Question: Who or what is
queueing at baggage pickup? The passengers, the baggage or both?
Stuck in traffic:
Clogged roads / traffic jams.
Traffic lights.
Wait-listed for a class.
Getting help from an instructor during office hours.
Programs running on your computer.
Data packets traveling across the Internet.
Milk cartons in the dairy section of the grocery store.
Assembly line (wait may be zero).
Calling the airline, customer service, social security administration, the US
Citizenship and Immigration Service, etc.
Getting a new roof on your house; having a kitchen installed, making a doctor's appointment.
Etc.
Queues have some interesting characteristics:
They can pop up and disappear abruptly; e.g., traffic jams.
They seem to defy logic; e.g.,
The other lane on a busy highway always moves faster.
The moment you switch lanes, the lane you just came from speeds up.
Call center example:
You manage a call center which can answer an average of 20
calls per hour.
Your call center gets 17.5 calls in an average hour.
What is the average time a customer is on hold waiting for
service?
On average, customers should not have to wait on hold since
capacity is greater than demand.
Less than 10 minutes.
Between 10 and 20 minutes.
Greater than 20 minutes.
Who knows? There's no way to tell.
Problem: why do queues form?
Whenever demand arrivals exceed available service capacity AND
all the demand must be served.
Note that what matters here is the timing of the
arrivals. E.g., in the call center example, if all people all
call at the same time, there's going to be a long wait for some.
Queuing terminology amd mechanisms:
Queue: waiting line.
Arrival: the next person, machine, part, etc.
that arrives and demands service.
Arrival rate: number of arrivals per time interval (λ =
mean arrival rate = 17.5 calls per hour in above example)
Problem: Arrival processes are most often stochastic ==>
Which distribution?
Inter-arrival time: time between arrivals (1 / λ = mean
inter-arrival time = 1 / 17.5 hour in example above)
Service rate: number of customers or units served per
time interval (μ = mean service rate = 20 calls per hour in the above example).
Service time: time it takes to execute the service (1 / μ
= mean service time = 1 / 20 hour in above example).
Problem: which distribution?
In the system: arrivals in line or being worked on.
Phases: number of steps in service for each arrival.
Channels: number of servers.
Recall call center example:
You manage a call center which can answer an average of 20 calls per hour (μ).
Your call center gets 17.5 calls in an average hour (λ).
What is the average time a customer is on hold waiting for service?
Queue equations for one channel, all demand must be served, Poisson-distributed arrival and service rates
(exponential inter-arrival and service times), steady-state process (M/M/1 process):
Problem: Can you find the
solution to the call center problem we talked about earlier?
Note the assumptions:
One channel (one server).
Arrival and service rates are Poisson distributed.
Inter-arrival and service times are exponentially distributed.
Recall our discussion on deterministic vs. stochastic
systems: "We can use the characteristics of these distributions
to estimate the likelihood of certain outcomes."
Another one:
You manage a call center which can answer an average of 20 calls per hour.
Your call center gets 17.5 calls in an average hour.
What is the average number of people in the system?
One more:
What is the average number of people on hold?
Important note:
All the numbers in this basic waiting line model are averages.
Recall our discussions on quality: averages tell only half the story:
Customers do not experience averages.
==> How about variation? ==> simulation.
p. 195: Psychology of waiting: perception of a wait is often very
different from the actual wait.
Customers have good & bad days.
Unoccupied wait time feels longer:
Problem: Examples
of how to keep customers occupied while waiting?
In-process waits ("foot in the door") seem shorter:
Medical service providers: General wait-->intake nurse-->special wait.
Informed waits are not as bad as uninformed waits:
Being told how many calls are in front of you; your
expected waiting time, etc.
Physical length of the airport security line does not
matter as much when you're told expected wait is X minutes.
Unexpected effects: example of the Texas bank (Metters et al.): many
teller stations (extra capacity) staffed on (busy) Fridays; customers unhappy the rest of the week
(perception of understaffed facility while standing in line).
Unfair waits feel longer:
Single queue, multiple channel (p. 198: "snake") vs.
multiple queue, multiple channel example:
Average queue times are identical.
Variation in single queue, multiple channel is less:
Equal distribution of misery.
Collective sense of progress.
Continuous progress.
Waiting line poka-yokes:
Take a ticket.
Ask 'who's last?'
Others?
Some ways to manage waiting lines:
Automate: offload customers to automated answering services.
Presort (partition) the demand (p. 198: "discriminate"):
Bank: demand for teller services is separated from loan applications.
Customer Relationship Management (CRM) information
systems can direct emergency or priority customers into separate
(priority) queue.
15-items-max grocery store checkouts.
High mileage frequent flyers.
Have to be careful; e.g., what about priority treatment at airport security?
Others?
Queue discipline: rules for determining the order in which
arrivals receive service: e.g.,
First In First Out (FIFO) (First Come First Served (FCFS).
Last In First Out (LIFO).
Shortest Processing Time (SPT): serve the short service time ones first; delay the rest.
cμ priority: move short service time / high delay cost customers to the
front of the line.
Note how information systems (e.g., CRM systems) can help you filter
out these customers.
Preemptive priority: ongoing service is interrupted for a new
arrival; e.g., emergency rooms.
Test questions:
In our discussion of deterministic and stochastic processes, we
explored the relationship between probability distributions and
modeling the stochastics of a process. Does this also apply to waiting
line models?
Can you think of waiting lines that do not involve humans? Do
we have to care about those?
Recall some of the lessons and principles of the 'psychology of
waiting lines.'
From the waiting person's point of view, what is the difference
between a 'single line, multiple server' system and a 'multiple line,
multiple server' system?
What are some of the advantages and disadvantages of an appointment-based process?
Give yourself a few waiting line problems and try solving them
with the equations above.
Note how the waiting line equations all result in average waiting line performance measures. Yet we
know that averages only covey limited information and that we are just as interested in the variability
of these measures. Can you think of a way of obtaining that variability information?
