CHAPTER 5
Service Processes
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
Learning Objectives
After completing the chapter you will:

Understand the characteristics of service
processes and how they are different from
manufacturing processes

Be able to classify service processes

Understand what waiting line (queuing) analysis
is

Be able to model some common waiting line
situations and estimate server utilization, the
length of the waiting line, and average customer
wait time
Service Businesses
A service business is the management
of organizations whose primary
business requires interaction with the
customer to produce the service


Generally classified according to who the
customer is:

Financial services

Health care
A contrast to manufacturing
Service-System Design Matrix
Degree of customer/server contact
High
Buffered
core (none)
Permeable
system (some)
Reactive
system (much)
Low
Face-to-face
total
customization
Face-to-face
loose specs
Sales
Opportunity
Face-to-face
tight specs
Production
Efficiency
Phone
Internet & Contact
on-site
technology
Mail contact
Low
High
Characteristics of Workers, Operations, and
Innovations Relative to the Degree of
Customer/Service Contact
Components of the Queuing System
Servicing System
Servers
Queue or
Customer
Arrivals
Waiting Line
Exit
Customer Service Population Sources
Population Source
Finite
Example: Number
of machines
needing repair
when a company
only has three
machines.
Infinite
Example: The
number of people
who could wait in
a line for
gasoline.
Service Pattern
Service
Pattern
Constant
Example: Items
coming down an
automated
assembly line.
Variable
Example: People
spending time
shopping.
The Queuing System
Length
Queue Discipline
Queuing
System
Service Time
Distribution
Number of Lines &
Line Structures
Examples of Line Structures
Single
Phase
One-person
Single Channel
barber shop
Multichannel
Bank tellers’
windows
Multiphase
Car wash
Hospital
admissions
Degree of Patience
No Way!
BALK
No Way!
RENEG
Waiting Line Models
Model Layout
1
Single channel
Source
Population
Infinite
Service Pattern
Exponential
2
Single channel
Infinite
Constant
3
Multichannel
Infinite
Exponential
These three models share the following characteristics:
 Single phase
 Poisson arrival
 FCFS
 Unlimited queue length
Notation: Infinite Queuing: Models 1-3
 = Arrival rate
 = Service rate
1
 Average service time
1
 Average time between arrivals



 = = Ratio of total arrival rate to sevice rate

for a single server
Lq  Average number wai ting in line
Infinite Queuing Models 1-3 (Continued)
Ls = Average number in system
(including those being served)
Wq = Average time waiting in line
Ws  Average total time in system
(including time to be served)
n  Number of units in the system
S = Number of identical service channels
Pn  Probabilit y of exactly n units in system
Pw  Probabilit y of waiting in line
Example: Model 1
Assume a drive-up window at a fast food restaurant.
Customers arrive at the rate of 25 per hour.
The employee can serve one customer every two
minutes.
Assume Poisson arrival and exponential service
rates.
Determine:
A) What is the average utilization of the employee?
B) What is the average number of customers in line?
C) What is the average number of customers in the
system?
D) What is the average waiting time in line?
E) What is the average waiting time in the system?
F) What is the probability that exactly two cars will be
in the system?
Example: Model 1
A) What is the average utilization of the
employee?
 = 25 cust / hr
1 customer
 =
= 30 cust / hr
2 mins (1hr / 60 mins)

25 cust / hr
 =
=
= .8333

30 cust / hr
Example: Model 1
B) What is the average number of customers in
line?

(25)
Lq =
=
= 4.167
 (  -  ) 30(30 - 25)
2
2
C) What is the average number of customers in the
system?

25
Ls =
=
=5
 -  (30 - 25)
Example: Model 1
D) What is the average waiting time in line?
Wq =
Lq

= .1667 hrs = 10 mins
E) What is the average waiting time in the system?
Ws =
Ls

= .2 hrs = 12 mins
Example: Model 1
F) What is the probability that exactly two cars
will be in the system (one being served and the
other waiting in line)?
pn
 
= (1 - )( )
 
n
25 25 2
p 2 = (1- )( ) = .1157
30 30
Example: Model 2
An automated pizza vending machine
heats and
dispenses a slice of pizza in 4 minutes.
Customers arrive at a rate of one every 6
minutes with the arrival rate exhibiting a
Poisson distribution.
Determine:
A) The average number of customers in line.
B) The average total waiting time in the system.
Example: Model 2
A) The average number of customers in line.
2
(10) 2
Lq =
=
= .6667
2 (  -  ) (2)(15)(15 - 10)
B) The average total waiting time in the system.
Lq
.6667
Wq =
=
= .06667 hrs = 4 mins

10
1
1
Ws = Wq + = .06667 hrs +
= .1333 hrs = 8 mins

15/hr
Example: Model 3
Recall the Model 1 example:
Drive-up window at a fast food restaurant.
Customers arrive at the rate of 25 per hour.
The employee can serve one customer every
two minutes.
Assume Poisson arrival and exponential
service rates.
If an identical window (and an identically trained
server) were added, what would the effects be on
the average number of cars in the system and the
total time customers wait before being served?
Example: Model 3
Average number of cars in the system
Lq = 0.176
(Exhibit TN7.11 - -using linear interpolat ion)

25
Ls = Lq + = .176 + = 1.009

30
Total time customers wait before being served
Lq
.176 customers
Wq =
=
= .007 mins ( No Wait! )
 25 customers/ min
Queuing Approximation

This approximation is quick way to analyze a queuing
situation. Now, both interarrival time and service time
distributions are allowed to be general.

In general, average performance measures (waiting time in
queue, number in queue, etc) can be very well
approximated by mean and variance of the distribution
(distribution shape not very important).

This is very good news for managers: all you need is
mean and standard deviation, to compute average waiting
time
Define:
Standard deviation of X
Mean of X
Variance
2
Cx2  squared coefficient of variation (scv) = Cx  
mean2
Cx  coefficient of variation for r.v. X =
Queue Approximation
Inputs: S, , , Ca2 ,Cs2
(Alternatively: S, , , variances of interarrival and service time distributions)

Compute  
S

2( S 1)
Ca2  Cs2
Lq 

1 
2
as before, Wq 
Ls  Lq  S 
Lq

, and Ws 
Ls

Approximation Example

Consider a manufacturing process (for example making
plastic parts) consisting of a single stage with five
machines. Processing times have a mean of 5.4 days
and standard deviation of 4 days. The firm operates
make-to-order. Management has collected date on
customer orders, and verified that the time between
orders has a mean of 1.2 days and variance of 0.72
days. What is the average time that an order waits
before being worked on?
Using our “Waiting Line Approximation” spreadsheet we
get:
Lq = 3.154 Expected number of orders waiting to be completed.
Wq = 3.78 Expected number of days order waits.
Ρ = 0.9 Expected machine utilization.
End of Chapter 5