to track
patient counseling) if desired.
Finally, AQT can also provide
pharmacy customers with information
that can directly improve their queuing
experience, such as with a ticket with a
unique number and the estimated wait
time. This makes for a less confusing,
more relaxed, and much more positive
waiting environment for the patient. At
the time this article was submitted for
publication, only one company, the Q-
Matic Corporation, that distributes
automated queuing technology systems
could be identified. Their website
address is http://us.q-matic.com.
27
CONCLUSION
Queuing theory is a powerful man-
agement tool that often gets over-
looked, especially in pharmacy opera-
tions management. Proper application
Queuing Theory: A Review
Hospital Pharmacy 279
Queuing Theory: A Review
of this effective management tool can
yield impressive results. There are vol-
umes of additional material on queuing
theory and in fact this paper has only
touched the surface. The goal of this
paper was to give the reader a general
understanding of concepts, current
technology, and applications of queuing
theory as it relates to customer satisfac-
tion and waiting time.
Undoubtedly, there are numerous
factors—physical, psychological, and
emotional, to name a few—that affect a
customer’s perception of the waiting
experience. By better understanding
queuing theory and the various mea-
sures associated with customer waiting
time, service managers can make deci-
sions that have a beneficial impact on
the satisfaction of all relevant partici-
pants: customers, employees and man-
agement. There are several tools such
as computer simulation, modeling , and
automated queuing technology that can
assist in this process improvement
endeavor.
Waiting in line will always be
prevalent in our society and in our phar-
macies. As the health care industry con-
tinues to evolve, pharmacists are under
continued and growing pressure to do
more and more. Wouldn’t it be nice to
practice pharmacy in a setting where
the worry and burden of wait time man-
agement was eased, even eliminated —
keeping customers happy and decreas-
ing the anxiety of those behind the
counter trying to provide the best phar-
macy service?
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