chapter 18: waiting line analysis

Question 1

when do waiting lines occur?

Answer 1

when there is a temporary imbalance between supply (capacity) and demand

Question 2

downsides of waiting lines

Answer 2

add to the cost of operation

they reflect negatively on customer service

loss of goodwill

loss of business due to customers refusing to wait and going elsewhere

Question 3

queueing theory

Answer 3

a mathematical approach to the analysis of waiting lines

Question 4

Why Is There Waiting?

Answer 4

arrival times and service durations exhibit a high degree of variability

the system at times becomes temporarily overloaded, giving rise to waiting lines; at other times, the system is idle because there are no customers

Question 5

The goal of queueing analysis

Answer 5

to minimize total costs

Question 6

The two types of costs in a queueing situation

Answer 6

“cost” of customers waiting for service

cost of provision of capacity

Question 7

ways management can reduce their customers’ perception of the waiting time

Answer 7

• Determine the acceptable wait time for the operation
• Try to keep the waiting time experienced by a customer consistent over time
• Install distractions that entertain and involve customers
• Inform the customer of the cause of an abnormal wait and peak times
• Keep the line moving continuously
• Use first come, first served discipline (fairness is important)
• Allow customers to serve themselves
• Prepare the customers for service before the actual service
• Make people conscious of time only if they overestimate the wait time.
• Keep staff who are not serving customers out of sight.
• Try to segment customers by personality
• Never underestimate the power of a friendly and attentive server

Question 8

ways in which management can reduce waiting times by fixing the system constraints

Answer 8

Use temporary workers

Shift demand

Standardize the service

Look for a bottleneck

Question 9

Model choice is dependent on which characteristics of the waiting line system under investigation

Answer 9

1. Potential number of customers.
2. Number of servers and structure of queueing system.
3. Arrival and service patterns.

4 . Queue discipline (i.e., order of service).

Question 10

an infinite source of customers situation

Answer 10

the potential number of customers greatly exceeds system capacity

Question 11

a finite source of customers situation

Answer 11

When the potential number of customers is limited

Question 12

Each server in the queueing system can handle how many customers at a time?

Answer 12

can handle one customer at a time

Question 13

queueing system can have how many servers?

Answer 13

single or multiple serνers

Question 14

true or false

Another distinctive of the queueing system characteristic is the number of steps or phases in a queueing system

Answer 14

true

Question 15

advantage of a joint line of people waiting leading to multiple servers

Answer 15

first come first serve (fairness)

wait time will be less

Question 16

disadvantage of a joint line of people waiting leading to multiple servers

which type of customers would prefer it

Answer 16

it might appear too long

may take a large space

servers may not work as fast as if they were responsible
for their own line

customers cannot choose their favorite server

homogeneous customers would prefer it

Question 17

advantages of separate lines leading to servers

which type of customer would prefer this

Answer 17

reduces the total variability of service durations, resulting in a reduced average wait time for all customers

heterogenous customers

Question 18

The most commonly used queueing models assume that the customer arrival rate can be described by which distribution?

Answer 18

The Poisson distribution

Question 19

The Poisson distribution

Answer 19

a one-parameter discrete probability distribution of the number of events occurring in an interval of time

–> provided that these events occur with a known average rate and independently of the time since the last event

Question 20

The exponential distribution

Answer 20

a one-parameter continuous probability distribution of the times between events that happen continuously and independently at a constant average rate

Question 21

reneging

Answer 21

customers grow impatient and leave the line

Question 22

jockeying

Answer 22

customers switch to another line

Question 23

balking

Answer 23

customers decide the line is too long and, therefore, do not enter the line

Question 24

Queue discipline

Answer 24

the order in which customers are served

Question 25

Operations managers typically look at which four measures when evaluating existing or proposed queueing systems

Answer 25

1. The average number of customers waiting, either in line (not counting those being served) or in the system (including those being served)
2. The average length of time customers wait, either in line or in the system
3. Server utilization
4. The probability that an arriving customer will have to wait for service or will have to wait more than a specified length of time before being served

Question 26

Server utilization

Answer 26

the proportion of time a server will be busy

reflects the extent to which the servers are busy rather than idle

Question 27

why would operations manager not necessarily want 100% server utilization?

Answer 27

increases in server utilization are achieved at the expense of greater increases in the average customer wait time

average customer wait time becomes exceedingly large as server utilization approaches 100 percent

100 percent utilization of servers leads to burnout

Question 28

which server utilization proportion is the most adequate?

Answer 28

between 80% and 90%

Question 29

the simplest queuing model

why?

Answer 29

model 1: Single Server, Exponential Service Durations

a system that has one server (or a single crew)

the queue discipline is First Come First Serve

customer arrival rates can be approximated by a Poisson distribution

service durations by an exponential distribution

Question 30

Model 3: Single Server, Constant Service Durations

Answer 30

a queueing system with constant service durations (and Poisson arrival rates)

–> to cut the average number of customers waiting in line in half (relative to Model 1)

Question 31

Model 5: Multiple Servers, Exponential Service Durations

Answer 31

poisson arrival rates with average tent symbol and exponential service durations with average 1/u

all M servers work at the same rate

customers form a single waiting line

the multiple server formulas are more complex than the single server formulas for Lq and Po.

Question 32

when does a multiple server system exist?

Answer 32

whenever there are two or more servers working individually to provide service to customers

Question 33

customer waiting cost

Answer 33

costs incurred by the organization due to customer waiting

Question 34

The optimal capacity (usually in terms of number of channels)

Answer 34

one that minimizes the sum of customer waiting costs and capacity or server costs

Minimize total cost = Total average customer wait cost + Total server pay cost

Question 35

what is used to identify the capacity size that will minimize total costs?

Answer 35

An iterative process

Question 36

Because the total cost curve is U-shaped, what does it mean for the total cost

Answer 36

the total cost will initially decrease as capacity is increased, and then it will eventually begin to increase

Once it begins to increase, additional increases in capacity will cause it to continue to increase